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Improving Patient Adherence

Alan M. Delamater
Apr 1, 2006; 24:71-77
Feature Articles




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Standards of Medical Care in Diabetes--2018 Abridged for Primary Care Providers

American Diabetes Association
Jan 1, 2018; 36:14-37
Position Statements




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Standards of Medical Care in Diabetes--2017 Abridged for Primary Care Providers

American Diabetes Association
Jan 1, 2017; 35:5-26
Position Statements




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Standards of Medical Care in Diabetes--2015 Abridged for Primary Care Providers

American Diabetes Association
Apr 1, 2015; 33:97-111
Position Statements




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Empowerment and Self-Management of Diabetes

Martha M. Funnell
Jul 1, 2004; 22:123-127
Feature Articles




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Microvascular and Macrovascular Complications of Diabetes

Michael J. Fowler
Apr 1, 2008; 26:77-82
Diabetes Foundation




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The Heroic Leadership Imperative

Allison, S. T. & Goethals, G. R. (2020). The heroic leadership imperative: How leaders inspire and mobilize change. West Yorkshire: Emerald. Our next book describes a new principle that we call the heroic leadership imperative. We show how leaders who fulfill the imperative will inspire followers and initiate social change.   The imperative consists of … Continue reading The Heroic Leadership Imperative



  • Our latest books on HEROIC LEADERS

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COVID-19 Pandemic Turns Heroism Upside-Down

By Scott T. Allison William James, who authored the first psychology texbook, was taken and moved by the quiet heroism in everyday working people. He noticed “the great fields of heroism lying round about” him. He was mesmerized by small, seemingly inconsequential everyday acts that, in effect, exemplified unsung heroism in everyone. Before the COVID-19 … Continue reading COVID-19 Pandemic Turns Heroism Upside-Down



  • Commentary and Analysis

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10 Examples of Heroism Arising From the COVID-19 Pandemic

By Scott T. Allison In any tragedy or crisis, you will see many people standing out and stepping up to save lives and make the world a better place. These heroic individuals can range from leaders of nations to ordinary citizens who rise to the occasion to help others in need. During this COVID-19 pandemic, … Continue reading 10 Examples of Heroism Arising From the COVID-19 Pandemic




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The Miniseries ‘Devs’ Delivers a Delicious Dose of Heroism and Villainy

By Scott T. Allison Devs is the ideal TV mini-series for people to sink their teeth into, for many reasons: (1) It’s both science and science-fiction; (2) it’s brilliant mix of psychology, philosophy, religion, and technology; (3) it tantalizes us with the mysteries of love, life, death, time, and space; and (4) it features a … Continue reading The Miniseries ‘Devs’ Delivers a Delicious Dose of Heroism and Villainy



  • Commentary and Analysis

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Heroism Science: Call for Papers, Special Issue: The Heroism of Whistleblowers

Heroism Science: Call for Papers, Special Issue The Heroism of Whistleblowers Edited by Ari Kohen, Brian Riches, and Matt Langdon Whistleblowers speak up with “concerns or information about wrongdoing inside organizations and institutions.” As such, whistleblowing “can be one of the most important and difficult forms of heroism in modern society” (Brown, 2016 p. 1). … Continue reading Heroism Science: Call for Papers, Special Issue: The Heroism of Whistleblowers




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The Innovation Dilemma

"If it ain't broken, don't fix it."Sound advice, but limited to situations where "fixing it" only entails restoring past performance. In contrast, innovations entail substantive improvements over the past. Innovations are not just corrections of past mistakes, but progress towards a better future.

However, innovations often present a challenging dilemma to decision makers. Many decisions require choosing between options, one of which is both potentially better in the outcome but markedly more uncertain. In these situations the decision maker faces an "innovation dilemma."

The innovation dilemma arises in many contexts. Here are a few examples.

Technology. New and innovative technologies are often advocated because of their purported improvements on existing products or methods. However, what is new is usually less well-known and less widely tested than what is old. The range of possible adverse (or favorable) surprises of an innovative technology may exceed the range of surprise for a tried-and-true technology. The analyst who must choose between innovation and convention faces an innovation dilemma.

Investment. The economic investor faces an innovation dilemma when choosing between investing in a promising but unknown new start-up and investing in a well-known existing firm.

Auction. "Nothing ventured, nothing gained" is the motto of the risk-taker, while the risk-avoider responds: "Nothing ventured, nothing lost". The innovation dilemma is embedded in the choice between these two strategies. Consider for example the "winner's curse" in auction theory. You can make a financial bid for a valuable piece of property, which will be sold to the highest bidder. You have limited information about the other bidders and about the true value of the property. If you bid high you might win the auction but you might also pay more than the property is worth. Not bidding is risk-free because it avoids the purchase. The choice between a high bid and no bid is an innovation dilemma.

Employer decision. An employer must decide whether or not to replace a current satisfactory employee with a new candidate whose score on a standardized test was high. A high score reflects great ability. However, the score also contains a random element, so a high score may result from chance, and not reflect true ability. The innovation dilemma is embedded in the employer's choice between the current adequate employee and a high-scoring new candidate.

Natural resource exploitation. Permitting the extraction of offshore petroleum resources may be productive in terms of petroleum yield but may also present officials with significant uncertainty about environmental consequences.

Public health. Implementation of a large-scale immunization program may present policy officials with worries about uncertain side effects.

Agricultural policy. New technologies promise improved production efficiency or new consumer choices, but with uncertain benefits and costs and potential unanticipated adverse effects resulting from use of manufactured inputs such as fertilizers, pesticides, and machinery, and, more recently, genetically engineered seed varieties and information technology. (I am indebted to L. Joe Moffitt and Craig Osteen for these examples in natural resources, public health and agriculture.)

An essay like this one should - according to custom - end with a practical prescription: What to do about the innovation dilemma? You need to make a decision - a choice between options - and you face an innovation dilemma. How to choose? All I'll say is that the first step is to identify what you need to achieve from this decision. Recognizing the vast uncertainties which accompany the decision, choose the option which achieves the required outcome over the largest range of uncertain contingencies.

If you want more of an answer than that, consult your favorite decision theory (like info-gap theory, for instance).

I will conclude by drawing a parallel between the innovation dilemma and one of the oldest quandaries in political philosophy. In The Evolution of Political Thought C. Northcote Parkinson explains the historically recurring tension between freedom and equality.

Freedom. People have widely varying interests and aptitudes. Hence a society that offers broad freedom for individuals to exploit their abilities, will also develop a wide spread of wealth, accomplishment, and status. Freedom enables individuals to explore, invent, discover, and create. Freedom is the recipe for innovation. Freedom induces both uncertainty and inequality.

Equality. People have widely varying interests and aptitudes. Hence a society that strives for equality among its members can achieve this by enforcing conformity and by transferring wealth from rich to poor. The promise of a measure of equality is a guarantee of a measure of security, a personal and social safety net. Equality reduces both uncertainty and freedom.

The dilemma is that a life without freedom is hardly human, but freedom without security is the jungle. And life in the jungle, as Hobbs explained, in "solitary, poor, nasty, brutish and short".




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No-Failure Design and Disaster Recovery: Lessons from Fukushima

One of the striking aspects of the early stages of the nuclear accident at Fukushima-Daiichi last March was the nearly total absence of disaster recovery capability. For instance, while Japan is a super-power of robotic technology, the nuclear authorities had to import robots from France for probing the damaged nuclear plants. Fukushima can teach us an important lesson about technology.

The failure of critical technologies can be disastrous. The crash of a civilian airliner can cause hundreds of deaths. The meltdown of a nuclear reactor can release highly toxic isotopes. Failure of flood protection systems can result in vast death and damage. Society therefore insists that critical technologies be designed, operated and maintained to extremely high levels of reliability. We benefit from technology, but we also insist that the designers and operators "do their best" to protect us from their dangers.

Industries and government agencies who provide critical technologies almost invariably act in good faith for a range of reasons. Morality dictates responsible behavior, liability legislation establishes sanctions for irresponsible behavior, and economic or political self-interest makes continuous safe operation desirable.

The language of performance-optimization  not only doing our best, but also achieving the best  may tend to undermine the successful management of technological danger. A probability of severe failure of one in a million per device per year is exceedingly  and very reassuringly  small. When we honestly believe that we have designed and implemented a technology to have vanishingly small probability of catastrophe, we can honestly ignore the need for disaster recovery.

Or can we?

Let's contrast this with an ethos that is consistent with a thorough awareness of the potential for adverse surprise. We now acknowledge that our predictions are uncertain, perhaps highly uncertain on some specific points. We attempt to achieve very demanding outcomes  for instance vanishingly small probabilities of catastrophe  but we recognize that our ability to reliably calculate such small probabilities is compromised by the deficiency of our knowledge and understanding. We robustify ourselves against those deficiencies by choosing a design which would be acceptable over a wide range of deviations from our current best understanding. (This is called "robust-satisficing".) Not only does "vanishingly small probability of failure" still entail the possibility of failure, but our predictions of that probability may err.

Acknowledging the need for disaster recovery capability (DRC) is awkward and uncomfortable for designers and advocates of a technology. We would much rather believe that DRC is not needed, that we have in fact made catastrophe negligible. But let's not conflate good-faith attempts to deal with complex uncertainties, with guaranteed outcomes based on full knowledge. Our best models are in part wrong, so we robustify against the designer's bounded rationality. But robustness cannot guarantee success. The design and implementation of DRC is a necessary part of the design of any critical technology, and is consistent with the strategy of robust satisficing.

One final point: moral hazard and its dilemma. The design of any critical technology entails two distinct and essential elements: failure prevention and disaster recovery. What economists call a `moral hazard' exists since the failure prevention team might rely on the disaster-recovery team, and vice versa. Each team might, at least implicitly, depend on the capabilities of the other team, and thereby relinquish some of its own responsibility. Institutional provisions are needed to manage this conflict.

The alleviation of this moral hazard entails a dilemma. Considerations of failure prevention and disaster recovery must be combined in the design process. The design teams must be aware of each other, and even collaborate, because a single coherent system must emerge. But we don't want either team to relinquish any responsibility. On the one hand we want the failure prevention team to work as though there is no disaster recovery, and the disaster recovery team should presume that failures will occur. On the other hand, we want these teams to collaborate on the design.

This moral hazard and its dilemma do not obviate the need for both elements of the design. Fukushima has taught us an important lesson by highlighting the special challenge of high-risk critical technologies: design so failure cannot occur, and prepare to respond to the unanticipated.




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Robustness and Locke's Wingless Gentleman

Our ancestors have made decisions under uncertainty ever since they had to stand and fight or run away, eat this root or that berry, sleep in this cave or under that bush. Our species is distinguished by the extent of deliberate thought preceding decision. Nonetheless, the ability to decide in the face of the unknown was born from primal necessity. Betting is one of the oldest ways of deciding under uncertainty. But you bet you that 'bet' is a subtler concept than one might think.

We all know what it means to make a bet, but just to make sure let's quote the Oxford English Dictionary: "To stake or wager (a sum of money, etc.) in support of an affirmation or on the issue of a forecast." The word has been around for quite a while. Shakespeare used the verb in 1600: "Iohn a Gaunt loued him well, and betted much money on his head." (Henry IV, Pt. 2 iii. ii. 44). Drayton used the noun in 1627 (and he wasn't the first): "For a long while it was an euen bet ... Whether proud Warwick, or the Queene should win."

An even bet is a 50-50 chance, an equal probability of each outcome. But betting is not always a matter of chance. Sometimes the meaning is just the opposite. According to the OED 'You bet' or 'You bet you' are slang expressions meaning 'be assured, certainly'. For instance: "'Can you handle this outfit?' 'You bet,' said the scout." (D.L.Sayers, Lord Peter Views Body, iv. 68). Mark Twain wrote "'I'll get you there on time' - and you bet you he did, too." (Roughing It, xx. 152).

So 'bet' is one of those words whose meaning stretches from one idea all the way to its opposite. Drayton's "even bet" between Warwick and the Queen means that he has no idea who will win. In contrast, Twain's "you bet you" is a statement of certainty. In Twain's or Sayers' usage, it's as though uncertainty combines with moral conviction to produce a definite resolution. This is a dialectic in which doubt and determination form decisiveness.

John Locke may have had something like this in mind when he wrote:

"If we will disbelieve everything, because we cannot certainly know all things; we shall do muchwhat as wisely as he, who would not use his legs, but sit still and perish, because he had no wings to fly." (An Essay Concerning Human Understanding, 1706, I.i.5)

The absurdity of Locke's wingless gentleman starving in his chair leads us to believe, and to act, despite our doubts. The moral imperative of survival sweeps aside the paralysis of uncertainty. The consequence of unabated doubt - paralysis - induces doubt's opposite: decisiveness.

But rational creatures must have some method for reasoning around their uncertainties. Locke does not intend for us to simply ignore our ignorance. But if we have no way to place bets - if the odds simply are unknown - then what are we to do? We cannot "sit still and perish".

This is where the strategy of robustness comes in.

'Robust' means 'Strong and hardy; sturdy; healthy'. By implication, something that is robust is 'not easily damaged or broken, resilient'. A statistical test is robust if it yields 'approximately correct results despite the falsity of certain of the assumptions underlying it' or despite errors in the data. (OED)

A decision is robust if its outcome is satisfactory despite error in the information and understanding which justified or motivated the decision. A robust decision is resilient to surprise, immune to ignorance.

It is no coincidence that the colloquial use of the word 'bet' includes concepts of both chance and certainty. A good bet can tolerate large deviation from certainty, large error of information. A good bet is robust to surprise. 'You bet you' does not mean that the world is certain. It means that the outcome is certain to be acceptable, regardless of how the world turns out. The scout will handle the outfit even if there is a rogue in the ranks; Twain will get there on time despite snags and surprises. A good bet is robust to the unknown. You bet you!


An extended and more formal discussion of these issues can be found elsewhere.




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Squirrels and Stock Brokers, Or: Innovation Dilemmas, Robustness and Probability

Decisions are made in order to achieve desirable outcomes. An innovation dilemma arises when a seemingly more attractive option is also more uncertain than other options. In this essay we explore the relation between the innovation dilemma and the robustness of a decision, and the relation between robustness and probability. A decision is robust to uncertainty if it achieves required outcomes despite adverse surprises. A robust decision may differ from the seemingly best option. Furthermore, robust decisions are not based on knowledge of probabilities, but can still be the most likely to succeed.

Squirrels, Stock-Brokers and Their Dilemmas




Decision problems.
Imagine a squirrel nibbling acorns under an oak tree. They're pretty good acorns, though a bit dry. The good ones have already been taken. Over in the distance is a large stand of fine oaks. The acorns there are probably better. But then, other squirrels can also see those trees, and predators can too. The squirrel doesn't need to get fat, but a critical caloric intake is necessary before moving on to other activities. How long should the squirrel forage at this patch before moving to the more promising patch, if at all?

Imagine a hedge fund manager investing in South African diamonds, Australian Uranium, Norwegian Kroners and Singapore semi-conductors. The returns have been steady and good, but not very exciting. A new hi-tech start-up venture has just turned up. It looks promising, has solid backing, and could be very interesting. The manager doesn't need to earn boundless returns, but it is necessary to earn at least a tad more than the competition (who are also prowling around). How long should the manager hold the current portfolio before changing at least some of its components?

These are decision problems, and like many other examples, they share three traits: critical needs must be met; the current situation may or may not be adequate; other alternatives look much better but are much more uncertain. To change, or not to change? What strategy to use in making a decision? What choice is the best bet? Betting is a surprising concept, as we have seen before; can we bet without knowing probabilities?

Solution strategies.
The decision is easy in either of two extreme situations, and their analysis will reveal general conclusions.

One extreme is that the status quo is clearly insufficient. For the squirrel this means that these crinkled rotten acorns won't fill anybody's belly even if one nibbled here all day long. Survival requires trying the other patch regardless of the fact that there may be many other squirrels already there and predators just waiting to swoop down. Similarly, for the hedge fund manager, if other funds are making fantastic profits, then something has to change or the competition will attract all the business.

The other extreme is that the status quo is just fine, thank you. For the squirrel, just a little more nibbling and these acorns will get us through the night, so why run over to unfamiliar oak trees? For the hedge fund manager, profits are better than those of any credible competitor, so uncertain change is not called for.

From these two extremes we draw an important general conclusion: the right answer depends on what you need. To change, or not to change, depends on what is critical for survival. There is no universal answer, like, "Always try to improve" or "If it's working, don't fix it". This is a very general property of decisions under uncertainty, and we will call it preference reversal. The agent's preference between alternatives depends on what the agent needs in order to "survive".

The decision strategy that we have described is attuned to the needs of the agent. The strategy attempts to satisfy the agent's critical requirements. If the status quo would reliably do that, then stay put; if not, then move. Following the work of Nobel Laureate Herbert Simon, we will call this a satisficing decision strategy: one which satisfies a critical requirement.

"Prediction is always difficult, especially of the future." - Robert Storm Petersen

Now let's consider a different decision strategy that squirrels and hedge fund managers might be tempted to use. The agent has obtained information about the two alternatives by signals from the environment. (The squirrel sees grand verdant oaks in the distance, the fund manager hears of a new start up.) Given this information, a prediction can be made (though the squirrel may make this prediction based on instincts and without being aware of making it). Given the best available information, the agent predicts which alternative would yield the better outcome. Using this prediction, the decision strategy is to choose the alternative whose predicted outcome is best. We will call this decision strategy best-model optimization. Note that this decision strategy yields a single universal answer to the question facing the agent. This strategy uses the best information to find the choice that - if that information is correct - will yield the best outcome. Best-model optimization (usually) gives a single "best" decision, unlike the satisficing strategy that returns different answers depending on the agent's needs.

There is an attractive logic - and even perhaps a moral imperative - to use the best information to make the best choice. One should always try to do one's best. But the catch in the argument for best-model optimization is that the best information may actually be grievously wrong. Those fine oak trees might be swarming with insects who've devoured the acorns. Best-model optimization ignores the agent's central dilemma: stay with the relatively well known but modest alternative, or go for the more promising but more uncertain alternative.

"Tsk, tsk, tsk" says our hedge fund manager. "My information already accounts for the uncertainty. I have used a probabilistic asset pricing model to predict the likelihood that my profits will beat the competition for each of the two alternatives."

Probabilistic asset pricing models are good to have. And the squirrel similarly has evolved instincts that reflect likelihoods. But a best-probabilistic-model optimization is simply one type of best-model optimization, and is subject to the same vulnerability to error. The world is full of surprises. The probability functions that are used are quite likely wrong, especially in predicting the rare events that the manager is most concerned to avoid.

Robustness and Probability

Now we come to the truly amazing part of the story. The satisficing strategy does not use any probabilistic information. Nonetheless, in many situations, the satisficing strategy is actually a better bet (or at least not a worse bet), probabilistically speaking, than any other strategy, including best-probabilistic-model optimization. We have no probabilistic information in these situations, but we can still maximize the probability of success (though we won't know the value of this maximum).

When the satisficing decision strategy is the best bet, this is, in part, because it is more robust to uncertainty than another other strategy. A decision is robust to uncertainty if it achieves required outcomes even if adverse surprises occur. In many important situations (though not invariably), more robustness to uncertainty is equivalent to being more likely to succeed or survive. When this is true we say that robustness is a proxy for probability.

A thorough analysis of the proxy property is rather technical. However, we can understand the gist of the idea by considering a simple special case.

Let's continue with the squirrel and hedge fund examples. Suppose we are completely confident about the future value (in calories or dollars) of not making any change (staying put). In contrast, the future value of moving is apparently better though uncertain. If staying put would satisfy our critical requirement, then we are absolutely certain of survival if we do not change. Staying put is completely robust to surprises so the probability of success equals 1 if we stay put, regardless of what happens with the other option. Likewise, if staying put would not satisfy our critical requirement, then we are absolutely certain of failure if we do not change; the probability of success equals 0 if we stay, and moving cannot be worse. Regardless of what probability distribution describes future outcomes if we move, we can always choose the option whose likelihood of success is greater (or at least not worse). This is because staying put is either sure to succeed or sure to fail, and we know which.

This argument can be extended to the more realistic case where the outcome of staying put is uncertain and the outcome of moving, while seemingly better than staying, is much more uncertain. The agent can know which option is more robust to uncertainty, without having to know probability distributions. This implies, in many situations, that the agent can choose the option that is a better bet for survival.

Wrapping Up

The skillful decision maker not only knows a lot, but is also able to deal with conflicting information. We have discussed the innovation dilemma: When choosing between two alternatives, the seemingly better one is also more uncertain.

Animals, people, organizations and societies have developed mechanisms for dealing with the innovation dilemma. The response hinges on tuning the decision to the agent's needs, and robustifying the choice against uncertainty. This choice may or may not coincide with the putative best choice. But what seems best depends on the available - though uncertain - information.

The commendable tendency to do one's best - and to demand the same of others - can lead to putatively optimal decisions that may be more vulnerable to surprise than other decisions that would have been satisfactory. In contrast, the strategy of robustly satisfying critical needs can be a better bet for survival. Consider the design of critical infrastructure: flood protection, nuclear power, communication networks, and so on. The design of such systems is based on vast knowledge and understanding, but also confronts bewildering uncertainties and endless surprises. We must continue to improve our knowledge and understanding, while also improving our ability to manage the uncertainties resulting from the expanding horizon of our efforts. We must identify the critical goals and seek responses that are immune to surprise. 




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Mind or Stomach? Imagination or Necessity?

"An army marches on its stomach" said Napoleon, who is also credited with saying "Imagination rules the world". Is history driven by raw necessity and elementary needs? Or is history hewn by people from their imagination, dreams and ideas?

The answer is simple: 'Both'. The challenge is to untangle imagination from necessity. Consider these examples:

An ancient Jewish saying is "Without flour, there is no Torah. Without Torah there is no flour." (Avot 3:17) Scholars don't eat much, but they do need to eat. And if you feed them, they produce wonders.

Give a typewriter to a monkey and he might eventually tap out Shakespeare's sonnets, but it's not very likely. Give that monkey an inventive mind and he will produce poetry, a vaccine against polio, and the atom bomb. Why the bomb? He needed it.

Necessity is the mother of invention, they say, but it's actually a two-way street. For instance, human inventiveness includes dreams of cosmic domination, leading to war. Hence the need for that bomb. Satisfying a need, like the need for flour, induces inventiveness. And this inventiveness, like the discovery of genetically modified organisms, creates new needs. Necessity induces inventiveness, and inventiveness creates new dangers, challenges and needs. This cycle is endless because the realm of imagination is boundless, far greater than prosaic reality, as we discussed elsewhere.

Imagination and necessity are intertwined, but still are quite different. Necessity focusses primarily on what we know, while imagination focusses on the unknown.

We know from experience that we need food, shelter, warmth, love, and so on. These requirements force themselves on our awareness. Even the need for protection against surprise is known, though the surprise is not.

Imagination operates in the realm of the unknown. We seek the new, the interesting, or the frightful. Imagination feeds our fears of the unknown and nurtures our hopes for the unimaginable. We explore the bounds of the possible and try breaking through to the impossible.

Mind or stomach? Imagination or necessity? Every 'known' has an 'unknown' lurking behind it, and every 'unknown' may some day be discovered or dreamed into existence. Every mind has a stomach, and a stomach with no mind is not human.




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The Age of Imagination


This is not only the Age of Information, this is also the Age of Imagination. Information, at any point in time, is bounded, while imagination is always unbounded. We are overwhelmed more by the potential for new ideas than by the admittedly vast existing knowledge. We are drunk with the excitement of the unknown. Drunks are sometimes not a pretty sight; Isaiah (28:8) is very graphic.

It is true that topical specialization occurs, in part, due to what we proudly call the explosion of knowledge. There is so much to know that one must ignore huge tracts of knowledge. But that is only half the story. The other half is that we have begun to discover the unknown, and its lure is irresistible. Like the scientific and global explorers of the early modern period - The Discoverers as Boorstin calls them - we are intoxicated by the potential "out there", beyond the horizon, beyond the known. That intoxication can distort our vision and judgment.

Consider Reuven's comment, from long experience, that "Engineers use formulas and various equations without being aware of the theories behind them." A pithier version was said to me by an acquisitions editor at Oxford University Press: "Engineers don't read books." She should know.

Engineers are imaginative and curious. They are seekers, and they find wonderful things. But they are too engrossed in inventing and building The New, to be much engaged with The Old. "Scholarship", wrote Thorstein Veblen is "an intimate and systematic familiarity with past cultural achievements." Engineers - even research engineers and professors of engineering - spend very little time with past masters. How many computer scientists scour the works of Charles Babbage? How often do thermal engineers study the writings of Lord Kelvin? A distinguished professor of engineering, himself a member of the US National Academy of Engineering, once told me that there is little use for journal articles more than a few years old.

Fragmentation of knowledge results from the endless potential for new knowledge. Seekers - engineers and the scientists of nature, society and humanity - move inexorably apart from one another. But nonetheless it's all connected; consilient. Technology alters how we live. Science alters what we think. How can we keep track of it all? How can we have some at least vague and preliminary sense of where we are heading and whether we value the prospect?

The first prescription is to be aware of the problem, and I greatly fear that many movers and shakers of the modern age are unaware. The second prescription is to identify who should take the lead in nurturing this awareness. That's easy: teachers, scholars, novelists, intellectuals of all sorts.

Isaiah struggled with this long ago. "Priest and prophet erred with liquor, were swallowed by wine."(Isaiah, 28:7) We are drunk with the excitement of the unknown. Who can show the way?




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We're Just Getting Started: A Glimpse at the History of Uncertainty


We've had our cerebral cortex for several tens of thousands of years. We've lived in more or less sedentary settlements and produced excess food for 7 or 8 thousand years. We've written down our thoughts for roughly 5 thousand years. And Science? The ancient Greeks had some, but science and its systematic application are overwhelmingly a European invention of the past 500 years. We can be proud of our accomplishments (quantum theory, polio vaccine, powered machines), and we should worry about our destructive capabilities (atomic, biological and chemical weapons). But it is quite plausible, as Koestler suggests, that we've only just begun to discover our cerebral capabilities. It is more than just plausible that the mysteries of the universe are still largely hidden from us. As evidence, consider the fact that the main theories of physics - general relativity, quantum mechanics, statistical mechanics, thermodynamics - are still not unified. And it goes without say that the consilient unity of science is still far from us.

What holds for science in general, holds also for the study of uncertainty. The ancient Greeks invented the axiomatic method and used it in the study of mathematics. Some medieval thinkers explored the mathematics of uncertainty, but it wasn't until around 1600 that serious thought was directed to the systematic study of uncertainty, and statistics as a separate and mature discipline emerged only in the 19th century. The 20th century saw a florescence of uncertainty models. Lukaczewicz discovered 3-valued logic in 1917, and in 1965 Zadeh introduced his work on fuzzy logic. In between, Wald formulated a modern version of min-max in 1945. A plethora of other theories, including P-boxes, lower previsions, Dempster-Shafer theory, generalized information theory and info-gap theory all suggest that the study of uncertainty will continue to grow and diversify.

In short, we have learned many facts and begun to understand our world and its uncertainties, but the disputes and open questions are still rampant and the yet-unformulated questions are endless. This means that innovations, discoveries, inventions, surprises, errors, and misunderstandings are to be expected in the study or management of uncertainty. We are just getting started. 




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I am a Believer


There are many things that I don't know. About the past: how my great-great-grandfather supported his family, how Charlemagne consolidated his imperial power, or how Rabbi Akiva became a scholar. About the future: whether I'll get that contract, how much the climate will change in the next 100 years, or when the next war will erupt. About why things are as they are: why stones fall and water freezes, or why people love or hate or don't give a damn, or why we are, period.

We reflect about questions like these, trying to answer them and to learn from them. For instance, we are interested in the relations between Charlemagne and his co-ruling brother Carloman. This can tell us about brothers, about emperors, and about power. We are interested in Akiva because he purportedly started studying at the age of 40, which tells us something about the indomitable human spirit.

We sometimes get to the bottom of things and understand the whys and ways of our world. We see patterns and discover laws of nature, or at least we tell stories of how things happen. Stones fall because it's their nature to seek the center of the world (Aristotle), or due to gravitational attraction (Newton), or because of mass-induced space warp (Einstein). Human history has its patterns, driven by the will to power of heroic leaders, or by the unfolding of truth and justice, or by God's hand in history.

We also think about thinking itself, as suggested by Rodin's Thinker. What is thinking (or what do we think it is)? Is thinking a physical process, like electrons whirling in our brain? Or does thinking involve something transcendental; maybe the soul whirling in the spheres? Each age has its answers.

We sometimes get stuck, and can't figure things out or get to the bottom of things. Sometimes we even realize that there is no "bottom", that each answer brings its own questions. As John Wheeler said, "We live on an island of knowledge surrounded by a sea of ignorance. As our island of knowledge grows, so does the shore of our ignorance."

Sometimes we get stuck in an even subtler way that is very puzzling, and even disturbing. Any rational chain of thought must have a starting point. Any rational justification of that starting point must have its own starting point. In other words, any attempt to rationally justify rational thought can never be completed. Rational thought cannot justify itself, which is almost the same as saying that rational thought is not justified. Any specific rational argument - Einstein's cosmology or Piaget's psychology - is justified based on its premises (and evidence, and many other things). But Rational Thought, as a method, as a way of life and a core of civilization, cannot ultimately and unequivocally justify itself.

I believe that experience reflects reality, and that thought organizes experience to reveal the patterns of reality. The truth of this belief is, I believe, self evident and unavoidable. Just look around you. Flowers bloom anew each year. Planets swoop around with great regularity. We have learned enough about the world to change it, to control it, to benefit from it, even to greatly endanger our small planetary corner of it. I believe that rational thought is justified, but that's a belief, not a rational argument.

Rational thought, in its many different forms, is not only justified; it is unavoidable. We can't resist it. Moses saw the flaming bush and was both frightened and curious because it was not consumed (Exodus 3:1-3). He was drawn towards it despite his fear. The Unknown draws us irresistibly on an endless search for order and understanding. The Unknown drives us to search for knowledge, and the search is not fruitless. This I believe. 




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Why We Need Libraries, Or, Memory and Knowledge


"Writing is thinking in slow motion. We see what at normal speeds escapes us, can rerun the reel at will to look for errors, erase, interpolate, and rethink. Most thoughts are a light rain, fall upon the ground, and dry up. Occasionally they become a stream that runs a short distance before it disappears. Writing stands an incomparably better chance of getting somewhere.

"... What is written can be given endlessly and yet retained, read by thousands even while it is being rewritten, kept as it was and revised at the same time. Writing is magic." 
Walter Kaufmann

We are able to know things because they happen again and again. We know about the sun because it glares down on us day after day. Scientists learn the laws of nature, and build confidence in their knowledge, by testing their theories over and over and getting the same results each time. We would be unable to learn the patterns and ways of our world if nothing were repeatable.

But without memory, we could learn nothing even if the world were tediously repetitive. Even though the sun rises daily in the east, we could not know this if we couldn't remember it.

The world has stable patterns, and we are able to discover these patterns because we remember. Knowledge requires more than memory, but memory is an essential element.

The invention of writing was a great boon to knowledge because writing is collective memory. For instance, the Peloponnesian wars are known to us through Thucydides' writings. People understand themselves and their societies in part through knowing their history. History, as distinct from pre-history, depends on the written word. For example, each year at the Passover holiday, Jewish families through the ages have read the story of the Israelite exodus from Egypt. We are enjoined to see ourselves as though we were there, fleeing Egypt and trudging through the desert. Memory, recorded for all time, creates individual and collective awareness, and motivates aspirations and actions.

Without writing, much collective memory would be lost, just as books themselves are sometimes lost. We know, for instance, that Euclid wrote a book called Porisms, but the book is lost and we know next to nothing about its message. Memory, and knowledge, have been lost.

Memory can be uncertain. We've all experienced that on the personal level. Collective memory can also be uncertain. We're sometimes uncertain of the meaning of rare ancient words, such as lilit in Isaiah (34:14) or gvina in Job (10:10). Written traditions, while containing an element of truth, may be of uncertain meaning or veracity. For instance, we know a good deal, both from the Bible and from archeological findings, about Hezekiah who ruled the kingdom of Judea in the late 8th century BCE. About David, three centuries earlier, we can be much less certain. Biblical stories are told in great detail but corroboration is hard to obtain.

Memory can be deliberately corrupted. Records of history can be embellished or prettified, as when a king commissions the chronicling of his achievements. Ancient monuments glorifying imperial conquests are invaluable sources of knowledge of past ages, but they are unreliable and must be interpreted cautiously. Records of purported events that never occurred can be maliciously fabricated. For instance, The Protocols of the Elders of Zion is pure invention, though that book has been re-published voluminously throughout the world and continues to be taken seriously by many people. Memory is alive and very real, even if it is memory of things that never happened.

Libraries are the physical medium of human collective memory, and an essential element in maintaining and enlarging our knowledge. There are many types of libraries. The family library may have a few hundred books, while the library of Congress has 1,349 km of bookshelves and holds about 147 million items. Libraries can hold paper books or digital electronic documents. Paper can perish in fire as happened to the Alexandrian library, while digital media can be erased, or become damaged and unreadable. Libraries, like memory itself, are fragile and need care.

Why do we need libraries? Being human means, among other things, the capacity for knowledge, and the ability to appreciate and benefit from it. The written record is a public good, like the fresh air. I can read Confucius or Isaiah centuries after they lived, and my reading does not consume them. Our collective memory is part of each individual, and preserving that memory preserves a part of each of us. Without memory, we are without knowledge. Without knowledge, we are only another animal.




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MOOCs and the Unknown


MOOCs - Massive Open Online Courses - have fed hundreds of thousands of knowledge-hungry people around the globe. Stanford University's MOOCs program has taught open online courses to tens of thousands students per course, and has 2.5 million enrollees from nearly every country in the world. The students hear a lecturer, and also interact with each other in digital social networks that facilitate their mastery of the material and their integration into global communities of the knowledgable. The internet, and its MOOC realizations, extend the democratization of knowledge to a scale unimagined by early pioneers of workers' study groups or public universities. MOOCs open the market of ideas and knowledge to everyone, from the preacher of esoteric spirituality to the teacher of esoteric computer languages. It's all there, all you need is a browser.

The internet is a facilitating technology, like the invention of writing or the printing press, and its impacts may be as revolutionary. MOOCs are here to stay, like the sun to govern by day and the moon by night, and we can see that it is good. But it also has limitations, and these we must begin to understand.

Education depends on the creation and transfer of knowledge. Insight, invention, and discovery underlay the creation of knowledge, and they must precede the transfer of knowledge. MOOCs enable learners to sit at the feet of the world's greatest creators of knowledge.

But the distinction between creation and transfer of knowledge is necessarily blurred in the process of education itself. Deep and meaningful education is the creation of knowledge in the mind of the learner. Education is not the transfer of digital bits between electronic storage devices. Education is the creation or discovery by the learner of thoughts that previously did not exist in his mind. One can transfer facts per se, but if this is done without creative insight by the learner it is no more than Huck Finn's learning "the multiplication table up to six times seven is thirty-five".

Invention, discovery and creation occur in the realm of the unknown; we cannot know what will be created until it appears. Two central unknowns dominate the process of education, one in the teacher's mind and one in the student's.

The teacher cannot know what questions the student will ask. Past experience is a guide, but the universe of possible questions is unbounded, and the better the student, the more unpredictable the questions. The teacher should respond to these questions because they are the fruitful meristem of the student's growing understanding. The student's questions are the teacher's guide into the student's mind. Without them the teacher can only guess how to reach the learner. The most effective teacher will personalize his interaction with the learner by responding to the student's questions.

The student cannot know the substance of what the teacher will teach; that's precisely why the student has come to the teacher. In extreme cases - of really deep and mind-altering learning - the student will not even understand the teacher's words until they are repeated again and again in new and different ways. The meanings of words come from context. A word means one thing and not another because we use that word in this way and not that. The student gropes to find out how the teacher uses words, concepts and tools of thought. The most effective learning occurs when the student can connect the new meanings to his existing mental contexts. The student cannot always know what contexts will be evoked by his learning.

As an interim summary, learning can take place only if there is a gap of knowledge between teacher and student. This knowledge gap induces uncertainties on both sides. Effective teaching and learning occur by personalized interaction to dispel these uncertainties, to fill the gap, and to complete the transfer of knowledge.

We can now appreciate the most serious pedagogic limitation of MOOCs as a tool for education. Mass education is democratic, and MOOCs are far more democratic than any previous mode. This democracy creates a basic tension. The more democratic a mode of communication, the less personalized it is because of its massiveness. The less personalized a communication, the less effective it is pedagogically. The gap of the unknown that separates teacher and learner is greatest in massively democratic education.

Socrates inveighed against the writing of books. They are too impersonal and immutable. They offer too little room for Socratic mid-wifery of wisdom, in which knowledge comes from dialog. Socrates wanted to touch his students' souls, and because each soul is unique, no book can bridge the gap. Books can at best jog the memory of learners who have already been enlightened. Socrates would probably not have liked MOOCs either, and for similar reasons.

Nonetheless, Socrates might have preferred MOOCs over books because the mode of communication is different. Books approach the learner through writing, and induce him to write in response. In contrast, MOOCs approach the learner through speech, and induce him to speak in response. Speech, for Socrates, is personal and interactive; speech is the road to the soul. Spoken bilateral interaction cannot occur between a teacher and 20 thousand online learners spread over time and space. That format is the ultimate insult to Socratic learning. On the other hand, the networking that can accompany a MOOC may possibly facilitate the internalization of the teacher's message even more effectively than a one-on-one tutorial. Fast and multi-personal, online chats and other networking can help the learners to rapidly find their own mental contexts for assimilating and modifying the teacher's message.

Many people have complained that the internet undermines the permanence of the written word. No document is final if it's on the web. Socrates might have approved, and this might be the greatest strength of the MOOC: no course ever ends and no lecture is really final. If MOOCs really are democratic then they cannot be controlled. The discovery of knowledge, like the stars in their orbits, is forever on-going, with occasional supernovas that brighten the heavens. The creation of knowledge will never end because the unknown is limitless. If MOOCs facilitate this creation, then they are good. 




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Mathematical Metaphors


Theories in all areas of science tell us something about the world. They are images, or models, or representations of reality. Theories tell stories about the world and are often associated with stories about their discovery. Like the story (probably apocryphal) that Newton invented the theory of gravity after an apple fell on his head. Or the story (probably true) that Kekule discovered the cyclical structure of benzene after day-dreaming of a snake seizing its tail. Theories are metaphors that explain reality.

A theory is scientific if it is precise, quantitative, and amenable to being tested. A scientific theory is mathematical. Scientific theories are mathematical metaphors.

A metaphor uses a word or phrase to define or extend or focus the meaning of another word or phrase. For example, "The river of time" is a metaphor. We all know that rivers flow inevitably from high to low ground. The metaphor focuses the concept of time on its inevitable uni-directionality. Metaphors make sense because we understand what they mean. We all know that rivers are wet, but we understand that the metaphor does not mean to imply that time drips, because we understand the words and their context. But on the other hand, a metaphor - in the hands of a creative and imaginative person - might mean something unexpected, and we need to think carefully about what the metaphor does, or might, mean. Mathematical metaphors - scientific models - also focus attention in one direction rather than another, which gives them explanatory and predictive power. Mathematical metaphors can also be interpreted in different and surprising ways.

Some mathematical models are very accurate metaphors. For instance, when Galileo dropped a heavy object from the leaning tower of Pisa, the distance it fell increased in proportion to the square of the elapsed time. Mathematical equations sometimes represent reality quite accurately, but we understand the representation only when the meanings of the mathematical terms are given in words. The meaning of the equation tells us what aspect of reality the model focuses on. Many things happened when Galileo released the object - it rotated, air swirled, friction developed - while the equation focuses on one particular aspect: distance versus time. Likewise, the quadratic equation that relates distance to time can also be used to relate energy to the speed of light, or to relate population growth rate to population size. In Galileo's case the metaphor relates to freely falling objects.

Other models are only approximations. For example, a particular theory describes the build up of mechanical stress around a crack, causing damage in the material. While cracks often have rough or ragged shapes, this important and useful theory assumes the crack is smooth and elliptical. This mathematical metaphor is useful because it focuses the analysis on the radius of curvature of the crack that is critical in determining the concentration of stress.

Not all scientific models are approximations. Some models measure something. For example, in statistical mechanics, the temperature of a material is proportional to the average kinetic energy of the molecules in the material. The temperature, in degrees centigrade, is a global measure of random molecular motion. In economics, the gross domestic product is a measure of the degree of economic activity in the country.

Other models are not approximations or measures of anything, but rather graphical portrayals of a relationship. Consider, for example, the competition among three restaurants: Joe's Easy Diner, McDonald's, and Maxim's de Paris. All three restaurants compete with each other: if you're hungry, you've got to choose. Joe's and McDonald's are close competitors because they both specialize in hamburgers but also have other dishes. They both compete with Maxim's, a really swank and expensive boutique restaurant, but the competition is more remote. To model the competition we might draw a line representing "competition", with each restaurant as a dot on the line. Joe's and McDonald's are close together and far from Maxim's. This line is a mathematical metaphor, representing the proximity (and hence strength) of competition between the three restaurants. The distances between the dots are precise, but what the metaphor means, in terms of the real-world competition between Joe, McDonald, and Maxim, is not so clear. Why a line rather than a plane to refine the "axes" of competition (price and location for instance)? Or maybe a hill to reflect difficulty of access (Joe's is at one location in South Africa, Maxim's has restaurants in Paris, Peking, Tokyo and Shanghai, and McDonald's is just about everywhere). A metaphor emphasizes some aspects while ignoring others. Different mathematical metaphors of the same phenomenon can support very different interpretations or insights.

The scientist who constructs a mathematical metaphor - a model or theory - chooses to focus on some aspects of the phenomenon rather than others, and chooses to represent those aspects with one image rather than another. Scientific theories are fascinating and extraordinarily useful, but they are, after all, only metaphors.












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