Reduce your Worry

"What Ifs" Never Help Anyone

by Amy E. Barr, The Lukeion Project

Several times this semester I (or my faculty colleagues) have gotten a note explaining that a student couldn’t complete an assignment because he or she was so consumed with worry related to the pandemic. I even know that some have stopped schooling entirely until they find some unspecified worry-free point in the future. Maybe 2021? 2022? Nobody knows. With this in mind, today’s blog is a note to all our worriers.

 Many have successfully grappled with the “what if” monster and conquered that beast or come to terms with it. The whole planet is suffering under uncertainties (as we have before and as we will once again). Why are some utterly gutted with overwhelming worry while others soldier on? Why must some pause life to tend their mountainous concerns while others adapt and move forward?

As a mother of three grown-and-flown children, the caretaker of a small homestead, and a small business owner, I suppose I have my share of concerns but I am not consumed with worry. This trait can annoy those that prefer to foster their worries. “You are lucky,” they say. “I must have a lot more to worry about than you do.” I doubt it but I do adhere to the principle that being worried is a choice, not a necessity.

Let's return to the idea that some foster their worries. True worriers tend their concerns like they are growing a garden full. If worry were a buffet, some go back for extra helpings at the worry bar. For some, worry is the main thing in the schedule and the main course on the dinner plate. Even when all energy is exhausted on “what if” concerns, worriers never grow closer to finding the much-desired hypothetical safe zone so they redouble their efforts to find more “what ifs” even as outdated ones fade away in the past.

Worry doesn’t live on one end of a continuum with safety perched tantalizingly on the other. The force of your virulent worry will never peddle you closer toward safety. Worry only gets bigger and it will certainly never repay you for your efforts. It will always consume more time and energy even as you increase your appetite for it daily. Worry takes you nowhere. There’s no reward in it. None. 

The obvious answer is this: stop worrying. Having lived for years with natural-born-worriers, I know you now ask, “how does one just stop it, especially when worry seems so unavoidable and so uncontrollable?” 

Humans are the only creatures that think ahead fully. We cultivate savings accounts, we take vitamin supplements, we reserve vacation time, we exercise when we’d rather sit, we get 20-year mortgages. We fervently plan or problem-solve for potential events many years in our future. Good problem-solving skills separate successful people--those with savings, health, a rewarding job, happy kids--from unsuccessful people burdened by debt, drama, doom. Neither group knew for certain what to expect in the years to come and luck is not always to blame.

Problem solving for the future is like a paved road going off into the distance. Most of us can look down this road to see roughly where it swoops over the horizon line or around a curve. Some have it easier because a mentor demonstrated how he or she has stayed on track during rough patches. Others, after a few halts, move down the road just the same. There will always be a point at which we can’t see the road in the distance. We’ll come to curves and hit major bumps (finances, health, relationships, disaster) so we recalibrate, we problem-solve, and we push on. The road ahead is visible but only poorly and only in patches. This is normal and unavoidable.

Worry is mismanaged problem solving for the future. Instead of working out a variety of strategies to move ahead down life’s unseen road—come what may—we build massive hypothetical worst-case scenarios. Instead of saving money for a rainy day, we focus on getting struck by lightning in that same rainstorm. We are going down the same road as before, but white-knuckled and terrified. We only have eyes for the hypothetical disaster (of our own design). Sure, some have it harder because a mentor or trusted source demonstrated the necessity to stay terrified about the road ahead or, the worse, your mentor failed to clue you in about life’s normal bumps and curves.

If worry is devouring your life, understand that it really is avoidable and controllable. First, look at your pile of worries. Listing them or discussing them with a non-worrier is a great idea (do bring them cookies). Sometimes just saying them reduces their scale and terror. Evaluate your worries. Some are worth a bit of energy right now –like how to get work done this week or how to help a sick family member--but most future "what if” worries are entirely unproductive. They are ready for the trash bin. “What if” worries are out of your control. There’s no productive course of action or reasonable solution for such uncertainties and hypotheticals because they do not exist now, and they will likely never exist in the future.

Stop equating feelings of uncertainty with foreboding and doom. Life, at least the kind that is worth living, is full of uncertainty. You can’t have it all planned and sorted as you smoothly round every blind curve. Life will never go this way. Accept uncertainty and put all your energy into things you can control like doing today’s work and taking care of today’s health and loved ones. There are certainly dips and curves ahead. You will never be in control of the road, only how you drive it. Apply all that misspent worry-energy on today’s troubles right now, small, or large. Come at life full tilt, learn how to do the tough stuff of the future by doing the manageable stuff today. You’ll find you have reduced your “what if” worry pile by half.  

“The art of life is to deal with problems as they arise, rather than destroy one’s spirit by worrying about them too far in advance.” Marcus Tullius Cicero

3 Myths About Studying Logic

Let's Think about this Logically

By Dr. Kim Johnson, Lukeion Logic Sage and Maths Expert

You may have seen Lester’s Logic Lounge offered at the Lukeion Project but been hesitant to enroll your students for various reasons. Maybe your learner has taken a few lessons on types of fallacies, and you think that is sufficient. Or maybe logic seems like a nice brainy topic for others with extra time but not right for your family. Maybe formal logic is something that is theoretically interesting, but not terribly applicable in the real world. Maybe the study of logic just hasn’t appeared on your radar at all!
Let’s explore the 3 main myths about studying formal logic.

Myth #1: You don’t need a formal logic course, it is enough to learn logical fallacies.

Logical fallacies are fun to learn, and they are important for maintaining clear thinking in this modern life. Advertisers, politicians, and everybody on the planet use a variety of wily methods to convince us to think, eat, watch, or buy things that may or may not be good for us.  If we can recognize a bad argument when we see one, we are better prepared to defend ourselves against the “dark arts” of persuasion.
It is not enough to learn informal fallacies. Imagine if you were taught mathematics by learning only incorrect computations, or history if you were taught only events that didn’t occur. It is important to recognize falsehood, but it is also important to be able to construct and use correct reasoning. Formal logic begins with the beginnings of correct argument: definitions and statements.  After mastering the basics, we consider how to put them together to make valid arguments. We analyze both good and bad arguments so we can recognize them in others and formulate them for ourselves.

Myth #2: Logic is only important for those following the classical philosophy of homeschooling.

Dorothy Sayers helped inspire today’s classical school of education with her essay, “The Lost Tools of Learning.”  She praised education that had its basis in the Trivium, emphasizing three stages: Grammar, Logic, and Rhetoric. Today, there are plenty of curricula and groups which subscribe to this idea. All of them suggest logic as one of the required courses during middle school years when a student has moved into the “logic” stage (usually around age 13 or 14 for many students).
Formal logic has its place in every educational philosophy, from traditional to unschooling. No matter what your child ends up studying before or after graduation, being able to create and understand sound arguments will help him or her. 
Formal logic will help students in mathematics as well as philosophy, which focus on logical arguments. Students in the sciences also need to show the data they collect logically supports their hypotheses. Logic will help any student who must complete formal academic writing of any kind. He or she must analyze and explain sound theories based on data, regardless if that data is 17th century English authors or biology. Logic will help sociologists and psychologists develop studies that prove what they purport to show. Students in political science and economics need logic to create sound policies and then convince others that they are appropriate. The study of logic applies to every branch of higher learning.

Myth #3: Formal logic has no bearing on arguments in real life.

It is true that few arguments these days follow the classical syllogism form. The syllogistic argument goes like this: 

• All men are mortal, 

• Socrates was a man, 

• Therefore, Socrates was mortal. 

While we spend a lot of time discussing classical syllogisms in formal logic, it is not an end in itself. We study the classic syllogism to understand arguments in a tame environment before going out into the wilds of everyday language. 
We start with finding the conclusion of an argument and separating it from the premises. Sometimes just doing this helps us to understand what is really going on in an argument! We look at how statements are related to each other. For example, two statements can be consistent without being logically equivalent, or contrary but not contradictory. We can link these statements into arguments.
In the end we move on to arguments, formally stated and informally stated. Since no one speaks in formal syllogisms, the end of formal logic is to analyze ordinary arguments. We first translate the arguments into formal language to get rid of the imprecision of ordinary language. Then, when we are sure we understand the terms and how they relate to each other, we can attack the argument itself and whether it is valid (which may or may not lead to a true conclusion) or sound (which has true premises, a valid argument, and a true conclusion).
After spending time in formal logic, most students start looking at the world from a new (and more logical) perspective. They may start translating everyday-sentences into logical form and explaining why the argument you make about whether they get more dessert is invalid. Don’t fear! The next step your student takes is effectively arguing points in a history class or an English paper.
Our textbook writers Nance and Wilson define logic as “the art and science of reasoning well.”  In Lester’s Logic Lounge, we break down real-life arguments into their smallest components, put them together carefully, and analyze them in simple cases so that, when the complexity of reality breaks in, the student is prepared to respond with their mind instead of gut feelings. Don’t let these myths stop you from studying logic. The benefits of logic reach well beyond a single class and spread through students’ entire lives. We apologize in advance if your child starts making a much-improved case for more dessert.

The Follow Instructions Mindset

Can Academic Success be Found THAT Easily?

By global blogger Amy Barr, The Lukeion Project

A regular topic of conversation among educators is, “WHY do so many students fail to follow basic instructions?” While some teachers stick to complaining about the issue, most place the blame on ourselves at first. We double efforts to clarify instructions as we add bullet-points, illustrations, recaps, finger-puppets, examples, charts, modern dancing… but the problem persists as handouts get longer and sometimes weirder. First, our email inbox is filled with notes asking basic questions already answered in handouts. Next, the inbox is filled with notes from students who scored poorly on something because they didn’t “know” what to do (even though that was spelled out in finest detail). 

Because the art and science of instruction-following have become rare, educators place an increasingly large percentage of assignment scores on doing all of what is asked on assignment. Even after students know this is the case, they will still refuse to follow instructions, as grade points diminish week after week. Watch a competitive baking show (or any other creative competition) to see people make the best biscuit for thousands of dollars yet “fail to follow the brief.” Often the big winner is just the one that ticked all boxes.

Why is this simple skill so poorly represented? Is there a science to following instructions? Is it an art form? Is it a state of mind?

25 years of teaching experience tells me that there is a connection between people who consider themselves clever or “excellent” at something and their refusal to follow directions. For example, students who have been strongly praised by others in the past for their writing skills will invariably ignore instructions for a writing assignment or, if they don’t’ ignore them, they will claim they don’t understand the instructions given. When pressed, I normally find the issue isn’t so much that they didn’t understand instructions but that surely the assignment specifics shouldn't apply to them. After all, they have been “writing novels for years!” The instructions for authoring an academic essay are being unfair to THEM. 

A study on this topic was published several years ago by a joint research team from Cornell and Harvard Medical School. People who refuse to follow instructions are an expensive problem in corporations, government positions, and in college classes. Hundreds of thousands of dollars and hours are lost over this challenge. Perfectly intelligent people utterly fail at basic tasks because they can’t or won’t follow the steps necessary to complete assignments. Why? The results of the study were clear. People who see themselves as “special or entitled” would “rather lose at something than submit to the rules of others.” 

Aside from the obvious, that some of us can blame an overly generous dollop of old-fashioned narcissism, there are several other contributing factors when perfectly smart students ignore instructions. Here are a few things I see at the front lines.

Dumb Tourist Approach

I devised this term for the behavior I witness repeatedly when traveling abroad (and especially when I was working as an archaeologist) from tourists who cut in line, wander across clearly barricaded areas as a shortcut, wander fecklessly into closed museum galleries, or stagger into blockaded excavation areas for a quick sneak peek. When caught violating all rules of “tourism good behavior,” they would feign ignorance and plead for special help getting themselves back on the tourist path. Flummoxed and harassed staff would comply just to get the “dumb tourist” out of their hair. The “dumb” tourist would still enjoy that shortcut, a special sneak peek, and subsequent boasting rights, just as he or she planned all along. 

Some students discover there are big benefits to being a “dumb tourist.” They exert minimal effort, but when they forget an assignment or ignore instructions, they claim ignorance and seek second chances, extensions, and do-overs. This technique works well for them so they place bets that all flummoxed and harassed instructors (bosses, coaches, and parents in their lives) will give them help just to get them out of their hair or go easy on them when grading. This technique has short-term benefits. Even the most forgiving instructor and most encouraging coach will catch on. 

Instructions are for Dummies Approach

Everyone has heard about the guy who tries to assemble a massive backyard playset without looking at the instruction booklet. It is practically a cliché for how stubborn people can be about reading instructions! All of us are guilty of similar foolish moves (there was the time we didn’t add chain grease to a new chainsaw until after we cut up a medium-sized tree). As we get older and hopefully wiser, we learn that only dummies SKIP instructions. This knowledge comes with experience and the cost of losses. Students need to gain this valuable insight for themselves. Tasked with a long writing project, will they or won’t they find out what is expected before they hand it in? Suffering a major grade gauge once or twice is a small price to pay for this important experience.

Genuinely Confused Approach

Sometimes instructions are genuinely confusing! Ever ordered something online only to discover that even the English instructions were not written in English? If you’ve never assembled a thingamajiggy before, the first time can be tricky. Since there aren’t YouTube videos on how to complete your assignments in your classes, you will have to find clarity. Try these steps:

1. Read the whole assignment handout from beginning to end. Read all of it. Don’t skip anything.

2. Next, go back and write out a project flow list for yourself using the instructions. You can be as detailed as you need to be but organize the steps for what your instructor wants from you in this assignment. Don’t forget details like formatting and the due date but include special instructions for yourself like “visit local university library on Saturday” or “interview uncle Steve about this topic.” Writing out the steps for yourself will help you visualize the whole project and how long it might take you. The flow list might be short (put it in your planner) or be longer and include multiple self-set due dates.

3. If you are still confused, contact your instructor to ask. Sometimes you aren’t so much confused but irritated that you are being asked to do something different than you’ve done in past classes. Ask for clarification but follow the instructions. How will you master new skills if your abilities have been perfected at age 16? You have much more to learn over the next 80 years. If you are being asked to do things differently, DO them differently by following the instructions.

Instructions are fabulous things. Instead of avoiding them, become excellent at following them. Aside from brain surgery or pygmy goat herding, being able to follow instructions can lead you to great heights of excellence. Cooking beautiful feasts just like Nana, or crafting extravagant art pieces, or making great smelling handmade soap all come from following instructions. Following instructions can turn you into a top-level student who is a joy to have in class both now and in the future. Adopt a good mindset for following instructions and then make it a habit.

Murderous Mathematicians

Math Can Be Dangerous

By Dr. Kim Johnson, Lukeion Project Logic Sage

The life of a mathematician may seem completely devoid of intrigue, and perhaps of any interest at all. On the contrary! There are many mathematicians who lived exceptionally exciting lives, facing dangers like conspiracies, duels, and even murder.

Pythagoras

Pythagoras was one of the first to have the job description read, “mathematician.”  He was born around 470 B.C. in Samos, Greece and died in Croton, Italy, about 75 years later.  Most famous for the theorem named after him, he and his followers introduced other mathematical innovations.  They used letters to refer to angles and sides in the drawings they made in the sand.  They used colored chalk to demonstrate the equality of lines or angles. According to some legends, Pythagoras was the first teacher paid by his students. The Pythagoreans were an interesting cult. Adhering to a vegetarian lifestyle, men and women studied together. Using their superior math skills, they invented the 8-tone scale, determined by ratios between the notes.  

Pythagoras may or may not have authorized the first mathematical murder. One of the cult’s most strongly held beliefs was, “All is number,” or more accurately, “All is ratio.”  When one of his followers noticed the hypotenuse of a triangle with two equal legs could not be written as the ratio of two whole numbers, the followers of Pythagoras tipped him over the side of the boat. Most of what we know about Pythagoras comes from texts written well after his death so the details of this hypotenuse homicide are a bit unclear.

Perhaps Pythagoras deserved his eventual fate.  His school at Croton got involved in some politics which angered the local populace.  They burned down the Pythagorean academy and chased Pythagoras himself across the fields.  Some stories suggest he was killed because he refused to cross a field of beans, sacred to the Pythagoreans.

Descartes

Rene Descartes (1596-1650) was another mathematician who lived a life worthy of a spy novel.  He was very sickly as a child and, because of this, when he was sent to Jesuit school the rector allowed him to remain in bed until he felt like getting up.  As a young man he joined various volunteer armies mainly for the purpose of seeing the world rather than seeing battle.  His travels and conversations around Europe led to his philosophical and mathematical insights.

Descartes invented a way to locate points on the plane by noting how far they were from two lines, the “x-axis” and the “y-axis”.  Each point was identified by a coordinate pair, (x,y).  This was revolutionary because it allowed mathematicians to link geometry (great pictures and relationships between shapes) to algebra (filled with equations, x’s, and y’s). One can build a solution using equations — or one can graph the equation using the Cartesian plane to see the same solution.

Later in life Descartes retired to the Netherlands.  His peaceful life was interrupted by a letter from Princess Christina from Sweden. To her credit, she wanted to make the capital of Sweden an intellectual center.  Unlike Descartes, the princess enjoyed waking up incredibly early to study in a cold room and insisted that Descartes join her at 5 AM for lessons in philosophy and ethics.  He died later that year from pneumonia. Feel free to use this the next time someone wants you to get up early to study math. 

Galois

French mathematician Evariste Galois (1811-1832) lived a perilous life, at least for a mathematician. He grew up after the French Revolution and the Napoleonic empire, but politics problematic.  He was accepted into the second-best school in Paris, only to be kicked out when he complained that the students of the academy were not allowed to help overthrow Charles X.  

He was arrested twice for making controversial political statements including raising a toast to King Louis-Phillipe with a dagger in his glass. He wrote some brilliant papers but had a few were rejected due to political bias. One was lost when the person he sent it to, died before reviewing it. In the end, Galois got into a duel over the honor of a “floozy” (his words). The night before he died, he wrote several farewell letters, including directions to find his groundbreaking mathematical writings.  Thus he died at the age of 20 while his techniques for finding roots of equations inspired a new branch of mathematics named after him, Galois Theory. 

Math can be dangerous  

Not included in this list are many other mathematicians who died in mysterious or violent circumstances. Archimedes was murdered by a Roman soldier for telling the soldier not to mess up his drawings. Hypatia was murdered by a mob for mixing religion, politics, and mathematics. Cardano committed suicide on the day he had astrologically predicted he would die. Ramanujan died from cold weather and bad food in England. Fourrier died after falling down the stairs while wrapped in too many blankets. 

Although the Bureau of Labor and Statistics has ranked mathematician as one of the safest jobs in the world, mathematicians themselves have historically interesting deaths.