Today we are going to look at some Quora questions from mathematics and physics. And then check out some of the answers given by others, before giving our own answer. The answers provided by others should give an interesting oversight into what one might expect in mainstream mathematics and physics.
Please note that when giving some peoples answers, we may abridge the answers to leave out any non-essential, distracting or just confusing parts.
But without further ado, let us start with our Quora questions.
Here is one answer:
“It’s metaphysics, the study of, and speculations about, the nature of physics. The question, “Why does it seem all of the physical laws are conservation symmetries?” is a metaphysical question.“
No, it most certainly isn’t. Metaphysics is not a combination of physics and philosophy. It is the philosophical study of the fundamental nature of the universe. It answers basic questions about existence which we must address before attempting physics.
Consider metaphysical questions such as “Is reality a constant thing” or “Is the world I observe reality?” and the like. Without answers to questions such as these, one is no position to tackle physics. To study the fundamental nature of matter, one must first decide what kind of universe they think they live in!
In fact, physics has no bearing on metaphysics, nothing to say about it. Physics cannot answer these kinds of questions.
However, the metaphysics one has will dictate the kind of physics they work on. If they have a rational metaphysics, they are likely to have a rational physics that holds reality and matter as primary. If one holds an irrational metaphysics, one will have an irrational physics and is likely to hold ideas as metaphysically primary.
In a way, physics and philosophy must always interact. By necessity, metaphysics influences one’s physics. There is no way around this.
But one has a choice.
One can consciously develop their philosophy, including their metaphysics thus consciously influence what kind of physics they would like to perform. Better yet, one can deliberately embrace a rational metaphysics and use it to try to develop a rational physics.
Or, one can deliberately embrace irrational philosophy and develop an irrational physics. Founders of modern physics, such as Bohr, Heisenberg and Einstein in his neo-Kantian youth, took this approach. We have seen the consequences of this approach and it has left modern physics in a crippled state.
No, I am saying that physics and philosophy must by necessity mix, in the sense that philosophy informs physics.
Also, you can use your philosophy to direct and correct your physics. If your physics clashes with rational philosophy, then your physics is in error and needs to be corrected.
No, philosophy has nothing to do with why the physical laws may be conservation symmetries. As it describes fundamental aspects of matter or the relationships between such, then that is a question for physics and/or mathematics to answer. Philosophy has nothing to say about specific scientific issues such as this.
Here is another answer:
“That would be like trying to mix water and oil or magnesium with gymnasium.”
Well, in a sense, this is true. Physics and philosophy are very different things. But I take it this answer is meant to imply that they are not compatible and that they should stay away from each other.
This expresses a fairly typical, although hardly universally accepted, view that physics and philosophy have no real relationship and that philosophy should stay away from physics and vice versa. I think we have seen that this is just not possible and not desirable in any case.
Not real? Well, they are not “real” numbers in the mathematical sense. They are no less “real” than any of the other “numbers”.
Indeed, one cannot count the imaginary numbers out on their fingers. They cannot get a ruler and measure out x imaginary units of length. This is because the concept of imaginary numbers is a higher-level concept and does not describe quantities that are so easily measurable as that.
All the same, the concept of imaginary numbers is important. Without it, certain kinds of attributes and relationships could not be quantified, particularly when it comes to certain areas of physics, engineering and mathematics. We simply have no other known way to calculate or express some of these quantities but to use imaginary numbers.
If you have studied engineering, then you probably know that a lot of important equations use imaginary numbers in order to quantify things or to help quantify things. You might hope to get real numbers out at some point, but that does not make imaginary numbers any less useful.
The non-imaginary numbers are simply conceptual units used to identify quantitative relationships. As are complex numbers. They are just somewhat less intuitive, but no more or less “real” than non-imaginary numbers are.
This part of one of the given answers is quite good:
“The word “imaginary” is not being used in the typical dictionary sense in which you seem to be talking [about] it. It has a purely technical meaning in the complex number context of mathematics. Perhaps it is unfortunate that that word was chosen as it causes so many people unnecessary concern.“
It would probably have been better had the word “imaginary” not been used. A better term which is also commonly used is that of a “complex” number.
I would argue that imaginary numbers are not actually numbers. What we are dealing with here is a concept of method that is used to help quantify things. Yes, they might be useful if you want to directly quantify the length of this or the weight of that, but they are important mathematical methods that can be used to quantify things and to measure real things.
Let’s not dismiss them just because of their unfortunate name.