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Answer key · Unit 14

How animals live.

Each lesson’s practice questions, their correct answers and the mistakes they spot. Answers read off the Scene use the same setting the learner sees.

Lesson 1 of 5 · About 25 minutes

Broods and care

Four mothers and two bets: a million cheap eggs left to chance, or a few young looked after. External and internal fertilisation, one budget shared out, and why about one or two from each brood grow up.

Open the lesson

The 6 steps and their answers
  1. Step 1 of 6

    Open this step

    Inside or out

    Practice · Choose

    Question

    Which of the Scene’s four mothers have their eggs fertilised outside the body? Choose all of them.

    Correct answer

    • Correct The cod

    • Correct The frog

    Setup, choices and feedback

    The Scene at this step

    Brood size
    1 ×
    Parental care
    As in nature
    Time
    Laid or born

    Choices

    Shown in a random order. More than one choice is correct: every one must be selected.

    • Correct The cod

    • Correct The frog

    • Wrong The blackbird, since she lays eggs

      Misconception: Thinks any animal that lays eggs has them fertilised outside its body.

      Feedback from the catalogue

      Laying eggs and external fertilisation are two different things. Birds, reptiles and insects lay eggs, but their fertilisation is internal: the male passes sperm into the female’s body, and the egg gets its yolk and shell only after it is fertilised. External fertilisation happens only in water, as in most fish and frogs.

    • Wrong The hind

      Feedback

      Mammals fertilise inside, and the calf grows within the mother.

    Feedback for a right answer

    The cod and the frog. Both breed in water: the female releases eggs and the male releases sperm beside them, and the sperm swim the short way. It takes water, so the eggs do not dry out, and many eggs, because many are lost. The blackbird lays eggs, but they were fertilised inside her body before they got their yolk and shell.

    Worked solution

    1. External fertilisation: eggs and sperm meet in water, outside the body.
    2. The cod and the frog breed in water and release both: external.
    3. Blackbird: the male passes sperm into the female; the egg is laid after fertilisation: internal.
    4. Hind: a mammal, internal fertilisation, and the calf grows inside the mother.
  2. Step 2 of 6

    Open this step

    Almost all die

    Practice · Predict, then look

    Question

    The cod lays a million eggs, and the hind has one calf. Predict how many young cod from this brood are alive when Time reaches Three years on.

    Correct answer

    • Correct One or two

    Setup, choices and feedback

    The Scene at this step

    Brood size
    1 ×fixed
    Parental care
    As in naturefixed
    Time
    Laid or born

    Choices

    • Wrong About a hundred thousand: a million eggs leave plenty

      Misconception: Thinks an animal that produces more eggs or young leaves more grown offspring.

      Feedback from the catalogue

      The number of young at the start hardly decides how many grow up. A million cod eggs and a single calf both end at about one or two. Enlarge a brood from the same budget and each young gets less: weaker larvae, hungrier chicks. And in a population that lasts, each pair leaves on average about two that grow up, or it would grow or vanish.

    • Wrong About a thousand

      Feedback

      Even a thousand adults from one brood would flood the sea with cod within a few generations.

    • Correct One or two

    Once the prediction is locked in, the Scene changes

    Time
    Three years on

    The Scene then shows: 1 · Young cod alive at the time shown/nodes/broods/outputs/cod

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    One. Almost all of the million eggs and larvae are eaten, starve or drift away, mostly in the first weeks. And in the end, about as many as from the hind’s single calf: one or two from each brood. That is how a population lasts: each pair leaves on average about two that grow up and breed.

    Worked solution

    1. Adults must replace their parents: one pair, about two grown young over a whole life.
    2. A cod spawns many times in her life, so each brood needs to give fewer than two.
    3. If hundreds or thousands grew up from one brood, the population would explode.
    4. In the Scene: a million eggs, one grown cod.
  3. Step 3 of 6

    Open this step

    The first weeks

    Practice · Calculate

    Question

    About 4545⁠ days after laying. Read how many young cod are still alive out of the million eggs. What percentage of the eggs is that?

    Correct answer

    0.2924 ± 3%

    Setup, choices and feedback

    The Scene at this step

    Brood size
    1 ×fixed
    Parental care
    As in naturefixed
    Time
    0.3 (Laid or born → Three years on)fixed
    Accepted within
    ± 3%
    Computed from the Scene at this step’s setting
    Young cod alive at the time shown/nodes/broods/outputs/cod

    Feedback for a right answer

    About 0.3%: about 29002900⁠ of a million, so more than 99.7% were lost within six weeks. The blackbird, which warms and feeds hers, still has two of four at that time, 50%. Losses are sharpest at the start, when the young are smallest and nobody guards them.

    Hint

    One percent of a million is 10 00010\,000⁠.

    Worked solution

    1. In the cod’s case: about 29242924⁠ alive.
    2. 29241 000 000×100≈0.29\dfrac{2924}{1\,000\,000} \times 100 \approx 0.29⁠.
    3. About 0.3%.

    If you answered about 99.799.7⁠, you gave the share lost, not the share left.

  4. Step 4 of 6

    Open this step

    One budget

    Practice · Predict, then look

    Question

    The blackbird raises one grown young from four eggs. Predict how many grow up when Brood size rises to 2×, eight eggs from the same budget.

    Correct answer

    • Correct None

    Setup, choices and feedback

    The Scene at this step

    Brood size
    1 ×
    Parental care
    As in naturefixed
    Time
    Three years onfixed

    Choices

    • Wrong Two: twice the eggs, twice the young

      Misconception: Thinks an animal that produces more eggs or young leaves more grown offspring.

      Feedback from the catalogue

      The number of young at the start hardly decides how many grow up. A million cod eggs and a single calf both end at about one or two. Enlarge a brood from the same budget and each young gets less: weaker larvae, hungrier chicks. And in a population that lasts, each pair leaves on average about two that grow up, or it would grow or vanish.

    • Wrong Still one

      Feedback

      That is what happens to the cod and the frog. But eight chicks share what feeds four.

    • Correct None

    Once the prediction is locked in, the Scene changes

    Brood size
    2 ×

    The Scene then shows: 0 · Young blackbirds alive at the time shown/nodes/broods/outputs/blackbird

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    None. The two parents bring the same number of caterpillars to the nest, and eight chicks each get half. All are too weak to survive. That is why many birds lay about as many eggs as they can feed, and fewer in lean years. The cod and the frog, by contrast, start with twice as many and end almost as before.

    Worked solution

    1. The parents’ food budget is fixed.
    2. Twice the chicks: each gets half.
    3. Blackbird chicks on half rations do not grow up.
    4. More eggs, fewer adults: an oversized clutch loses.
  5. Step 5 of 6

    Open this step

    Care makes few possible

    Practice · Predict, then look

    Question

    Predict what happens to the four broods when Parental care switches to None.

    Correct answer

    • Correct The blackbird and the hind lose everything; the cod and the frog are unaffected

    Setup, choices and feedback

    The Scene at this step

    Brood size
    1 ×fixed
    Parental care
    As in nature
    Time
    Three years onfixed

    Choices

    • Correct The blackbird and the hind lose everything; the cod and the frog are unaffected

    • Wrong All four lose about equally

      Feedback

      The cod and the frog never cared for their eggs, so they have nothing to lose.

    • Wrong The cod and the frog are hit hardest, since they have the most young

      Feedback

      The reverse: whoever depends on care is hit, and whoever does not, is not.

    Once the prediction is locked in, the Scene changes

    Parental care
    None

    The Scene then shows: 0 · Calves alive at the time shown/nodes/broods/outputs/deer

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    The blackbird’s eggs chill and never hatch, and the calf has no milk: none survive. The cod and the frog end as before, since they never cared. A few young are possible only with care; care buys them the chance that a million eggs buy with numbers.

    Worked solution

    1. Cod and frog: no care in nature either, so nothing changes.
    2. Blackbird: eggs need warming, and chicks need feeding.
    3. Hind: a calf needs milk.
    4. Without care, the last two lose everything.
  6. Step 6 of 6

    Open this step

    Two strategies

    Practice · Choose

    Question

    Why do whales and elephants need decades to recover from hunting, while a cod population can bounce back in a few good years?

    Correct answer

    • Correct They are K-strategists: one young every few years, so the population can only grow slowly

    Setup, choices and feedback

    The Scene at this step

    Brood size
    1 ×
    Parental care
    As in nature
    Time
    Three years on

    Choices

    Shown in a random order.

    • Correct They are K-strategists: one young every few years, so the population can only grow slowly

    • Wrong They need more food, and find it hard to get

      Feedback

      Even with plenty of food, a mother with one young every few years cannot grow the population fast.

    • Wrong They have more predators

      Feedback

      The reverse: the adults have almost no predators. The limit is the breeding rate.

    Feedback for a right answer

    The breeding rate. A cod lays millions of eggs, and in most years nearly all die; but in a good year far more survive, and the population leaps. An elephant gives birth about once in four years, and even in perfect conditions the population grows by a few percent a year. That is why large, slow-breeding animals are especially vulnerable to hunting.

    Worked solution

    1. A population recovers when more young are born than individuals die.
    2. An r-strategist: huge numbers of young; one good year brings back many.
    3. A K-strategist: few young, far apart; even with no losses, growth is slow.
    4. So whales and elephants need decades.

Lesson 2 of 5 · About 25 minutes

A new body

One animal, two bodies: a caterpillar that grows in jumps inside a skin that will not stretch, a chrysalis in which most of the body is broken down and rebuilt, a tadpole whose tail is absorbed into the froglet, and the hormones that decide when.

Open the lesson

The 6 steps and their answers
  1. Step 1 of 6

    Open this step

    One animal, two bodies

    Practice · Predict, then look

    Question

    The caterpillar hatched 2 mm long. Predict how many millimetres long it is about two weeks later, when it stops eating and hangs in a J.

    Correct answer

    45.23 mm ± 8 mm

    A number prediction counts as right within ± 8 mm

    Setup, choices and feedback

    The Scene at this step

    Animal
    Monarch butterflyfixed
    Hormones
    Normalfixed
    Cut open
    offfixed
    Time
    0.15 (Egg → Weeks later)

    Once the prediction is locked in, the Scene changes

    Time
    0.6 (Egg → Weeks later)

    The Scene then shows: 45.23 mm · Length of the body (a tadpole with its tail, a froglet snout to vent)/nodes/life/outputs/length

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    About 45 mm, more than twenty times as long, and about two thousand times as heavy, in two weeks. All the caterpillar does is eat: its leaf disappears. The adult will never grow again; all an insect’s growing is done as a larva.

    Worked solution

    1. The caterpillar hatches on day four, 2 mm long.
    2. Five instars, and each moult lets it grow again.
    3. By about day 1919⁠ it is about 45 mm long, and hangs up.
  2. Step 2 of 6

    Open this step

    Growing inside a skin

    Practice · Choose

    Question

    The caterpillar stops eating and sheds its skin, five times in two weeks. Why does it need to?

    Correct answer

    • Correct The skin, and above all the head, are stiff and cannot grow; to grow it needs a new skin

    Setup, choices and feedback

    The Scene at this step

    Animal
    Monarch butterflyfixed
    Hormones
    Normalfixed
    Cut open
    off
    Time
    0.45 (Egg → Weeks later)

    Choices

    Shown in a random order.

    • Correct The skin, and above all the head, are stiff and cannot grow; to grow it needs a new skin

    • Wrong The skin stretches with the body, and is shed only when it wears out

      Feedback

      The soft body does stretch the skin a little, but the hard head cannot grow at all: it jumps in size only at a moult.

    • Wrong To get rid of the milkweed’s poison

      Feedback

      The reverse: the caterpillar keeps the poison in its body, and it protects it from birds.

    • Wrong To change colour before it becomes a butterfly

      Feedback

      The stripes stay almost the same from instar to instar. The moult is for size.

    Feedback for a right answer

    The cuticle is stiff. The soft body can stretch it a little, but the hard head cannot grow at all, so it jumps in size at each moult, about one and a half times as wide. The caterpillar grows a new, loose skin under the old, splits it and climbs out, then goes back to eating.

    Worked solution

    1. An insect has no inside skeleton; its stiff skin is its skeleton.
    2. An outside skeleton cannot grow.
    3. So the caterpillar swaps it for a bigger one: a moult, and a new instar.
  3. Step 3 of 6

    Open this step

    Inside the chrysalis

    Practice · Predict, then look

    Question

    From outside, nothing happens in the chrysalis for nine days. Predict what you will see when you switch on Cut open in the middle of the chrysalis stage.

    Correct answer

    • Correct Most of the caterpillar’s body is broken down, and the adult is built from small pockets of cells

    Setup, choices and feedback

    The Scene at this step

    Animal
    Monarch butterflyfixed
    Hormones
    Normalfixed
    Cut open
    off
    Time
    0.75 (Egg → Weeks later)fixed

    Choices

    • Correct Most of the caterpillar’s body is broken down, and the adult is built from small pockets of cells

    • Wrong A sleeping caterpillar, with wings growing on its sides

      Misconception: Thinks a chrysalis is a resting caterpillar that simply grows wings onto its old body.

      Feedback from the catalogue

      The chrysalis is still from outside, but inside the body is being rebuilt. Digestive enzymes break down most of the caterpillar, its crawling muscles, much of its gut and its silk glands, and the adult is built from the imaginal discs the caterpillar has carried since it was an embryo, feeding on the broken-down tissue. Only the nervous system, the heart and the breathing tubes are rebuilt without being destroyed.

    • Wrong A finished butterfly, waiting to come out

      Feedback

      The butterfly is finished only on the last day, when the case turns clear.

    Once the prediction is locked in, the Scene changes

    Cut open
    on

    The Scene then shows: 42 · What the cut shows, one code per Callout (INSIDE in the model), 0 when not cut open/nodes/life/outputs/inside

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    The case is full of broken-down tissue. Digestive enzymes break down the crawling muscles, much of the gut and the silk glands, and the imaginal discs, carried since the embryo, unfold into wings, eyes, antennae and legs by ordinary cell division, feeding on the broken-down tissue. It is not a complete soup: the nervous system and the heart are rebuilt without being destroyed.

    Worked solution

    1. The caterpillar already holds small blue discs: future wings, legs and eyes.
    2. In the chrysalis, enzymes break down most of the caterpillar’s organs.
    3. The discs grow on the broken-down material and unfold into the adult’s parts.
    4. On the last day the adult is complete, and the case turns clear.
  4. Step 4 of 6

    Open this step

    Who decides when

    Practice · Predict, then look

    Question

    Normally there is a butterfly after 3232⁠ days. Predict what there is on day 3232⁠ when Hormones switches to Kept young, with juvenile hormone kept high.

    Correct answer

    • Correct A giant caterpillar, after more moults into caterpillars

    Setup, choices and feedback

    The Scene at this step

    Animal
    Monarch butterflyfixed
    Hormones
    Normal
    Cut open
    off
    Time
    Weeks laterfixed

    Choices

    • Correct A giant caterpillar, after more moults into caterpillars

    • Wrong A butterfly that arrived sooner

      Feedback

      That happens when juvenile hormone is taken away, at Hurried: a tiny butterfly.

    • Wrong A giant butterfly

      Feedback

      While juvenile hormone is high, the next moult makes a caterpillar, not a chrysalis, so there is no butterfly at all.

    Once the prediction is locked in, the Scene changes

    Hormones
    Kept young

    The Scene then shows: 1 · 0 egg, 1 larva (caterpillar or tadpole), 2 changing (chrysalis, or legs and climax), 3 adult or froglet/nodes/life/outputs/stage

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    A giant caterpillar, about 7 cm long. The moult that should have made a chrysalis made another caterpillar, and another. Juvenile hormone does not cause the change; it holds it back. Wigglesworth showed this in the 1930s in bugs, and silkworms whose glands were removed turned into tiny moths.

    Worked solution

    1. Ecdysone starts each moult; juvenile hormone decides what it makes.
    2. Plenty of juvenile hormone: caterpillar. Little: chrysalis. None: adult.
    3. If it stays high, every moult makes another, bigger caterpillar.
  5. Step 5 of 6

    Open this step

    The tadpole’s way

    Practice · Predict, then look

    Question

    The tadpole has legs, and is about 42 mm long with its tail. Predict what happens to its length as Time moves on until it is a froglet.

    Correct answer

    • Correct It gets much shorter: the tail is absorbed into the body

    Setup, choices and feedback

    The Scene at this step

    Animal
    Common frogfixed
    Hormones
    Normalfixed
    Cut open
    off
    Time
    0.7 (Egg → Weeks later)

    Choices

    • Correct It gets much shorter: the tail is absorbed into the body

    • Wrong It gets shorter all at once, when the tail drops off

      Misconception: Thinks a tadpole's tail drops off when it becomes a frog.

      Feedback from the catalogue

      The tail does not drop off: it is absorbed. The tail’s cells kill themselves on cue, by apoptosis, and their material is recycled to feed the body through the two weeks the tadpole does not eat. That is why the froglet is far shorter than the tadpole was, about 1.6 cm instead of about 4 cm with the tail.

    • Wrong It keeps getting longer, as it keeps growing

      Feedback

      At the climax the tadpole does not eat at all, so it cannot grow.

    Once the prediction is locked in, the Scene changes

    Time
    0.9 (Egg → Weeks later)

    The Scene then shows: 16 mm · Length of the body (a tadpole with its tail, a froglet snout to vent)/nodes/life/outputs/length

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    From 42 mm to about 16 mm, gradually over about two weeks. The tail’s cells kill themselves on cue, by apoptosis, and their material is recycled. Meanwhile the gut shortens for an insect-hunter’s diet, the lungs grow and the gills disappear.

    Worked solution

    1. At the climax the tadpole stops eating.
    2. The tail shrinks day by day: its cells die by apoptosis, and the material is recycled.
    3. The body is left: a froglet about 1.6 cm long, far shorter than the tadpole.
  6. Step 6 of 6

    Open this step

    A giant tadpole

    Practice · Reach the target

    Question

    Time is locked at about 1414⁠ weeks, and a 1.6 cm froglet sits in the tank. An ordinary tadpole never reaches 5 cm. Change Hormones so that on the same day a tadpole at least 5 cm long swims in the tank, and press Check.

    Goal

    • 53.5 mm ± 3.5 mm

      At the start of the step: 16 mm

    Setup, choices and feedback

    The Scene at this step

    Animal
    Common frogfixed
    Hormones
    Normal
    Cut open
    off
    Time
    0.9 (Egg → Weeks later)fixed
    Read from the Scene at
    Length of the body (a tadpole with its tail, a froglet snout to vent)/nodes/life/outputs/length

    One setting that reaches it

    Hormones
    Kept young
    Cut open
    off

    Feedback for a right answer

    At Kept young thyroid hormone is blocked: the tadpole grows no legs, and keeps growing into a giant tadpole. That is how the hormone’s role was found: tadpoles without a thyroid do not change, and tadpoles fed its tissue turned early into tiny frogs. Mexico’s axolotl stays like this in the wild, breeding as a larva all its life.

    Feedback for a wrong answer

    Not yet. With normal hormones the tadpole starts changing before it gets that big; what would stop it?

    Hint

    The frog’s metamorphosis starts when thyroid hormone rises. What happens to a tadpole in which it is blocked?

    Worked solution

    1. At Normal the tadpole reaches at most about 42 mm, then the tail is absorbed.
    2. At Kept young thyroid hormone is blocked, and metamorphosis does not start.
    3. The tadpole keeps growing: after about 1414⁠ weeks it is about 5.5 cm long.

Lesson 3 of 5 · About 20 minutes

Built for their food

Five heads and five foods: a cow grinding grass from side to side, a cat shearing meat with scissor-like teeth, a whale sieving krill through baleen, a hummingbird lapping nectar with a forked tongue, and guts that lengthen when food is hard to digest.

Open the lesson

The 6 steps and their answers
  1. Step 1 of 6

    Open this step

    Built for food

    Practice · Choose

    Question

    What kind of feeder is the humpback whale?

    Correct answer

    • Correct A filter feeder

    Setup, choices and feedback

    The Scene at this step

    Food
    Krill
    Skin and muscle
    on
    Labels
    offdefault
    Time
    0.3 (First bite → Swallowed)

    Choices

    Shown in a random order.

    • Correct A filter feeder

    • Wrong A bulk feeder: it swallows tonnes at once

      Feedback

      It does take in a lot, but not pieces: it sieves countless tiny krill out of the water.

    • Wrong A fluid feeder: it drinks sea water

      Feedback

      The water is squeezed back out. What stays and is swallowed is the krill.

    • Wrong A substrate feeder: it lives in its food

      No feedback of its own; the learner sees the standard message

      Not yet. Look again and try once more.

    Feedback for a right answer

    A filter feeder. It fills its throat with tonnes of water and krill, shuts its mouth and squeezes the water out between the baleen plates; the krill stay caught in the bristles. Filter feeders eat very small creatures in huge amounts, which is why the largest animals that ever lived, the baleen whales, are filterers.

    Worked solution

    1. Drag Time: the mouth opens, the throat swells, the mouth shuts and the water leaves.
    2. The food, krill, is very small and gathered out of the water.
    3. Separating small food from water is filtering: a filter feeder.
  2. Step 2 of 6

    Open this step

    Grinding grass

    Practice · Predict, then look

    Question

    The cow starts grinding the grass with its cheek teeth. Predict how its lower jaw moves as Time moves on.

    Correct answer

    • Correct From side to side, opening only a little

    Setup, choices and feedback

    The Scene at this step

    Food
    Grassfixed
    Skin and muscle
    on
    Labels
    offdefault
    Time
    0.32 (First bite → Swallowed)

    Choices

    • Correct From side to side, opening only a little

    • Wrong Up and down, opening wide

      Feedback

      That is how a cat bites. Grinding needs the upper and lower teeth moving across each other.

    • Wrong Forward and back, like a saw

      Feedback

      Some rodents chew that way, but the cow pulls its jaw sideways.

    Once the prediction is locked in, the Scene changes

    Time
    0.6 (First bite → Swallowed)

    The Scene then shows: 6 ° · How far the lower jaw is open, degrees/nodes/head/outputs/gape

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    From side to side, opening only a few degrees. The cow’s jaw joint sits high above the teeth, and the masseter pulls the lower jaw sideways across the upper, so the ridges of the cheek teeth shred the grass between them, like millstones.

    Worked solution

    1. Grass is tough and full of cellulose: it has to be shredded into tiny bits.
    2. Shredding between two surfaces needs them to slide across each other.
    3. So the jaw moves sideways, opening only a little.
  3. Step 3 of 6

    Open this step

    Cutting meat

    Practice · Choose

    Question

    What do the cat’s carnassials do as the jaw closes?

    Correct answer

    • Correct They slide past each other like scissor blades, shearing the meat

    Setup, choices and feedback

    The Scene at this step

    Food
    Meat
    Skin and muscle
    off
    Labels
    offdefault
    Time
    0.45 (First bite → Swallowed)

    Choices

    Shown in a random order.

    • Correct They slide past each other like scissor blades, shearing the meat

    • Wrong They grind the meat to a paste

      Feedback

      The cat hardly chews: it cuts chunks and swallows them. Meat is easy to digest.

    • Wrong They grip the prey so it cannot escape

      Feedback

      That is what the long canines at the front do.

    Feedback for a right answer

    Scissors. The upper blade passes just outside the lower, so a cat chews at the side of its mouth and tilts its head. The jaw joint is a tight hinge, and the jaw moves only up and down, never sideways: good for cutting, poor for grinding grass.

    Worked solution

    1. Switch off Skin and muscle and drag Time to the jaw closing.
    2. The two carnassials, upper and lower, pass each other.
    3. Two blades passing each other shear: like scissors.
  4. Step 4 of 6

    Open this step

    Sieving the sea

    Practice · Calculate

    Question

    The scale bar beside the whale’s head marks one metre. Measure with it: how long is the head really?

    Correct answer

    1.7 m ± 12%

    Setup, choices and feedback

    The Scene at this step

    Food
    Krillfixed
    Skin and muscle
    off
    Labels
    offdefault
    Time
    0.35 (First bite → Swallowed)fixed
    Accepted within
    ± 12%
    Computed from the Scene at this step’s setting
    Real length of the head shown/nodes/head/outputs/headLength

    Any unit of the same quantity is accepted; it is converted before checking.

    Feedback for a right answer

    About 4.2 m, nearly a third of the whole whale. A huge head is a huge mouth: one gulp holds tonnes of water and thousands of krill. The same plinth also shows a hummingbird’s head, under 4 cm long: for each head the bar shows a different scale.

    Hint

    How many times does the bar fit along the head, from the tip of the jaw to the back of the skull?

    Worked solution

    1. The bar: one metre.
    2. It fits along the head a little over four times.
    3. The head’s length: about 4.2 m.
  5. Step 5 of 6

    Open this step

    Lapping nectar

    Practice · Choose

    Question

    How does the hummingbird get nectar out of the bottom of the flower?

    Correct answer

    • Correct The tongue slides out past the tip of the bill, traps nectar in its forked tip and draws back

    Setup, choices and feedback

    The Scene at this step

    Food
    Nectar
    Skin and muscle
    on
    Labels
    offdefault
    Time
    0.5 (First bite → Swallowed)

    Choices

    Shown in a random order.

    • Correct The tongue slides out past the tip of the bill, traps nectar in its forked tip and draws back

    • Wrong It sucks the nectar up through the bill, like a straw

      Misconception: Thinks a hummingbird sucks nectar up through its bill like a straw.

      Feedback from the catalogue

      A hummingbird’s bill hardly opens, and it does not suck. The tongue does the work: it slides out past the tip of the bill into the nectar, the two halves of its tip, fringed troughs, close round the liquid, and it draws back, about 1515⁠ times a second.

    • Wrong It opens its bill and scoops the nectar

      Feedback

      The bill hardly opens at all. All the movement is the tongue’s.

    Feedback for a right answer

    The tongue. Its tip is split into two fringed troughs, which open in the nectar and close round it as it draws back. It reaches so far because its roots, the hyoid horns, wrap round the back of the skull to the forehead and slide forward. About 1515⁠ licks a second, since a hummingbird burns energy faster than almost any other animal.

    Worked solution

    1. Drag Time slowly: the bill stays almost closed.
    2. The tongue goes out past the bill’s tip into the nectar, and the pink rods behind the skull slide down.
    3. The tongue comes back with the nectar: lapping, not sucking.
  6. Step 6 of 6

    Open this step

    Long guts, short guts

    Practice · Choose

    Question

    Why are a cow’s intestines twenty times its body length, and a cat’s only four?

    Correct answer

    • Correct Plant food digests slowly, and microbes need time and room to ferment the cellulose

    Setup, choices and feedback

    The Scene at this step

    Food
    Grass
    Skin and muscle
    on
    Labels
    offdefault
    Time
    Swallowed

    Choices

    Shown in a random order.

    • Correct Plant food digests slowly, and microbes need time and room to ferment the cellulose

    • Wrong The cow has enzymes for cellulose, and they need a long gut to work

      Misconception: Thinks a cow digests the cellulose in grass with its own enzymes.

      Feedback from the catalogue

      No mammal makes an enzyme that breaks down cellulose. Billions of bacteria and other tiny organisms in the cow’s rumen do the work, fermenting the cellulose to fatty acids, which the cow absorbs. The chewing, the cud and the long gut give them time and room to work.

    • Wrong A cow is simply bigger than a cat

      Feedback

      The question is relative to the body: twenty times against four. Size alone does not explain it.

    • Wrong A cow eats more, so needs room to store it

      Feedback

      The rumen does hold a lot, but for slow digestion, not as a store.

    Feedback for a right answer

    Slow digestion. No mammal breaks down cellulose itself. In the rumen, billions of microbes ferment it, the cow brings up cud and chews again, and a long gut gives more time to absorb. Meat digests quickly, so meat-eaters have a short, simple gut. Even an algae-grazing tadpole has a long gut, which shortens when it becomes an insect-eating frog.

    Worked solution

    1. Grass: mostly cellulose, which the cow cannot break down itself.
    2. Microbes in the rumen ferment it, and that takes time.
    3. A long gut and a big rumen give the time and the room.
    4. Meat digests quickly: a short gut is enough for a cat.

Lesson 4 of 5 · About 25 minutes

Push back to go forward

A dog, a trout and a pigeon move in place in a lab: each pushes the ground, the water or the air backwards and gets an equal push back. A walk that turns into a run, feet that push harder than the weight, and what a metre costs on land, in water and in air.

Open the lesson

The 6 steps and their answers
  1. Step 1 of 6

    Open this step

    Push and push back

    Practice · Choose

    Question

    One of the dog’s feet pushes the belt backwards. What is true of the belt’s push on the dog?

    Correct answer

    • Correct It is equal in size to the foot’s push, and points the opposite way

    Setup, choices and feedback

    The Scene at this step

    Animal
    Dog on a treadmill
    Speed
    1.3 m/s
    Labels
    offdefault
    Show the pushes
    Pushesfixed

    Choices

    Shown in a random order.

    • Correct It is equal in size to the foot’s push, and points the opposite way

    • Wrong It is weaker, or the dog would not move forward

      Misconception: Thinks the ground, water or air pushes back on an animal less hard than the animal pushes on it.

      Feedback from the catalogue

      By Newton’s third law the two pushes are always equal in size and opposite in direction, at every moment. The dog does not move forward because it pushes harder than the ground; it moves because the ground’s push on it points forward. What decides whether something speeds up is the total of the forces on that one body, not a comparison between two bodies.

    • Wrong There is none: the belt only moves, it does not push

      Feedback

      Without the belt’s push, the dog would neither stay up nor move forward relative to it.

    • Wrong It is stronger, since the belt is driven by a motor

      Feedback

      The motor only moves the belt at a steady speed. The pushes between foot and belt are always equal.

    Feedback for a right answer

    Equal and opposite, like the Scene’s two arrows: always the same length. Most of a foot’s push goes straight down and holds the dog up, and only a little of it forward and back. The same goes for the trout’s tail and the pigeon’s wing: to move forward is to throw something back.

    Worked solution

    1. Newton’s third law: if body A pushes body B, B pushes A with the same force in the opposite direction.
    2. The foot pushes the belt down and back.
    3. So the belt pushes the dog up and forward, just as hard.
    4. That push, on the dog, is what holds it up and drives it.
  2. Step 2 of 6

    Open this step

    Walk to trot

    Practice · Reach the target

    Question

    Find the highest Speed at which the dog still walks rather than trotting, and press Check.

    Goal

    • 1 ± 0

      At the start of the step: 1

    • 1.5 m/s ± 0.04 m/s

      At the start of the step: 1 m/s

    Setup, choices and feedback

    The Scene at this step

    Animal
    Dog on a treadmillfixed
    Speed
    1 m/s
    Labels
    offdefault
    Show the pushes
    Animal
    Read from the Scene at
    1 walk, 2 trot, 3 gallop, 4 swimming, 5 flying/nodes/lab/outputs/gait
    Read from the Scene at
    The speed the animal holds (no faster than its top speed)/nodes/lab/outputs/speed

    One setting that reaches it

    Speed
    1.5 m/s
    Labels
    off

    Feedback for a right answer

    1.5 m/s. At 1.6 m/s the Froude number passes 0.50.5⁠, and the dog breaks into a trot: diagonal pairs of legs land together. A person, with a leg of about 0.9 m, breaks into a run at the same Froude number, at about 2 m/s, and an elephant, with longer legs still, walks faster still.

    Feedback for a wrong answer

    Not yet. If the dog is already trotting, slow down; if it is walking, try a little faster.

    Hint

    Solve Fr=v2g h=0.5Fr = \dfrac{v^2}{g\,h} = 0.5⁠ with h=0.5h = 0.5⁠ m, then take the nearest speed below.

    Worked solution

    1. v2g h=0.5\dfrac{v^2}{g\,h} = 0.5⁠, so v=0.5×9.81×0.5v = \sqrt{0.5 \times 9.81 \times 0.5}⁠.
    2. v=2.45≈1.57v = \sqrt{2.45} \approx 1.57⁠ m/s.
    3. On the slider, in steps of 0.1 m/s, the highest speed below that is 1.5 m/s.
  3. Step 3 of 6

    Open this step

    Legs like springs

    Practice · Calculate

    Question

    The dog gallops at 7 m/s. What is the largest push of a leg on the belt in each stride? Compare it with its weight, 245 N.

    Correct answer

    665.9 N ± 5%

    Setup, choices and feedback

    The Scene at this step

    Animal
    Dog on a treadmillfixed
    Speed
    7 m/sfixed
    Labels
    offdefault
    Show the pushes
    Pushes
    Accepted within
    ± 5%
    Computed from the Scene at this step’s setting
    The largest push on the ground, water or air during a stride or beat/nodes/lab/outputs/peakPush

    Any unit of the same quantity is accepted; it is converted before checking.

    Feedback for a right answer

    Nearly three times: about 670 N. In a gallop each leg has little time on the ground, and for part of each stride no leg touches it. For the upward pushes to add up to the weight over a whole stride, each leg must push far harder than it in the short time it is down.

    Hint

    Follow the amber arrow through a stride, and read it at its peak.

    Worked solution

    1. The peak push in a gallop: about 666 N.
    2. Against the weight: 666/245≈2.7666 / 245 \approx 2.7⁠, nearly three times.
    3. Averaged over a whole stride the upward push equals the weight, but it is packed into a short time, so the peak is far higher.
  4. Step 4 of 6

    Open this step

    What a metre costs

    Practice · Calculate

    Question

    The dog, 25 kg, runs at 3 m/s burning about 347 W. What is its cost of transport, in J per kilogram per metre?

    Correct answer

    4.627 ± 3%

    Setup, choices and feedback

    The Scene at this step

    Animal
    Dog on a treadmillfixed
    Speed
    3 m/sfixed
    Labels
    offdefault
    Show the pushes
    Animal
    Accepted within
    ± 3%
    Computed from the Scene at this step’s setting
    Cost of transport: food energy to carry each kilogram one metre, J/(kg·m)/nodes/lab/outputs/cost

    Feedback for a right answer

    About 4.6 J per kilogram per metre. In running this cost hardly changes with speed: running faster burns more each second, but also covers more metres. A trout at its best speed pays less than one joule.

    Hint

    How many joules a second, how many metres a second, and how many kilograms?

    Worked solution

    1. Energy per metre: 347/3≈116347 / 3 \approx 116⁠ joules for each metre the dog covers.
    2. Per kilogram: 116/25≈4.6116 / 25 \approx 4.6⁠.
    3. In one formula: Pm v=34725×3≈4.6\dfrac{P}{m\,v} = \dfrac{347}{25 \times 3} \approx 4.6⁠ J/(kg·m).

    If you got about 116116⁠, you forgot to divide by the mass: that is the cost per metre for the whole dog.

  5. Step 5 of 6

    Open this step

    Fins in water

    Practice · Predict, then look

    Question

    Running costs the dog about 4.6 J per kilogram per metre. Predict what it costs the trout, at its cheapest speed, about half a metre a second.

    Correct answer

    • Correct Much less, under one joule

    Setup, choices and feedback

    The Scene at this step

    Animal
    Dog on a treadmill
    Speed
    3 m/s
    Labels
    offdefault
    Show the pushes
    Animalfixed

    Choices

    • Correct Much less, under one joule

    • Wrong Much more: dense water is hard to push through

      Feedback

      Water is hard to push through, but it holds the fish up for free, and the fish swims slowly.

    • Wrong About the same: muscle is muscle

      No feedback of its own; the learner sees the standard message

      Not yet. Look again and try once more.

    Once the prediction is locked in, the Scene changes

    Animal
    Trout in a swim tunnel
    Speed
    0.5 m/s

    The Scene then shows: 0.85 · Cost of transport: food energy to carry each kilogram one metre, J/(kg·m)/nodes/lab/outputs/cost

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    About 0.85 J per kilogram per metre, about a fifth of the dog’s. A fish is about as dense as water, and buoyancy balances its weight, so none of its muscle goes into staying up. It pays only for drag. But drag grows with the square of speed: at 2 m/s the trout pays almost as much as the dog.

    Worked solution

    1. The dog pays with every stride to carry its weight.
    2. For the trout, the water carries the weight: buoyancy.
    3. It pays only for drag, and drag is very small at low speed.
    4. So slow swimming is the cheapest way to move.
  6. Step 6 of 6

    Open this step

    Wings in air

    Practice · Predict, then look

    Question

    At 10 m/s the pigeon burns about 17 W. Predict what happens to the power when Speed drops to 3 m/s.

    Correct answer

    • Correct It rises, about twofold

    Setup, choices and feedback

    The Scene at this step

    Animal
    Pigeon in a wind tunnelfixed
    Speed
    10 m/s
    Labels
    offdefault
    Show the pushes
    Wake

    Choices

    • Correct It rises, about twofold

    • Wrong It falls: slower is easier, as in running

      Feedback

      In running, yes, but a bird must hold itself up, and at low speed little air passes over the wings.

    • Wrong It does not change: same bird, same weight

      No feedback of its own; the learner sees the standard message

      Not yet. Look again and try once more.

    Once the prediction is locked in, the Scene changes

    Speed
    3 m/s

    The Scene then shows: 35.16 W · Food energy burned each second at this speed, resting metabolism included/nodes/lab/outputs/power

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    It rises to about 35 W, twofold. In slow flight little air passes over the wings each second, so it must be thrown down fast, with deep, quick wingbeats: the rings in the wake dive steeply. At very high speed the body’s drag drives the power up again: a U-shaped power curve.

    Worked solution

    1. A bird carries its weight by throwing air down.
    2. At low speed, less air reaches the wings each second.
    3. To carry the same weight, that little air must be thrown down faster, which takes more power.
    4. So slow flight is costly, and a pigeon can hover for only a few seconds.

Lesson 5 of 5 · About 20 minutes

Moving as one

A starling flock with no leader: each bird applies three rules, separation, alignment and cohesion, to its seven nearest neighbours, and the shape of the whole flock emerges by itself. What happens when you switch a rule off, and why the same happens in fish, ants and crowds.

Open the lesson

The 5 steps and their answers
  1. Step 1 of 5

    Open this step

    No one in charge

    Practice · Choose

    Question

    Who decides which way the flock turns?

    Correct answer

    • Correct Nobody: each bird responds only to its nearest neighbours, and the turn passes from bird to bird

    Setup, choices and feedback

    The Scene at this step

    Separation
    50 %
    Alignment
    50 %
    Cohesion
    50 %
    Follow one bird
    Murmuration

    Choices

    Shown in a random order.

    • Correct Nobody: each bird responds only to its nearest neighbours, and the turn passes from bird to bird

    • Wrong A lead bird at the front, and the others follow it

      Misconception: Thinks a flock or swarm moves together because it follows a leader who knows the way.

      Feedback from the catalogue

      There is no leader, and no bird sees the whole flock. Each responds only to its seven nearest neighbours, by three rules: separation, alignment and cohesion. The flock’s shape and movement emerge from these local rules. A turn that starts at the edge passes from bird to bird, with no command.

    • Wrong The older, experienced birds, which know the roost

      Misconception: Thinks a flock or swarm moves together because it follows a leader who knows the way.

      Feedback from the catalogue

      There is no leader, and no bird sees the whole flock. Each responds only to its seven nearest neighbours, by three rules: separation, alignment and cohesion. The flock’s shape and movement emerge from these local rules. A turn that starts at the edge passes from bird to bird, with no command.

    • Wrong Every bird sees the flock’s shape and fits itself to it

      Feedback

      In a flock of thousands, a bird sees only those around it. None sees the whole shape.

    Feedback for a right answer

    Nobody. In the Scene, each bird reads only its seven nearest neighbours and acts by three rules. When birds at the edge turn, their neighbours copy them, and a wave of turning runs back through the flock. In real flocks over Rome, such waves were measured at about 20 m/s to 40 m/s.

    Worked solution

    1. Every bird has the same three rules, and applies them only to its near neighbours.
    2. No rule mentions the flock or where it is going.
    3. So no one “decides”: the flock’s turn is the sum of many small turns, each in response to neighbours.
  2. Step 2 of 5

    Open this step

    Three rules, seven neighbours

    Practice · Choose

    Question

    Each starling follows its seven nearest neighbours, however far away they are. Why is that better than following everyone within a fixed distance?

    Correct answer

    • Correct When the flock thins out, each bird still has neighbours to follow, and the flock stays connected

    Setup, choices and feedback

    The Scene at this step

    Separation
    50 %
    Alignment
    50 %
    Cohesion
    50 %
    Follow one bird
    One bird’s rules

    Choices

    Shown in a random order.

    • Correct When the flock thins out, each bird still has neighbours to follow, and the flock stays connected

    • Wrong That way each bird sees the whole flock

      Feedback

      Seven birds are a tiny handful out of thousands. No bird sees the whole flock, and that is just the point.

    • Wrong That way the birds fly faster

      Feedback

      Speed does not depend on it. The question is what happens to the flock as it thins out or crowds together.

    Feedback for a right answer

    It stays connected. The number was measured by a team in Rome, who rebuilt starling flocks in three dimensions. If birds responded to everyone within a fixed distance, a flock spreading out would lose touch and break up, and a dense flock would load each bird with hundreds of neighbours. When each always watches the handful nearest it, the flock holds up either way.

    Worked solution

    1. A fixed distance: in a sparse flock there is no one in range, no one to respond to, and the flock breaks up.
    2. A fixed number: there are always seven neighbours, even if far.
    3. So following the seven nearest holds the flock together even as it thins.
  3. Step 3 of 5

    Open this step

    Take away a rule

    Practice · Predict, then look

    Question

    Predict what happens to the flock when Alignment goes down to 0%, with separation and cohesion as they are.

    Correct answer

    • Correct The birds stay together, but each heads its own way, like a swarm of gnats

    Setup, choices and feedback

    The Scene at this step

    Separation
    50 %fixed
    Alignment
    50 %
    Cohesion
    50 %fixed
    Follow one bird
    Murmurationfixed

    Choices

    • Correct The birds stay together, but each heads its own way, like a swarm of gnats

    • Wrong The flock breaks up and every bird flies off

      Feedback

      That is what switching off cohesion does. Here cohesion still draws them all to the middle.

    • Wrong The birds pack into tight knots

      Feedback

      That is what switching off separation does. Here separation still keeps them apart.

    Once the prediction is locked in, the Scene changes

    Alignment
    0 %

    The Scene then shows: 1 · 0 murmuration, 1 swarm, 2 scatter, 3 clump/nodes/flock/outputs/regime

    A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.

    Feedback for a right answer

    A swarm. Cohesion still holds the birds together and separation still keeps them apart, but nothing makes them agree on a direction. The cloud churns in place. Alignment is what turns a crowd of birds into a flock that moves as one.

    Worked solution

    1. Separation: keeps distance; still on.
    2. Cohesion: holds together; still on.
    3. Alignment: matches heading; off.
    4. Together, but with no shared heading: a swarm.
  4. Step 4 of 5

    Open this step

    Knots

    Practice · Reach the target

    Question

    Change one rule so the birds pile into tight knots, and press Check.

    Goal

    • 3 ± 0

      At the start of the step: 0

    Setup, choices and feedback

    The Scene at this step

    Separation
    50 %
    Alignment
    50 %
    Cohesion
    50 %
    Follow one bird
    Murmuration
    Read from the Scene at
    0 murmuration, 1 swarm, 2 scatter, 3 clump/nodes/flock/outputs/regime

    One setting that reaches it

    Separation
    0 %
    Alignment
    0 %
    Cohesion
    0 %

    Feedback for a right answer

    Separation at 0%. Cohesion keeps drawing each bird to the middle of its neighbours, and nothing stops it. The birds pile into knots, which in real life would be a tangle of collisions. A murmuration is a balance between a pull inwards and a push apart.

    Feedback for a wrong answer

    Not yet. Which rule keeps each bird’s personal space?

    Hint

    Which rule stops a bird drawn towards its neighbours from crashing into them?

    Worked solution

    1. Cohesion pulls birds together; separation pushes them apart.
    2. To make them pile up, keep the pull and remove the push.
    3. Slide Separation down to 0%.
  5. Step 5 of 5

    Open this step

    Emergence

    Practice · Choose

    Question

    Which of these is not emergent behaviour?

    Correct answer

    • Correct A marching band following the drum major at its head

    Setup, choices and feedback

    The Scene at this step

    Separation
    50 %
    Alignment
    50 %
    Cohesion
    50 %
    Follow one bird
    Murmuration

    Choices

    Shown in a random order.

    • Correct A marching band following the drum major at its head

    • Wrong Ants finding the shortest way to food by scent trails

      Misconception: Thinks a flock or swarm moves together because it follows a leader who knows the way.

      Feedback from the catalogue

      There is no leader, and no bird sees the whole flock. Each responds only to its seven nearest neighbours, by three rules: separation, alignment and cohesion. The flock’s shape and movement emerge from these local rules. A turn that starts at the edge passes from bird to bird, with no command.

    • Wrong A school of fish splitting round a predator

      Misconception: Thinks a flock or swarm moves together because it follows a leader who knows the way.

      Feedback from the catalogue

      There is no leader, and no bird sees the whole flock. Each responds only to its seven nearest neighbours, by three rules: separation, alignment and cohesion. The flock’s shape and movement emerge from these local rules. A turn that starts at the edge passes from bird to bird, with no command.

    • Wrong Lanes that form when two streams of pedestrians pass through each other

      Misconception: Thinks a flock or swarm moves together because it follows a leader who knows the way.

      Feedback from the catalogue

      There is no leader, and no bird sees the whole flock. Each responds only to its seven nearest neighbours, by three rules: separation, alignment and cohesion. The flock’s shape and movement emerge from these local rules. A turn that starts at the edge passes from bird to bird, with no command.

    Feedback for a right answer

    The band. It has a leader and a plan of the whole: the drum major decides, and each player follows. In the other three nobody sees the whole picture: each ant, fish and pedestrian responds only to what is around it, and the large-scale order arises by itself.

    Worked solution

    1. Emergent behaviour: large-scale order arising from local rules, with no leader and no plan of the whole.
    2. Ants, fish and pedestrians: each responds to neighbours or its surroundings. Emergent.
    3. A marching band: everyone follows one leader. Not emergent.

Across the unit · 8 misconceptions

Misconception catalogue

Each common mistake this unit recognises, in a few words. Open one for what the learner reads when an answer matches it, and where it is asked.

  • Thinks any animal that lays eggs has them fertilised outside its body.

    The learner reads

    Laying eggs and external fertilisation are two different things. Birds, reptiles and insects lay eggs, but their fertilisation is internal: the male passes sperm into the female’s body, and the egg gets its yolk and shell only after it is fertilised. External fertilisation happens only in water, as in most fish and frogs.

  • Thinks an animal that produces more eggs or young leaves more grown offspring.

    The learner reads

    The number of young at the start hardly decides how many grow up. A million cod eggs and a single calf both end at about one or two. Enlarge a brood from the same budget and each young gets less: weaker larvae, hungrier chicks. And in a population that lasts, each pair leaves on average about two that grow up, or it would grow or vanish.

  • Thinks a chrysalis is a resting caterpillar that simply grows wings onto its old body.

    The learner reads

    The chrysalis is still from outside, but inside the body is being rebuilt. Digestive enzymes break down most of the caterpillar, its crawling muscles, much of its gut and its silk glands, and the adult is built from the imaginal discs the caterpillar has carried since it was an embryo, feeding on the broken-down tissue. Only the nervous system, the heart and the breathing tubes are rebuilt without being destroyed.

  • Thinks a tadpole's tail drops off when it becomes a frog.

    The learner reads

    The tail does not drop off: it is absorbed. The tail’s cells kill themselves on cue, by apoptosis, and their material is recycled to feed the body through the two weeks the tadpole does not eat. That is why the froglet is far shorter than the tadpole was, about 1.6 cm instead of about 4 cm with the tail.

  • Thinks a hummingbird sucks nectar up through its bill like a straw.

    The learner reads

    A hummingbird’s bill hardly opens, and it does not suck. The tongue does the work: it slides out past the tip of the bill into the nectar, the two halves of its tip, fringed troughs, close round the liquid, and it draws back, about 1515⁠ times a second.

  • Thinks a cow digests the cellulose in grass with its own enzymes.

    The learner reads

    No mammal makes an enzyme that breaks down cellulose. Billions of bacteria and other tiny organisms in the cow’s rumen do the work, fermenting the cellulose to fatty acids, which the cow absorbs. The chewing, the cud and the long gut give them time and room to work.

  • Thinks the ground, water or air pushes back on an animal less hard than the animal pushes on it.

    The learner reads

    By Newton’s third law the two pushes are always equal in size and opposite in direction, at every moment. The dog does not move forward because it pushes harder than the ground; it moves because the ground’s push on it points forward. What decides whether something speeds up is the total of the forces on that one body, not a comparison between two bodies.

  • Thinks a flock or swarm moves together because it follows a leader who knows the way.

    The learner reads

    There is no leader, and no bird sees the whole flock. Each responds only to its seven nearest neighbours, by three rules: separation, alignment and cohesion. The flock’s shape and movement emerge from these local rules. A turn that starts at the edge passes from bird to bird, with no command.

Index