Amplifying AgencyTechnology as an opportunity

Three children watch baseball from crates. In the second panel the tallest stands on the ground and the shortest has two crates.

Today

  • Why should everyone know the basics of how a computer works?
  • Can I compute anything computable with just 2 instructions?
  • How does the AI know?
  • Demonstration: BeagleBadge + BeagleConnect Zepto “Interactor”
  • How can we work together to amplify the agency of your students?
2–3 min2 / 43

Technology can be as simple as a stick

A bonobo holds a stick with ants beside an ant mound, in a colored-pencil illustration.
  • Using tools to amplify agency
  • Found everywhere
3–5 min3 / 43

Managing complexity

Woodland cabin, waterwheel and hand-operated wooden mechanism assembled from visible materials.
  • Doing good feels good
  • Agency requires predictable medium
  • Medium amplifies specific outcomes
  • Complexity drifts towards failure
  • Plentiful medium supports addressing risk

Meet Chloe

Chloe running with a soccer ball, looking across the field.
  • Entirely fictional character
  • Loves drawing
  • Learns tough lessons about her medium
  • Inspired by Pearl Jam 1992 concert t-shirt stating on one side
    “9 out of 10 kids prefer crayons to guns”
  • On the other side, something like this …
8–9 min5 / 43

Choices

Chloe drawing a colorful house with crayons, with a revolver lying untouched beside her.
9–10 min6 / 43

Chloe fell in love with drawing

Three scenes: Chloe at a crayon factory, watching a teacher pour purple wax, and looking at The Starry Night.

She was able to understand the source of her tools

She was even able to envision how to change those tools herself

And when seeing the masters in the craft, she was inspired, seeing only herself in her own way

10–11 min7 / 43

Chloe was able to express herself

Young Chloe discovers a purple evening sky by rubbing the side of her broken crayon over a house drawing.
  • She adapted to her tools and adapted her tools to her
  • When one crayon broke, she grabbed the next and it behaved mostly like she expected
11–12 min8 / 43

Chloe mastered

An older Chloe practices a glowing window in colored pencil beside a computer showing an early animation.

She still has the two purple crayons.

12–13 min9 / 43

The house answers, softly.

Adult Chloe sits beside a visitor moved by her immersive purple house, with luminous windows and rain.

Impossible rooms, rain becoming music, a visitor who asks to stay.

13–17 min · story continuation10 / 43

The windows stopped glowing

Adult Chloe at her desk in the evening looks up thoughtfully at her colored-pencil drawings of glowing houses pinned to the wall, while her laptop shows a grid of grey, empty animation thumbnails.

A folder of her first animations that no longer play. On the wall, the paper drawings from the same year, still glowing.

13–17 min · story continuation11 / 43

“You have exhausted your 100 credits”

Bridget stares in dismay at a school laptop showing her colorful flying alebrije with a sloth face, giraffe legs and antlers, half covered by a grey pop-up box, with marigolds beside her.

A sloth-faced alebrije with giraffe legs and enormous antlers, one burst of marigolds from finished.

13–17 min · story continuation12 / 43

What can the child carry away?

Bridget slides her purple-sky house drawing beneath a placemat as Chloe gently leans toward her.

Bridget slides her drawing under a placemat. “Mine doesn’t do anything.” Chloe pulls up a chair, and they ask it together.

13–17 min · story continuation13 / 43

A crayon for computing

A child’s hand draws with a purple crayon: on the left of the paper a house under a purple sky, on the right the marks turn into rows of tally marks and empty boxes.
  • Chloe understood her crayon: she could even make one
  • A crayon is a tiny tool that can draw any picture
  • Is there a tool that simple that can compute anything?
  • Three people found one
17–18 min14 / 43

Hilbert, Turing, Minsky

An imagined 1930s study: a paper tape of squares marked 0 and 1 runs under a brass read-and-write head, beside a rule table pinned to the wall and a window onto college rooftops.
  • 1928, David Hilbert: what can following fixed rules ever work out?
  • 1936, Alan Turing: a person with pencil and paper, following rules, can work out anything that can be worked out
  • … but some questions no rules can ever settle
  • 1961, Marvin Minsky: two rules are enough. Add one. Take one.
18–20 min15 / 43

What is a computation?

A child’s hand moves a purple crayon from one paper cup into another full of crayons on a classroom table, with five crayons lined up in front.
  • Marks go in
  • Rules are followed exactly
  • Marks come out
  • You already teach this: counting crayons into cups

3 crayons in one cup, 5 in another. Rule: move the crayons one at a time from the second cup to the first. Count: 8.

20–22 min16 / 43

Turing completeness

  • Read and write memory
  • Choose the next step by what you read
  • Repeat

With enough memory and time, a system that can do these can compute anything a Turing machine can.

22–23 min17 / 43

Exercise 1 · Understanding the mechanism

  • A machine with only two rules
  • Two programs: add and multiply
  • How small steps climb to any program
  • Why that makes it Turing complete

Read the logic. Predict its behavior. Change what it does.

23–24 min18 / 43

The counter machine

Four teachers around a table with four paper cups of crayons and a row of step cards; one points at a card, one moves a crayon between cups, one writes on a sheet.
  • Memory: four cups of crayons, numbered 1 to 4
  • Program: ADD and TAKE cards, each with its own Step number
  • Write the numbers on the cards
  • Keep a finger on the current card
24–25 min19 / 43

Two kinds of step

Step1ADDPut 1 crayon in the cupCup1Next step2
Step2TAKETake 1 crayon from the cupCup2Got one → step3Empty → stepSTOP
  1. Keep a finger on the current card and do what it says.
  2. Move your finger to the card with the Step number it names.
  3. Repeat until STOP.
25–26 min20 / 43

Program 1 · Add

Put 3 crayons in cup 1 and 5 in cup 2. Start at step 1. When it stops, count cup 1.

Step1TAKETake 1 crayon from the cupCup2Got one → step2Empty → stepSTOP
Step2ADDPut 1 crayon in the cupCup1Next step1
26–29 min21 / 43

Program 2 · Multiply

Put 3 crayons in cup 1 and 4 in cup 2. Start at step 1. When it stops, count cup 3.

Step1TAKETake 1 crayon from the cupCup1Got one → step2Empty → stepSTOP
Step2TAKETake 1 crayon from the cupCup2Got one → step3Empty → step5
Step3ADDPut 1 crayon in the cupCup3Next step4
Step4ADDPut 1 crayon in the cupCup4Next step2
Step5TAKETake 1 crayon from the cupCup4Got one → step6Empty → step1
Step6ADDPut 1 crayon in the cupCup2Next step5
29–34 min22 / 43

Bigger steps from small ones

Program 1’s two cards…
TAKE cup 2
got one → 2 · empty → STOP
ADD cup 1
→ 1
=
…are one new step:
MOVE
cup 2 into cup 1
→
Multiply is just:
repeat for every crayon in cup 1:
COPY cup 2 into cup 3
34–36 min23 / 43

Climbing to any program

  1. ADD · TAKE the whole machine
  2. CLEAR · MOVE · COPY a few cards each
  3. add · subtract · compare
  4. multiply · divide · remainder
  5. numbered memory cells packed into one big number
  6. a CPU’s instructions LOAD · STORE · ADD · JUMP · CALL
  7. any program a spreadsheet, a web browser, an AI model
36–38 min24 / 43

Why the counter machine is Turing complete

  • One machine; only the step cards changed
  • Any program can be climbed to from ADD and TAKE
  • Marvin Minsky, 1961: it can do anything a Turing machine can
  • The real limits are crayons and time
38–40 min25 / 43

Take it to your classroom

  • Euclid’s algorithm: the greatest common divisor (GCD)
  • Square roots, without multiplying
  • A program that never stops
  • Blank cards: write your own

Printable cards and setup pages: machine-cards.html. Homework, from two instructions to a processor: homework.html

40–41 min26 / 43

Exercise 1 · What we saw

  • Two rules, add one and take one, made a working computer
  • A program is just numbers written on cards
  • Small steps build bigger ones, all the way to any program
  • That is Turing completeness: as simple as a crayon
41–42 min27 / 43

Exercise 2 · A machine that seemed to think

Colored-pencil illustration of the chess automaton, with a concealed operator visible inside its cabinet.
  • 1770: Kempelen’s chess “automaton”
  • Shown across Europe and America
  • A hidden chess master worked it
  • Destroyed by fire, 1854
42–44 min28 / 43

The Turk returns

Colored-pencil illustration of six people in homes around the world, each labelling photos on a laptop, with dotted lines running from them to a softly glowing, featureless machine in the centre.
  • 2005: Amazon opens “Mechanical Turk”
  • People are paid per task to label, rate and write
  • Their answers become training data
  • The people are hidden again, inside the data
44–46 min29 / 43

What to watch for

  • Your table plays the people: everyone suggests the next word
  • The hat plays the model: it picks one suggestion by chance
  • One word at a time, the story grows
  • Watch: which words were likely? Why do two runs differ?
46–47 min30 / 43

A word from the hat

Five teachers around a table; one reaches into an upturned hat full of folded slips while the others watch, with pencils and a response sheet nearby.
  • Tables of 4 to 6 people
  • A hat or cup, small paper slips and pencils
  • One response sheet per table
  • Choose one reader

Your table will write one sentence together, one word at a time.

47–48 min31 / 43

The prompt

Tell a short story about a surprising discovery at school.

“At recess, we found a…”

Reader: write this at the top of the response sheet.

48–49 min32 / 43

Each turn

  1. Reader reads the prompt and every word added so far.
  2. Everyone writes one next word, or STOP, on a slip.
  3. Fold the slips, put them in the hat and mix.
  4. Reader draws one slip without looking.
  5. Add that word to the sheet. STOP ends the sentence.
  6. Empty the hat. Start the next turn.

Finish at STOP, or after 8 words.

49–53 min33 / 43

Run it again

  • New line, same prompt: “At recess, we found a…”
  • Same rules, fresh slips every turn
  • Don’t plan ahead or try to change the result
  • Compare your two sentences
53–55 min34 / 43

Same prompt. Same process.

  • Which words appeared on more than one slip?
  • Did one drawn word change what you wrote next?
  • Why are your two sentences different?

The slips in the hat were a probability distribution.

55–57 min35 / 43

Where do the probabilities come from?

Training changes parameters.
Generation uses them.

57–59 min36 / 43

Who can build the tool?

Data. Computation.
People. Infrastructure.

Using a model ≠ training its foundation

59–62 min37 / 43

Exercise 2 · What we saw

  • People supplied every possible next word
  • Chance picked one, weighted by how many suggested it
  • A model learns those chances from millions of people’s words
  • The people are still there, hidden in the data
62–63 min38 / 43

Demonstration · “Interactor”

BeagleBadge on a lanyard: an ePaper screen showing a menu, with a joystick, two seven-segment digits and two buttons below it.

BeagleBadge

The game board: a $99 Linux computer you wear

  • Runs the game and draws it on its ePaper screen
  • Sockets for plugging in other boards
A computer rendering of BeagleConnect Zepto: a one-inch black board with a chip, two buttons and two small white connectors.

BeagleConnect Zepto

The player: a computer for about $1

  • Each student programs one
  • Plugged in, its code plays on its own

Code is the controller: once the game starts, nobody touches it.

63–67 min39 / 43

Today, in one slide

  • Chloe’s crayon drawings outlasted her animations; Bridget’s alebrije ran out of credits
  • Two rules and some crayons can compute anything
  • A language model’s words come from people, chosen by chance
  • BadgeSnake: students’ code plays the game, with nothing hidden
  • Ask of every activity: what can students understand and change?
67–68 min40 / 43

Two feet in a supercar

  • We sit children in a million-dollar sports car
  • They drive it two feet, and we call it a success
  • Using a technology is not understanding it

For review: does this analogy belong in the deck, and if so, here or elsewhere?

68–69 min41 / 43

Amplifying agency after the activity

What can your students
understand and change?

69–73 min42 / 43

Questions

What would you like to understand, or change?

73–88 min43 / 43