Across fields
Connections
Range means seeing that two fields share a structure, and seeing where the likeness stops. Write that in your own words.
Opening the record.
1. Physics and Economics
What keeps going
Newton's laws · Opportunity cost
Newton's first law: a body keeps its velocity unless a net force changes it. Name a habit, a price, or an institution that keeps going for a similar reason. What would count as the net force that changes it?
Zero net force is not the same as zero motion. Something can keep moving because nothing is pushing back.
2. Biology and Economics
Two kinds of filter
Natural selection · Supply and demand
Natural selection and competition among firms both remove some variants and leave others. Write one similarity that is real, and one place the analogy fails.
Firms have plans. Mutations do not. Both filters can still change what is common in the next round.
3. Economics and Art and music
What you spend by choosing
Opportunity cost · Value and color
Opportunity cost is the value of the next best thing you give up. In a drawing, pushing one contrast often means softening another. Describe a choice, in a picture or in your own practice, where taking one option spends another.
The cost is the best forgone option, not every option added together.
4. Economics and Mathematics
Growth on a base
Compound interest · Linear equations
Compound interest pays the next gain on a larger base, which is why starting earlier matters. A review schedule does something similar with memory. Where does that comparison hold, and where does it break?
Money compounds by a formula. Memory does not. Forgetting, and a missed day, have no exact twin in a bank account.
5. Art and music and Economics
A picture is not the thing
Linear perspective · Supply and demand
A perspective drawing is a consistent picture of space, not space itself. A supply and demand diagram is a consistent picture of a market, not the market. What does each picture make easy to see, and what does it leave out?
Both pictures are useful because they drop detail on purpose. Name one dropped detail for each.
6. Philosophy and Mathematics
A step that preserves
Arguments and validity · Linear equations
A valid argument carries truth from the premises to the conclusion, even if the premises are false. A legal algebra step carries equality forward, even if you started from the wrong equation. Give a tiny example of each.
Validity is not soundness. A reversible algebra step is not a claim that the first line was true.
7. Biology and Economics
Specialization
Cell structure · Opportunity cost
A cell that specializes, and a person who specializes, both gain efficiency and both take on a risk. Name the gain and the risk in each case.
Comparative advantage is the economic half. A specialized cell depends on the rest of the body.
8. Philosophy and History
When a sight counts
Knowledge and justification · The Scientific Revolution
Galileo treated the moons of Jupiter, and the phases of Venus, as reasons to doubt an old model of the heavens. Using the idea of justification: why is an observation more than one more belief sitting beside the others?
A belief can be true by luck. Justification is the reason that ties the belief to something you could be wrong about.
9. Physics and Art and music
The same ratio
Waves and light · Rhythm and intervals
A musical octave is a 2:1 frequency ratio, and the pitch of a tone depends on frequency. Explain how a higher note and a higher-frequency wave are one idea, and name something a wave has besides frequency.
Wavelength and amplitude are still there. Pitch is not loudness.