What Can We Know?

101: Definitions and Their Properties

Introduction

It sounds like we're starting with vocabulary, but it turns out if you want to critically think about something, you need to know what things mean. If two people are discussing a topic and they are both using the same word, but one is using a different meaning of the word, then communication is failing. Agreeing on what things mean is required for a really good conversation that matters.

Lesson

A property is a quality, characteristic, or trait that you can use to describe something by observation or measurement.

A square always has for equal sides and four internal angles of 90 degrees each. The properties of a square are well known and consistent. Most people who talk about squares are not going to have an issue with them in a discussion. Some definitions are easy to work with and are very concrete.

People are much more complicated. Would I be right if I said a human being has two arms, two legs, two eyes, and two ears? Would that be four properties of a human being? Unfortunately no. If a person loses their legs in a horrible accident, or doesn't have complete legs due to birth circumstances, are they still a person without them? If those aren't the properties of a human, what is it about us that makes us human then? Some definitions aren't so easy to work with and are often abstract.

Activity

In a Google Doc, students will individually create the best and most accurate definition of a few words that they can. If the words have a property, they should be separate in a bulleted list with "all" statements.

Example: Square

  • Always has four sides

  • All four sides are equal length

  • Always has four corners of exactly 90 degrees

Define the words sandwich, soup, and salad.

Be prepared to share with the class if you are called on randomly.

Follow-Up

I will be listing off a few items and ask if they possess all of the properties required to be defined as that word. We will then discuss if we are comfortable with our definition. It is highly likely that we will have different definitions from each other.

Then we will probably argue a bunch and we will experience together why agreeing upon key definitions are critical for a good discussion.

102: Criteria and Conditional Statements

Introduction

First a few definitions

  • Criterion - A standard, rule, or test on which a judgment or decision can be based.

  • Criteria - The plural of criterion. Two or more tests to make a judgment (Irregular pluralization. Thanks Greece!)

Lesson

We completed an exercise that had us identifying the properties of a definition and turning those into tests. The tests are criteria. Rules we follow and check to see if a think has all of the qualities it needs to be called by that word.

When we are checking each criterion to see if it matches, we write this up using conditional statements.

    • If there is one criterion: IF this, THEN this is true.

    • If there are multiple criteria: IF this, AND IF this, AND IF this, THEN this is true.

    • (Don't actually use the all capital letters in your writing. I just needed you to notice those words)

    • When we write using conditional statements we will use: if, and if, if and only if, then, and therefore whenever we need to.

Activity

Today we will be turning the results of our sandwich analysis into paragraphs. One paragraph will define sandwich by its criteria. The second paragraph will evaluate a thing to see if it meets all of the criteria necessary to call it a sandwich.

103: Definitions and Subjectivity

Introduction

Definitions

  • Objective - adj. - Based on observable phenomena; empirical.

  • Objective things are true no matter what people think about them.

  • Subjective - adj. - Based on a given person's experience, understanding, and feelings; personal or individual.

  • Subjective things change based on what people think about them. The opinions of the individual and the collective opinions of the group can shift the meaning of a word. Words like "good" and "beautiful" and "enough" are harder to be precise about because of their subjective nature.

Activity

This will be a repeated process of what we did with sandwiches. We will be starting at the beginning again with a new word. This word is harder to process than sandwich. There will likely be more disagreements but we will be polite and provide reasons. All of the same resources will be provided as we explore the meaning of the new word.

  • The same Google Sheet Template with definition, tests/criteria, and a table for our results.

  • A new but similar presentation by the teacher testing your definition against things and examples in the world.

  • A follow up Google Doc that will allow you to process your final definitions and properties into paragraphs.

  • A sharing round to see what other people's conclusions are for comparison and praise.

104: Definitions, Conditional Language, Lots of Examples

Active Definitions

  • Criterion - A standard, rule, or test on which a judgment or decision can be based.

  • Criteria - The plural of criterion. Two or more tests to make a judgment (Irregular pluralization. Thanks Greece!)

Still Active

    • If there is one criterion: IF this, THEN this is true.

    • If there are multiple criteria: IF this, AND IF this, AND IF this, THEN this is true.

    • (Don't actually use the all capital letters in your writing. I just needed you to notice those words)

    • When we write using conditional statements we will use: if, and if, if and only if, then, and therefore whenever we need to.

Lesson

Sport is a little more subjective and harder to define. Everyone's definition is a bit different. When we compare these later, you will notice that there is more variability, more difference between each student. It is okay to disagree, but the key to winning an argument is to be able to break down what you really want to say into smaller and easier to explain parts. Activity Choose Your Adventure! Today you will have a choice.

  1. For the usual 10 points, demonstrate mastery of our last cycle.

  2. For an unusual 15 points, go beyond last time and include the layers. Details in the guidance document. Good luck!

105: Definition Imprecision (But Close Enough!)

Introduction

Revisiting our last conversation, things have properties and we disagree on even the meaning of the simplest things. The good part is we get pretty close most times and we tend to understand each other even when we're not all playing with the same dictionary. There are many examples of this disconnection in the world and we seem to get by okay.

  • Peanuts are not nuts, they are legumes.

  • Strawberries and Raspberries are not berries, berries have seeds on the inside.

  • An electric eel is not an eel, it is a knifefish.

  • The maned wolf is not a wolf. The maned wolf looks like a fox but is not a fox. It is a dog.

  • The horny toad is not a toad, it is a lizard.

  • The Caspian Sea is not a sea, it is a lake.

  • Vitamin D isn't a vitamin, it is a hormone.

Lesson

It turns out that we don't know the exact meaning of many words, and that's okay. We only have to get close. Today I would like to test that hypothesis. How far off do two people's meanings have to be before there is a problem?

Today I will ask you to rate some words and phrases and come up with a percent for each one. Always means 100% of the time. Never means 0% of the time. But what about some of the ones in between. I would like to see how close we are to one another. We will share later, so students will need to come up with their own answers before seeing anyone else's.

Task

I will give you statements one at a time. Evaluate it either on its own, or compared to the others as we go. At the end, fit it into your expanding chart of probability in order moving new phrases around as needed.

106 Dichotomies Usually Aren’t

We tend to over-simplify a great many things that are more complex that we care to admit. We like to put people and things into fences and categories so that we can pretend to understand. This has a side effect of creating otherness.

Take a group of three friends that have been a social group for some time. Let's say one of them ends up not liking one of the others. What about person number three? Do they hang out with friend one? Do they hang out with friend two?

Often the problem stops there. You are with us or you are against us. In or out. On or off. It is a light switch question. We call those a dichotomy (di = two).

Lesson

It turns out dichotomies are rare. The world is not black and white but shades of gray. Most situations are gradable. In other words, they have grades, levels, and degrees. Instead of black and white I want you to think about gradient.

Notice there is a gradual and increasingly different shift as you move from one side to the other in a gradient.

In language, we have a range of words to pick from to help express the exact gradient we want for the meaning we intend.

Harm maim annihilate obliterate damage shatter ruin cripple destroy crush bruise smash pulverize fracture decimate

107: Sometimes It's Not As Easy As Black, White, and Gray

Taking another step forward, not every situation is made up of shades of gray. Sometimes it can be more complex with more levels within levels and problems within problems. Even in really messy and complex scenarios with many variables, we will still try to label things with simple language and pretend that we understand everything and also pretend that we are in control.

Activity

Today all students will begin some notes and place in order from the best life possible to the worst life possible. Use the following words and phrases:

blooming, coping, depressed, doing well, hopeless, just ok, prospering, struggling, suffering, thriving

Then we will explain our process in a process paragraph. The new twist is that I can ask you to explain every single little decisions along the way and ask for your justification on why each word is in its own place. Be prepared to explain every choice this time.

108: Change is Inevitable Therefore Being Correct Is Often Temporary

Baby Steps - When knowledge is given in levels to help understanding

  • Baby Steps: Math Teachers will teach you 3.14 before showing more digits. The kinds of problems that require more digits of pi require much more foundational knowledge.

  • Baby Steps: English teachers will tell you that a noun is a "person, place or thing" before later teachers add in "Idea/Concept" because abstraction is harder to comprehend.

  • Baby Steps: We will teach you about the quadratic equation before proving the equation. So many things in life are like this. We can know how to use it, and we can know that it works without knowing why it works. We can put gas in the car, fire the ignition, and use the engine without knowing how a combustion engine works.

New Discovery - When knowledge is advanced in your lifetime

  • We used to be taught about elements and atoms and ionic bonding. Later we added in electron clouds. Now we have to teach you about quarks and bosons and other subatomic particles too.

  • Solid, Liquid, Gas, Plasma, Bose-Einstein Condensate (BEC)

  • Biology was about chromosomes, dominant genes and recessive genes. Now we have to teach you about genetics and genetic code.

When the World Changes - Human things change all the time

Activity

Today students will be responsible for bringing something to the party for everyone to enjoy. Each student will think about the changes they have experienced in their own life on all the levels of understanding that have transformed since they were born. What is wrong now that used to be right? What is true now that used to be nothing? Combine your experience with a little bit of research and during the sharing round we will see how much the world has grown up in half a generation.

109: Get Better At Search

Most of us use search engines like complete zombies with complete trust. We shouldn't do this. We type the buttons and click the first result and trust it. We are treating information like a food pellet in a cage. This is not research.

Search has strange filters these days. Results are customized based on your past results in preferences. It is more likely to recommend you media that you agree with rather than media that disagrees you. It is more likely to recommend you media that agrees with your politics rather than media that challenges your world view. By the time you've done a hundred searches and watched a hundred videos, you are in a spiral of the same flavor of ice cream every day for the rest of your life.

Search is also regionally assessed. The search you get in your zip code is based on the average interests of everyone in your community. A search in California has different results than in Florida, and different results compared to China. If you want to see this you will have to travel, or use a VPN that routes your web traffic through other countries. This creates opportunities for censorship. This creates opportunities for groupthink. Without a personal filter and an ongoing diligence to verify everything you see, this is very dangerous.

Here is a package of tools to use search better. Today you will walk through my testing and examples, try them for yourself, and then fully process them with your own experiments and examples.

110: Can We Have Knowledge?

We can know completely how many things there are when we count them. We know how to make a vehicle fly reliably. We know how wheels work. We can control electricity.

In things with no variation and fixed structures, like the structures of crystals, we can know exactly how many atoms make it.

For many other things we can get close. Refine our methods, refine our tools, refine our questions, and then get closer. It is hard to conclude that we know it all and have complete knowledge about things like this. What we do know is that progress is being made, and you can come to a point where you can learn more, but you can trust it.

For instance: We can calculate the ratio between the circumference of a circle and its diameter and we call it pi. You get told young that pi is 3.14 but we know that is rounded and simplified. We know that using 3.14 in your calculators get you pretty decent accuracy. Accuracy enough that you can get out a ruler and using paper and scissors cut out the right amount of string. The amount of error from using 3.14 is hard to notice and irrelevant to the kid with a ruler and scissors.

More accuracy is better in some cases, especially in very big things as you would find in astrophysics. NASA and the Jet Propulsion Lab (JPL) deals with this all the time. How many digits of pi do you think they use in their calculations? It turns out they use the 3, and they use 15 digits after the decimal. NASA calculates using 3.141592653589793. It turns out you don't need more digits of pi. At this time there isn't anything that NASA needs to calculate that requires more precision than that.

In the JPL's explanation on why they use exactly this many digits, they say that to calculate a the circumference of a circle 12.5 billion miles in diameter, the error by not using more digits of pi is 1.5 inches.

NASA also calculated what would be the most digits of pi anyone would ever use for any situation. To calculate the circumference of a circle that is the size of the universe with an error allowance equal to the diameter of a hydrogen atom, you will only need 40 decimal places of pi.

Memorizing more digits of pi will impress the math teachers, but you will likely never use that information.