Tag: Algebraic Equivalence

A Wandering Mind: How Travel Can Change the Way You Think

Most people travel as an observer, and as a result, “see” a lot. When you travel as an active participant, the experience can transform the way you think, and how you see the world.

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Here’s a situation familiar to many of us: We decide to take a vacation and go somewhere exotic. We plan the trip and mark our calendars, and as the date gets closer we get increasingly excited. Before we step on the plane, the possibilities seem endless. Anything could happen! Accidental encounters and adventures could change our lives!

We go. We have a good time. We see what we wanted to and enjoy the break from work. Upon returning home, we share the pictures and recount some of our experiences with friends. We give away the souvenirs. We step back into our lives. The glow fades and we settle to planning the next round of travel in our daydreams.

In the end, it’s a little sad. That incredible experience becomes like a mirage or a dream—similar to watching a movie, but a lot more expensive.

What if it doesn’t have to be like this?

Travel without participation and reflection is entertainment. Try to notice yourself in the journey, and capture the experience and insights when you interact with all the new things you are confronted with. You can get more out of your travel by using mental models to weave yourself into the experience, and come away enriched as well as entertained and rested.

First, inspiration from the past …

Just over 200 years ago, Mary Wollstonecraft, philosopher, feminist, and author of A Vindication of the Rights of Woman, was going through an emotionally difficult period. Her lover—the father of her child—wasn’t interested in being with her anymore. She was devastated and frustrated. As a philosopher, she believed it was important to live according to the ideals she espoused. The realities facing a middle-class woman in 18th-century England made that very hard. Women had essentially no rights. Having a child out of wedlock might have supported her ideas regarding how oppressive the institution of marriage was for women, but without the support of the child’s father, she knew she would struggle financially and socially. It was one of the lowest points of her life.

Wollstonecraft went to Scandinavia, mostly to recover some money for her lover and thus try to win him back. In this she failed. But she captured her journey in Letters Written During a Short Residence in Sweden, Norway, and Denmark. In doing so, she revolutionized travel writing and healed herself.

The Letters offer remarkable insight into Wollstonecraft’s lively mind. As she moves through the unfamiliar surroundings of three foreign countries, she asks herself questions and explores the ideas brought to mind. Observing the agricultural development of Norway, in many ways behind that of England at the time, she asks, “And, considering the question of human happiness, where, oh where does it reside? Has it taken up its abode with unconscious ignorance or with the high-wrought mind?”

She learns why the locals are nervous about serving coffee and how different their fashions are. She comments on the different gardening practices and the beauty of the trees. In contemplating how the Norwegians organize their social hierarchy she makes comparisons to England and infers conclusions about her native country—namely that the way things are is not necessarily how they have to be.

Most importantly, she records what effect the traveling has on her. “When a warm heart has received strong impressions, they are not to be effaced. Emotions become sentiments, and the imagination renders even transient sensations permanent by fondly retracing them. I cannot, without a thrill of delight, recollect views I have seen, which are not to be forgotten, nor looks I have felt in every nerve, which I shall never more meet.”

Here are some goals we can construct from Wollstonecraft’s approach to travel:

  1. Try to actively know the place you are in. Observe the customs. Interact with the locals.
  2. Learn the whys behind the observation. Explore the history. Ask questions. Try to understand the answers in relation to what you are experiencing now, setting aside any previous assumptions.
  3. Notice how the journey is affecting you. What memories surface? What new insights do you have? Are your opinions and beliefs challenged?
  4. Don’t plan out every detail. Explore. The map is not the territory.

So how do we put those goals into practice?

Here is where mental models can amplify the travel experience.

We all have a tendency to generalize from small samples. Our own little world becomes, without the infusion of new experiences, our frame for understanding the entire world. Travel broadens your sample set. You start to really understand the universals of the human condition versus the particulars of the area you occupy.

Travel is a great way to counter confirmation bias. Chances are, people in a different country will think differently than you. Interactions won’t reinforce your feedback loop. You will be exposed to new ideas and ways of approaching life that can remind you of the options you have when you go back home.

You can apply the power of algebraic equivalence. In algebra, as we solve abstractions such as x + y = 8, we learn that values can be equal without looking exactly the same. When you explore other cultures and ways of living, you see that there are many definitions of a good life and many ways to be happy. You begin to understand that equality of experience is different from sameness of experience. Not everyone wants what you want. This diversity in how we manifest our goals and desires accounts for differences in everything from personal philosophy to product markets.

The distance from your regular life can give you perspective. Using the terms of Galilean relativity, you get to be the fish instead of the scientist. The lens of travel can help you untangle problems back at home in many ways. The distance, both physical and psychological, also gives you the opportunity to observe yourself in your regular life without the day-to-day pressures clouding your judgment.

Try these specific tips to apply this mental models approach to travel:

  1. Keep a travel journal. It doesn’t have to be complicated. Travel is full of idle moments like waiting for transportation, or museum-feet recovery at the end of the day. Reflect and capture.
  2. Encourage serendipity in your experiences. Give yourself the chance to experience the unexpected. Over-planning reinforces your current biases. You can’t possibly know the best of a place before you get there.
  3. Be deliberate in setting your goal. Go somewhere with the intent of gaining something out of that experience. Don’t try to recreate your life at home, with the same restaurants and television shows.
  4. Be open to growth. Travel is an opportunity to choose to be different. Anticipate that you might add to the construct that is “you” when you travel. Embrace the additions to your identity so that you have new resources to draw on.

Through considering mental models and staying actively engaged, travel can jolt you awake, and show you the world in a different light.

5 Mental Models to Remove (Some of) the Confusion from Parenting

Just a few days ago, I saw a three-year-old wandering around at 10:30 at night and wondered if he was lost or jet-lagged. The parent came over and explained that they believed in children setting their own sleep schedule.

Interesting.

The problem with this approach is that it may work, or it may not. It may work for your oldest, but not your youngest. And therein lies the problem with the majority of the parenting advice available. It’s all tactics, no principles.

Few topics provoke more unsolicited advice than parenting. The problem is, no matter how good the advice, it might not work for your child. Parenting is the ultimate “the map is not the territory“ situation. There are so many maps out there, and often when we try to use them to navigate the territory that is each individual child, we end up lost and confused. As in other situations, when the map doesn’t match the territory, better to get rid of the map and pay attention to what you are experiencing on the ground. The territory is the reality.

We’ve all dealt with the seemingly illogical behavior of children. Take trying to get your child to sleep through the night—often the first, and most important, challenge. Do you sleep beside them and slowly work your way out of the room? Do you let them “cry it out?” Do you put them in your bed? Do you feed them on demand, or not until morning? Soft music or no music? The options are endless, and each of them has a decently researched book to back it up.

When any subsequent children come along, the problem is often exacerbated. You stick to what worked the first time, because it worked, but this little one is different. Now you’re in a battle of wills, and it’s hard to change your tactics at 3:00 a.m. Parenting is often a rinse and repeat of this scenario: ideas you have about how it should be, combined with what experience is telling you that it is, overlaid with too many options and chronic exhaustion.

This is where mental models can help. As in any other area of your life, developing some principles or models that help you see how the world works will give you options for relevant and useful solutions. Mental models are amazing tools that can be applied across our lives. Here are five principle-based models you can apply to almost any family, situation, or child. These are ones I use often, but don’t let this limit you—so many more apply!

Adaptation

Adaptation is a concept from evolutionary biology. It describes the development of genetic traits that are successful relative to their performance in a specific environment—that is, relative to organisms’ survival in the face of competitive pressures. As Geerat Vermeij explains in Nature: An Economic History, “Adaptation is as good as it has to be; it need not be the best that could be designed. Adaptation depends on context.”

In terms of parenting, this is a big one: the model we can use to stop criticizing ourselves for our inevitable parenting mistakes, to get out of the no-point comparisons with our peers, and to give us the freedom to make changes depending on the situation we find ourselves in.

Species adapt. It is a central feature of the theory of evolution—the ability of a species to survive and thrive in the face of changing environmental conditions. So why not apply this basic biological idea to parenting? Too often we see changing as a weakness. We’re certain that if we aren’t absolutely consistent with our children, they will grow up to be entitled underachievers or something. Or we put pressure on ourselves to be perfect, and strive for an ideal that requires an insane amount of work and sacrifice that may actually be detrimental to our overall success.

We can get out of this type of thinking if we reframe ‘changing’ as ‘adapting’. It’s okay to have different rules in the home versus a public space. I am always super grateful when a parent pacifies a screaming child with a cookie, especially on an airplane or in a restaurant. They probably don’t use the same strategy at home, but they adapt to the different environment. It’s also okay to have two children in soccer, and the third in music. Adapting to their interests will offer a much better return of investment on all those lessons.

No doubt your underlying goals for your children are consistent, like the desire of an individual to survive. How you meet those goals is where the adaptability comes in. Give yourself the freedom to respond to the individual characteristics of your children—and the specific needs of the moment—by trying different behaviors to see what works. And, just as with adaptation in the biological sense, you only need to be as good as you have to be to get the outcomes that are important to you, not be the best parent that ever was.

Velocity

There is a difference between speed and velocity. With speed you move, but with velocity you move somewhere. You have direction.

As many have said of parenting, the days are long but the years are short. It’s hard to be focusing on your direction when homework needs to be done and dinner needs to get made before one child goes off in the carpool to soccer while you rush the other one to art class. Every day begins at a dead run and ends with you collapsing into bed only to go through it all again tomorrow. Between their activities and social lives, and your need to work and have time for yourself, there is no doubt that you move with considerable speed throughout your day.

But it’s useful to sometimes ask, ‘Where am I going?’ Take a moment to make sure it’s not all speed and no direction.

When it comes to time with your kids, what does the goal state look like? How do you move in that direction? If you are just speeding without moving then you have no frame of reference for your choices. You might ask, did I spend enough time with them today? But ten minutes or two hours isn’t going to impact your velocity if you don’t know where you are headed.

When you factor in a goal of movement, it helps you decide what to do when you have time with them. What is it you want out of it? What kind of memories do you want them to have? What kind of parent do you want to be and what kind of children do you want to raise? The answers are different for everyone, but knowing the direction you wish to go helps you evaluate the decisions you make. And it might have the added benefit of cutting out some unnecessary activity and slowing you down.

Algebraic Equivalence

“He got more pancakes than I did!” Complaints about fairness are common among siblings. They watch each other like hawks, counting everything from presents to hugs to make sure everyone gets the same. What can you do? You can drive yourself mad running out to buy an extra whatever, or you can teach your children the difference between ‘same’ and ‘equal’.

If you haven’t solved for x in a while, it doesn’t really matter. In algebra, symbols are used to represent unknown numbers that can be solved for given other relevant information. The general point about algebraic equivalence is that it teaches us that two things need not be the same in order to be equal.

For example, x + y = 5. Here are some of the options for the values of x and y:

3 + 2

4 + 1

2.5 + 2.5

1.8 + 3.2

And those are just the simple ones. What is useful is this idea of abstracting to see what the full scope of possibilities are. Then you can demonstrate that what is on each side of those little parallel lines doesn’t have to look the same to have equal value. When it comes to the pancakes, it’s better to focus on an equal feeling of fullness then the number of pancakes on the plate.

In a deeper way, algebraic equivalence helps us deal with one accusation that all parents get at one time or another: “You love my sibling more than me.” It’s not true, but our default usually is to say, “No, I love you both the same.” This can be confusing for children, because, after all, they are not the same as their sibling, and you likely interact with them differently, so how can the love be the same?

Using algebraic equivalence as a model shifts it. You can respond instead that you love them both equally. Even though what’s on either side of the equation is different, it is equal. Swinging the younger child up in the air is equivalent to asking the older one about her school project. Appreciating one’s sense of humor is equivalent to respecting the other’s organizational abilities. They may be different, but the love is equal.

Seizing the middle

In chess, the middle is the key territory to hold. As explained on Wikipedia: “The center is the most important part of the chessboard, as pieces from the center can easily move to either flank with great speed. However, amateurs often prefer to concentrate on the king’s side of the board. This is an incorrect mindset.”

In parenting, seizing the middle means you must forget trying to control every single move. It’s impossible anyway. Instead, focus on trying to control what I think of as the middle territory. I don’t mind losing a few battles on the fringes, if I’m holding my ground in the area that will allow me to respond quickly to problems.

The other night my son and I got into perhaps our eighth fight of the week on the state of his room. The continual explosion makes it hard to walk in there, plus he loses things all the time, which is an endless source of frustration to both of us. I’ve explained that I hate buying replacements only to have them turn up in the morass months later.

So I got cranky and got on his case again, and he felt bad and cried again. When I went to the kitchen to find some calm, I realized that my strategy was all wrong. I was focused on the pawn in the far column of the chess board instead of what the pieces were doing right in front of me.

My thinking then went like this: what is the territory I want to be present in? Continuing the way I was would lead to a clean room, maybe. But by focusing on this flank I was sacrificing control of the middle. Eventually he was going to tune me out because no one wants to feel bad about their shortcomings every day. Is it worth saving a pawn if it leaves your queen vulnerable?

The middle territory with our kids is mutual respect and trust. If I want my son to come to me for help when life gets really complicated, which I do, then I need to focus on behaviors that will allow me to have that strategic influence throughout my relationship with him. Making him feel like crap every day, because his shirts are mixed in with his pants or because of all the Pokemon cards are on the floor, isn’t going to cut it. Make no mistake, seizing the middle is not about throwing out all the rules. This is about knowing which battles to fight, so you can keep the middle territory of the trust and respect of your child.

Inversion

Sometimes it’s not about providing solutions, but removing obstacles. Sociologist Kurt Lewin observes in his work on force field analysis[1] that reaching any goal has two components: augmenting the forces for, and removing the forces against. When it comes to parenting, we need to ask ourselves not only what we could be doing more of, but also what we could be doing less of.

When my friend was going on month number nine of her baby waking up four times a night, she felt at her wits’ end. Out of desperation, she decided to invert the problem. She had been trying different techniques and strategies, thinking that there was something she wasn’t doing right. When nothing seemed to be working, she stopped trying to add elements like new tactics, and changed her strategy. She looked instead for obstacles to remove. Was there anything preventing the baby from sleeping through the night?

The first night she made it darker. No effect. The second night she made it warmer. Her son has slept through the night ever since. It wasn’t her parenting skills or the adherence to a particular sleep philosophy that was causing him to wake up so often. Her baby was cold. Once she removed that obstacle with a space heater the problem was resolved.

We do this all the time, trying to fix problem by throwing new parenting philosophies at the situation. What can I do better? More time, more money, more lessons, more stuff. But it can be equally valuable to look for what you could be doing less of. In so doing, you may enrich your relationships with your children immeasurably.

Parenting is inherently complex: the territory changes almost overnight. Different environments, different children—figuring out how to raise your kids plays out against a backdrop of some fast-paced evolution. Some tactics are great, and once in a while a technique fits the situation perfectly. But when your tactics fail, or your experience seems to provide no obvious direction, a principle-based mental models approach to parenting can give you the insight to find solutions as you go.

[1] Lewin’s original work on force field analysis can be found in Lewin, Kurt. Field Theory in Social Science. New York: Harper and Row, 1951.