They are taught the basics first. In fact you can't even begin to touch String Theory [now M Theory] unless you are a physics graduate. Children may get an arm-waving version of physics to convey the most basic concepts and the underlying philosophical implications. For example, many students may be aware of Schrodinger's cat, But they can't begin to handle the math that leads to that concept. And if you aren't doing the math, it isn't physics. It is philosophy. Physics is generally taught by retracing the foundational developments in physics and duplicating the work and calculations. In other words, physics is generally taught in such a way that the student can see the proof with their own eyes, and solve the equations with their own brains. This means that it has to be age appropriate. For example, most 8th graders can only handle basic algebra. So they are taught the physics that can be done with basic algebra.
Yes, water-ice occupies more volume than the water that was frozen to make it. The next obvious question is, why?
The curve on the top of an airplane wing is there to make the wing stronger and streamline. Why does that statement fail?
Any positive number divided by zero, yields an infinite value. If false, why? What is the proper method of handling this problem?
I never was good at math but you don't have to do the math to understand some basic concepts of M theory or relativity. But physics and anything conceived by man consists of thought first. I mean you can't have something , even a brick without it existing in thought first. Even Einstein was a big proponent of thought experiments. I believe our minds produce our reality even if we know no math at all.
Yes but those are known as arm-waving explanations. If you don't understand the math, you really don't understand it. In fact, if you know the math, you sometimes realize that nobody understands it! Yes but thought experiments are philosophy. They can lead to logical conclusions that then must be proven mathematically, in order to be considered physics. I remember that one of my books in Quantum Mechanics always had a philosophical epilogue at the end of each chapter. That was the only time words were used much except to introduce the next equation or to state the source of some identity or equation. This page followed each chapter of almost nothing but equations. It was where the equations were interpreted philosophically to provide context.
One of the key differences between modern science and the ancient Greek philosophers, is they believed that all knowledge can be derived through critical thinking and logic. Modern science has taught us that this isn't true. Math leads to answers we couldn't anticipate. And experimentation leads to discoveries and the ability to test for flawed logic.
A conventional heat pump does it by first getting heat to flow from hot to cold, then moving what was cold, aka the refrigerant, to a condenser where it ends up being hotter than the surrounding air. IIRC, the H2O bonding angle increases slightly @ 0°C, which I suppose accounts for the volume increase. Why that should precisely coincide with a phase change I have no idea. Job 1 for a wing, other than not falling off or disintegrating, is to provide lift. This it does by creating a pressure differential from top to bottom, the convex surface on top creating a partial vacuum and the concave surface below creating increased pressure under the wing. A fuselage would be a lot more streamlined with no wings at all, but then it would be a missile rather than an aircraft. n/0 = ∞ <-> n = 0·∞ The conclusion being nonsensical, so is the premise. Dunno what problem you're talking about, but dividing by zero is not a solution to any problem.
Because that is NOT the primary purpose of a aerofoil form. There are several aspects that need to be considered. The first is that the strength of the wing has nothing whatsoever to do with the "curve on the top". The strength comes from internal load bearing structures. The purpose of an aerofoil form is to generate lift by making the air travel a greater distance across the upper surface than the lower surface. This causes the air above to have a lower pressure than the air below. This concept works in reverse on racing cars where the "negative" lift results in greater pressure on the wheels which increases grip. The concept of "streamlining" is to eliminate drag from the air flow. (The drag on the lower surface of the wing produces lift.) The streamlining at the leading edge of the wing reduces drag which enhances the lift effect. In summary the wing has internal structures for strength and it is formed into an aerofoil shape that creates lift from the differential in the air pressure below and above the wing. The streamlining applies primarily to the leading edge as a means to eliminate the drag of the internal strengthening structures.
When you think about it critically math is just logic reduced to numbers and the answers in the numbers require critical thought in order to reveal new knowledge. The ancient Greek philosophers did pretty well at coming up with knowledge given that they were handicapped by not having the benefit of math to test out their logic.
Science needs to be taught as a methodology. Forming proper hypotheses, doing the testing, etc. Thought experiments are a way of working toward useful hypotheses. It may even be interesting from an historical point of view - like how did Einstein approach questions. But, the thought experiments don't particularly illuminate scientific mehtod - which at the HS level needs to be the point. It would be great if people graduating HS could tell the difference between science and NOT science, for example.
Yes, but we discover most of mathematics by following rather simple rules, such as the five axioms of algebra. Descartes particularly made note of this when he discusses how we had to discover the properties of a triangle. It is a system of logic that allows us to extend our logic beyond what our brains can handle directly. I love philosophy but the limitations are the key distinction between what a lot of people think is science, and actual science. And the failure to understand this difference is a big reason why so many people don't trust science. They don't understand and can't even imagine the degree of rigor that leads to core concepts.
In particular the velocity of the air is increased over the top, which reduces the pressure as per Bernoulli's principle
Magnetic fields and electric fields are entirely different types of fields. True or false? Can you prove it?
It isn't the bond angle but the hydrogen bonding between molecules. As thermal energy [which is really a measure of the motion of the molecules] is removed, the molecules settle into a preferred orientation with respect to each other. This orientation causes the water to expand as it freezes. "Hydrogen bonding is a special type of dipole-dipole attraction between molecules, not a covalent bond to a hydrogen atom. It results from the attractive force between a hydrogen atom covalently bonded to a very electronegative atom such as a N, O, or F atom and another very electronegative atom." https://www.chem.purdue.edu/gchelp/liquids/hbond.html A core concept in Calculus is how an equation acts as something approaches zero or infinity.. For example, as x approaches zero, 1/x approaches infinity. This is particularly useful where we want to know who is going to win, say where we have 1/x vs 1/x^2, where x approaches zero. Conversely, the limit as x approaches 0, of 10000 * x, = 0 The limit as x approaches infinity, of 1/x, = 0
I agree! The ability to visualize a concept in your mind and then find a way to make it into a reality is not very common among the general population. To then be able to take the concept and mentally visualize it from all angles is the next step. Then to test the various interactions with the concept to ensure that it will work in theory is the final step before trying to do it in reality if that is the goal. I have used mental visualization of data to build both systems and databases from scratch. The more time I spend on this process the better the end product will be. Once it is built it is easier for others to grasp it. The same applies to philosophy and science but with different goals now from what they were when the Ancient Greeks first began to describe them. They were dealing with nature and trying to understand what it was and how it worked. FTR I suspect that the "distrust" of science is something that is taught rather than innate. Showing science to small children delights and awes them. They are curious and want to find out more about it. Those that distrust science are primarily doing so because they feel that it threatens their literal beliefs. If they were to grasp the concept that their beliefs are metaphorical as opposed to literal there would be no need for any distrust of science.
If you mix one part lye [NaOH] with one part hydrochloric acid [HCl], the resulting solution is highly toxic. Why does that statement fail?
Too much salt and too much water can be toxic however a base combined with an acid makes a neutral substance.
There is no gravity in space. This is obvious by watching the astronauts in the space station. Why does that statement fail?
The astronauts within the space station are subject to "micro-gravity" while the space station itself remains in orbit because of the Earth's gravitational attraction. In essence there is plenty of "gravity in space". The effect of the gravity is relative to the relative speed and distance of the objects themselves.
