# Simple but logical expanations have legs

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Mathematics alone, and math was my major in college, gives you little or no insight into what is happening. What would be the logical basis for SR, GR, or QM if there was an aether made up of dark matter, for instance.

I believe that the ultimate understanding of something in physics comes from an understanding of the math.

For example, you might say "The power density of a sound wave decreases as it expands" and that might give you a grade-school understanding of it, with very limited usefulness.

Or you could say "The power density of a sound wave is proportional to 1/r^2" and that gives you a precise and useful mathematical understanding of it, but you might not know why it is so.

Or you could say "The power of a sound wave propagating as a spherical shell remains the same as the sphere expands, and is spread evenly across the surface area of the sphere," but you might not know that surface area is proportional to r^2.

The last two statements say the same thing, and they are both mathematical (area is a geometrical concept which is mathematical).

Using just numbers and equations might work well but leave you unenlightened; using just words may give you knowledge without being able to apply it. Having the math and understanding why it works is in my opinion the essence of true understanding.

That said, it must be noted that physics can progress just fine without knowing why the equations correspond to reality. Observations still give you useful data, and those data can be used to evaluate the equations and suggest new ones. I do believe that knowing "why" (and having logical explanations to go along with the math) does provide extra insights that suggest new ideas which lead to new experiments, observations, and theories. Logical explanations are a bonus; the math is required.

Edited by md65536

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I believe that the ultimate understanding of something in physics comes from an understanding of the math.

For example, you might say "The power density of a sound wave decreases as it expands" and that might give you a grade-school understanding of it, with very limited usefulness.

Or you could say "The power density of a sound wave is proportional to 1/r^2" and that gives you a precise and useful mathematical understanding of it, but you might not know why it is so.

Or you could say "The power of a sound wave propagating as a spherical shell remains the same as the sphere expands, and is spread evenly across the surface area of the sphere," but you might not know that surface area is proportional to r^2.

The last two statements say the same thing, and they are both mathematical (area is a geometrical concept which is mathematical).

Using just numbers and equations might work well but leave you unenlightened; using just words may give you knowledge without being able to apply it. Having the math and understanding why it works is in my opinion the essence of true understanding.

That said, it must be noted that physics can progress just fine without knowing why the equations correspond to reality. Observations still give you useful data, and those data can be used to evaluate the equations and suggest new ones. I do believe that knowing "why" (and having logical explanations to go along with the math) does provide extra insights that suggest new ideas which lead to new experiments, observations, and theories. Logical explanations are a bonus; the math is required.

Physics as a science is often theoretical concerning its equations, but it is primarily math. Physics concerning its definition is:

The branch of science concerned with the nature and properties of matter and energy. The subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.

....Using just numbers and equations might work well but leave you unenlightened.

I agree very much with this quote of yours. I think that an understanding of reality should be an important goal of explanations in physics, even when such explanations explain a number of possibilities -- which I think is preferable to one illogical explanation.

Your above explanations of the related equations are logical, and therefore will probably always be part of a standard explanation, and you probably did not copy it, but explained it based upon your insight alone

I believe illogical explanations, on the other hand, are strong indications that they do not know what they are talking about even though the math is reliable -- Quantum Theory comes to mind

Edited by pantheory
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ajb,

....The point being if one were to follow Occam's razor to the letter then I expect that progress in physics would be slowed down. One has to allow a bit of imagination in physics. This is particularly true when probing the frontiers of knowledge.

I don't think Occam's Razor should be followed as the ultimate guide concerning theory, but if more consideration were given to it over the years, I believe we would be farther ahead concerning our understandings of reality.

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