This is how we make progress in theoretical physics. A good example is Newton's Second Law: f = m a. A lot people think that this is some discovery about a "fundamental law of the universe," but it is actually just a definition. The net force acting on an object is defined by humans to be equal to the product of the object's mass and acceleration. You could equally create another "law" that says f2 = m v, where v is velocity and f2 is "force 2.0." Both are correct by definition, but only one is useful. If you calculate the "force 2.0" of gravity, you'll get a complex mess; whereas the "force" of gravity is an elegant equation.
Well, I would take issue with that. Sure, mathematically one can choose any set of consistent concepts and true statementes as the starting point, and treat the remainder as derived.
However, that is not how f = ma developed historically. Acceleration of course is defined as the second derivative of position with respect to time, and Galileo, before Newton, was one who contributed to the understanding of uniformly accelerated motion. Force however can be "felt" and measured independently of any motion (e.g. with a dynamometer), and well before f = ma there was allready a large consistent quantitative theory of forces without motion, that included weight ("two identical objects have twice the weight of one"), levers, pulleys, and inclined planes, buoyancy and more. So when Newton stated f = ma, he indeed discovered a law of nature.
Jorge, you'll need to take it up with Richard Feynman because I borrowed the example from him (from Feynman Lectures on Physics; however, he called it a "gorce" rather than "force 2.0").
You interpretation of this history of physics and calculus shows that you've never questioned how our perception of reality is shaped by those among us with the courage to pursue truth.
What is a dynamometer? A simple way to construct one is to use a spring and mark equally-spaced lines to indicate how far the spring has stretched. You can then place a "mass" on the end of the spring and measure the spring's stretch by counting lines. You then say that "force is the change in the number of lines," but by doing this you are
implicitly assuming that Hooke's law holds (that f = k x). All of physics is a bunch of definitions and equations piled up on top of each other that are self-consistent and that explain what we see in the natural world. They are
human constructions.Satoshi Nakamoto once said that "humans are pattern-seeking, story-telling animals." Newton saw patterns and he made up a convincing story to explain it. That story proved to be so useful and so powerful that it became entrenched in our perception of reality, and now generations of physicists have built on top of it. But it is just a story that explains what we see in nature. It is not nature itself.
When Newton wrote "Principia," he planted the seeds that would
change mankind's perception of reality over the next several hundred years. When Satoshi wrote "Bitcoin: a peer-to-peer electronic cash system," I would argue that he did the same thing.
I think if you were alive in the days of Newton, you would have been a bishop of the Catholic Church. I believe you would have claimed that calculus was "pointless" and because of your mental obstinance, you wouldn't have even understood what it was that Newton meant by "acceleration is the second derivative of position." But you are also smart, and you would have realized that Newton was able to accurately explain the motion of the heavens, diligently recorded by Nicolaus Copernicus 200 years early. This would have frightened you, Jorge. You would have written about the evils that would come from physics and that no man can understand the complexity of God's creation.
Newton would have seemed to you a heretic, for he presented a theory that was strongly at variance with established beliefs and customs. This is not unlike how you view bitcoin as heresy today.
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