I'm on the cover

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Originally Posted by mklotz

The second reason is more subtle. Most everything else to which students are exposed is "fuzzy". History can have different interpretations, art is in the eye of the beholder, literature has always been personal, and even language has many features open to personal interpretation. Math, on the other hand, is the first time they are exposed to something that has only one correct interpretation; no amount of argument or literary *****footing will change that. Many students can't deal with that level of absolutism; they feel their freedom is being constrained. As a result they retreat from the subject, never attempt to learn and end up being mentally paralyzed if they have to make change or double a recipe.

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Agreed; some of the absolutism of math is fascinating. Like the cosmological belief that even in a separate universe, where the laws of physics are different, the math describing those laws would be the same.

I grew up during the Cold War, and I had a great math teacher who was fond of telling his students that, unlike every other subject taught at school, "math was the same everywhere".

Then he would pause for effect and say: "even in Russia!"

One of the more fascinating physics-mathematics mind-benders is:

Is math purely a construct of the human mind used to describe the world in which we live

or

is math an integral part of the world in which we live and we are only discovering it bit by bit?

Consider this...

Gravity is perfectly described by a 1/r^2 (one over distance squared) law. If that exponent deviates from two by only a tiny fraction of a percent stable orbits of stars and planets are impossible and the universe could never maintain its form as it has for billions of years.

Did we just luckily create a law where that integer exponent was forced upon us or are we simply discovering that nature happens to use the same integers we developed back in the days when our math knowledge consisted of nothing more than arithmetic-counting the number of bushels of wheat delivered to the temple.

Not being a mathematician or a physicist my engineering brain says that all the "laws" are just useful models to be discarded or enhanced when we find a better one.
Personally I manage with the much simplified gravity model of "stuff falls down so wear shoes".

I was particularly annoyed by my first year electrical engineering mathematics who not only wanted me to memorise proofs of things like Laplace Transforms but waited 2 more years to explain how certain things were relavent to electrical engineering.

Rather than memorising proofs we'd have been better off learning when a Fourier transform is an insufficient approximation for moving between time and frequency and how Laplace could be used in those scenarios instead.

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Originally Posted by Workshopshed

Not being a mathematician or a physicist my engineering brain says that all the "laws" are just useful models to be discarded or enhanced when we find a better one.

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Reminds me exactly of this week's SMBC comic, and it's a good one:

https://www.homemadetools.net/forum/.../2015/12/4.png

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Originally Posted by Workshopshed

Not being a mathematician or a physicist my engineering brain says that all the "laws" are just useful models to be discarded or enhanced when we find a better one.

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Don't confuse the laws with the explanations of why the laws exist. The latter can and have changed but the former, most often derived from direct observation of nature, tend to remain.

Newton described gravity mathematically but couldn't provide a convincing explanation for its source. Over the years other explanations were offered and discarded. Einstein finally had to bend space and time to provide a source for the force and an explanation of why it seems to act instantaneously.

Through all that messing about the law itself remained unchanged. It's probably correct based on the observation that we can fire off satellites, sling them around planets and effect intersections with objects billions of miles away by using it in its ancient form.

It's a major tenet of physics that, if you come up with a new theory, it most properly encompass already existing laws that are known to be correct. Einstein's relativistic equations have to reduce to Newtonian mechanics when the velocities are appreciably less than the speed of light.