In my world, a theory is falsified by experiment, unless you can show contradictions within the theory itself. However if a theory that solves the same set of problems can be formulated in a simpler framework, I would consider today's theories redundant.
To answer very roughly and with hand waving, this is how I see it, in the big picture.
Given two vectors you can either be interested in properties that these vectors has relative to each other. With this I for example mean such aspect as projections onto the other vectors direction. Or, you...
Lets put it like this, as long as you are pre-calculus or anywhere near calculus, you can take whichever path that suits you, preferably the one that the authors suggest for you, or the path found on any college plan focusing on the natural sciences.
If you want to get a grasp of string theory...
Devin-M, I think all that really needs to be said regarding this problem was expressed in the following post by PeroK:
https://www.physicsforums.com/threads/deceptively-simple-geometry-question-on-sat-test.1057821/post-6972664
Your journey to intuitively digest this phenomena is maybe too...
Yes this is true and its the reason that a cars have differential steering:
But it feels like you are taking a detour now. Either you focus on the center of the coin or you focus on the touching point. Let me see if I can lead you back from this, we start by focusing on the center of the...
Again, you are mixing up concepts and making it too complicated.
You where asking why a coin makes two revolutions when rolling along the perimeter of a stationary coin.
Revolutions has to do with rotation. I.e. the question is equivalent to asking: Why does the coin rotate 720 degrees when...
Following the perimeter of a circle implies a revolution itself.
I believe you are mixing up two concepts.
If you focus on how many revolutions the outer coin makes in the two dimensional plane, then the answer is two. If you focus on how much distance the coin travels on the perimeter of the...
To become researcher in the field is basically a life time investment, at least if you wanna get some work done as well. However with that said.. it doesnt mean you cant reach different orders of understanding. The more time you invest the deeper understanding is possible, of course.
Im by no...
I like to think of it this way:
i) Imagine a small arrow at the center of the smaller circle, intially pointing upwards. This will give a hint of the orientation of the small circle, which helps in order to count revolutions during the process.
ii) Now let the smaller circle slide around the...
I first encountered this phenomena from Verne's book as well. Im sure many students went from this SAT confused, knowing the difference between a solar day and a sidereal day. Although it take some guts to accuse the SAT writers of being wrong, thus they probably forgot about it instead of...
I argue that in order to combine the concepts of steam and engine and thus sketch the idea of a steam engine youll need a conceptual understanding of the two words. That is, if you've never heard of the concept steam engine before.
I order to prevent the illusion of understanding by mimicing...
You are missing the point.
Generating code for programs is a prime example of something that can be made by training the software in relative word frequence, sentence construction and so on. As long as there is a huge amount of programming code in the training data, chances are youll get...
A proposal for testing conceputal understanding would be to train models with data that excludes a specific concept, lets say steam engine. If there is no trace of the word steam engine in the training data (and no clues of what such a thing might be) but the model can still supply an educated...
Im in no position to answer what a quantum field is, but questions such as this one might often lead astray to rather philosophical inquiries. If thats not what is asked for, more concrete questions might help the understand the concept. Such as:
1. How does it transform under coordinate...