Should Studying Science be Mandated?
Most people won't become scientists so learning science is about satisfying curiosity about how the world works and came to be, not about learning a practical or career-oriented topic. Beyond the most essential understanding of how the word works, the physical sciences should be an optional part of the K-12 curriculum. Students who are interested in science can be encouraged to learn it since some of them may appreciate the opportunity and a fraction of them will later use it in their careers. Those who are uninterested are unlikely to become scientists themselves, but they can always catch up later if they desire to.
Once a student commits to learning a topic in high school or college, they can force themselves to continue learning it even when it's difficult, since they want to do well in the course. This is the one benefit of schools - they provide a structure or incentive system where people can learn. Once someone leaves school and is just learning on the side for enlightenment, they're less likely to "force" themselves through difficult topics. However, when you're learning on your own, you can choose to learn the most interesting topics.
Learning the Concepts in Science
If you're learning science just to satisfy curiosity, you don't need to learn every technical detail covered in textbooks.
Q: Can you learn physics without advanced math?
A: I think so:
- Many areas of physics (such as mechanics) can be understood with basic algebra and maybe a sprinkle of simple calculus.
- Even in other areas, it seems one can get at at least a partial conceptual understanding without covering all the mathematical details.
While a researcher or engineer may need to know all the mathematical nitty gritty, someone learning physics for knowledge can likely skip over some of these details. In the past it was even possible to make significant discoveries in physics with limited knowledge of math. For example Michael Faraday was "one one of the most influential scientists in history" despite the fact that "his mathematical abilities... did not extend as far as trigonometry and were limited to the simplest algebra". (Though even there, James Maxwell's equations were needed to fully understand the implications of Faraday's discoveries.) Physics became more complex over time, so later developments in physics require more math to truly understand them, but one can still learn a simpler version of any topic.
Books that cover concepts in Physics
These are books that give an overview of physics and its development:
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Seven Ideas That Shook the Universe - different paradigms in physics: Copernican astronomy, Newtonian mechanics, energy and entropy, relativity, quantum theory and conservation principles & symmetries.
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The Evolution of Physics (By Albert Einstein and Leopold Infeld) - As summarized by the table of contents, it covers The Rise of The Mechanical View; The Decline of the Mechanical View; Field, Relativity; and Quanta. Slightly similar to the above book, though from Einstein's perspective.
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The Character of Physical Law (by Richard Feynman) - Instead of covering all of physics, it goes through certain ideas as examples of physics. This is the written version of a series of lectures by Feynman so it isn't as edited as the above books, but it contains Feynman's unique style.
Specific Topics in Physics
Here are some interesting topics in physics they seem worth learning more about. -
Mechanics - Force & Motion & Inertia
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The basic formulas and their calculus.
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Example question: Intuitively, why is Kinetic Energy (KE) proportional to v2when momentum is proportional to v (velocity)?
Answer: Lets' say you want to stop a frictionless moving car by putting a friction block on which drags on the ground with a constant force. A car going 2x as fast will take 2x as much time to stop since, as expected since it has 2x the momentum. However it will take 4x as much distance to stop the car. All that distance involved the same rate of friction heat creation, so the car going 2x as fast must have 4x the KE. Similarly if you want to drop a block and have it go 2x as fast as another block, you'll need to raise it to 4x the height. This was also a controversy between followers of Newton and Leibniz, see Vis Viva. -
How/why is inertia and conservation of momentum so fundamental in all of physics?
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Gravity (Newtonian)
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How Newton discovered the law of gravity from a better understanding of motion.
(I.e. how Newton built on Galileo to create his Newton's laws of motion, then connected them with Kepler's laws of planets and then connected that with the moon's motion and universal gravitation.) -
Basic math of satellites and planets in orbit
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Key concepts in general relativity
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Electromagnetism
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Understanding what electric and magnetic fields are are and how they interact with charged particles.
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How special relativity resolved issues raised by Maxwell's equations.
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Interesting when reading Einstein's writings, how strong his intuition was to avoid any special frames of reference and how this took priority over other intuitive ideas such as about absolute time...
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Thermodynamics
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What is entropy? Besides the fundamental meaning for particles, how does it affect non-thermodynamic order? Whats was the entropy of the universe initially? How does gravity affect entropy? (See also heat death paradox, as well as this question.)
Understanding Physics (by Isaac Asimov) gives basic explanation the laws of thermodynamics. First law is about the "absolute" store of energy. But energy can only be used when it flows from "high" to "low". And over time differences even out so entropy increases. Book has this more philosophical observation:
We thus find there is an odd and rather paradoxical symmetry to this book. We began with the Greek philosophers making the first systematic’ attempt to establish the generalizations underlying the order of the universe. They were sure that such an order, basically simple and comprehensible, existed. As a result of the continuing line of thought to which they gave rise, such generalizations were indeed discovered. And of these, the most powerful of all the generalizations yet discovered — the first two laws of thermodynamics — succeed in demonstrating that the order of the universe is, first and foremost, a perpetually increasing disorder.
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How does "information" as a physical concept connect to this? (see wikipedia and stanford article.)
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Is the second law of thermodynamics more "proven" than other natural laws?
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How the theoretical science developed from the technological development of steam engines (and compare with how computers developed)
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Practical applications in everyday life (e.g opening fridge won't cool room)
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Nuclear physics
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The nuclear bonds (and how E=MC2 not that relevant).
Compare nuclear bonds with chemical energy.
(Bonus: the weak force and how it relates to electromagnetic force) -
Quantum mechanics - to what extent can it be understood by a layman?
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Consider reading parts of Scott Aaranson's Quantum computing since Democritus (or the lecture notes)
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Interpretations of quantum indeterminacy
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See lecture notes
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Bohemian mechanics (pilot wave theory)
Other topics in the physical sciences
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Astronomy & astrophysics - How the universe developed
The formation of all elements (Stellar nucleosynthesis). The cycle of stars. How matter regrouped after stars exploded.. (See Wikipedia on Stellar population.) - Chemistry
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how does the number of protons/electrons determine the properties of elements?
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Much of this is more basic chemistry, as seen in repetition in the periodic table
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Sometimes the specifics of how properties like color are determined can involve more complex areas, e.g. need relativistic quantum mechanics to explain why gold is gold-colored instead of silver.
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How does the structure of electrons in chemical compounds determine their properties?
- Earth science
- Development of earth
- Earth's magnetism
- Global warming
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