What is a Law of Nature?

A little bit of humility goes a long way. Mathematics, as a field of study, is built upon axioms, definitions, and logical reasoning. It is a rigorous and systematic approach to understanding patterns, quantities, and structures, and it is not something that can be "broken" in the traditional sense.

The problem is, as you must realise, is that those mathematical structures are then used to model something - and they only model that something inexactly. If you observe a reasonable correspondence between a theory and experiment over the range of the solar system, there is no axiom that lets you extend that relationship out to the galaxy or to the whole universe, or back in time to the supposed big bang.

As I have tried to point out here, even humanity's past experience of physics tells us that. The gas laws were (and still are) inexact, but useful within a limited domain.

It is not the mathematics that becomes 'broken' but the slavish assumption that the maths holds right back to time zero that is broken.

David

The notion that the natural laws are "habits" of nature seems to me to be incompatible with the notion that based on observation the natural laws were designed by an extreme intelligence or multiple extreme intelligences, since habits are arrived at merely by repetition and resultant ingraining in behavior from some random or indeterminate beginning.

I would have to disagree... I wouldn't define "habits" as merely being about repetition, as I think we come born with a number of instinctual habits, psychological and physical. That is to say... they have an initial state, but can be altered. That is, they are not set in stone, therefore are not "laws" that can be violated.

Rupert Sheldrake discovered that the speed of light had changed slightly over a period of time, which is why he developed the concept of them being more akin to "habits" than "laws". It's just seems to be a good-enough bit of terminology to describe patterns of how physical stuff can seemingly change.

Telekinesis appears to "violate" the "laws" of nature, for example. By the use of mind to affect physical stuff.

A little bit of humility goes a long way. Mathematics, as a field of study, is built upon axioms, definitions, and logical reasoning. It is a rigorous and systematic approach to understanding patterns, quantities, and structures, and it is not something that can be "broken" in the traditional sense.

Yes, but that doesn't mean mathematical equations can't be abused and misused for the purposes of careerism.

Mathematics isn't some perfect, pure thing that cannot be corrupted.

When I talk about "mathematics", I'm talking about the mathematical equations being broken.

I thought that may have been obvious, but alas, maybe I have to be brutally explicit in future...

As I have tried to point out here, even humanity's past experience of physics tells us that. The gas laws were (and still are) inexact, but useful within a limited domain.
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This doesn’t mean an exact equation doesn’t exists (or that it can’t be found). You have provided the ideal gas law, PV = nRT, a couple of times as an example. This is a very simple equation which probably is high school curicullum in the UK as well as it is in Denmark. The ideal gas law is not exact, but it is a good approximation for many gases under a wide range of conditions. To account for more advanced conditions than ideal gas behavior, one can use more advanced gas laws, such as the Van der Waals equation or the virial equation. These models account for intermolecular forces and the actual volume of gas particles, providing more accurate results under conditions where the ideal gas law is not a suitable approximation.

This doesn’t mean an exact equation doesn’t exists (or that it can’t be found). You have provided the ideal gas law, PV = nRT, a couple of times as an example. This is a very simple equation which probably is high school curicullum in the UK as well as it is in Denmark. The ideal gas law is not exact, but it is a good approximation for many gases under a wide range of conditions. To account for more advanced conditions than ideal gas behavior, one can use more advanced gas laws, such as the Van der Waals equation or the virial equation. These models account for intermolecular forces and the actual volume of gas particles, providing more accurate results under conditions where the ideal gas law is not a suitable approximation.

Exactly, now do you see the analogy with what has happened cosmology. The only real difference is that we don't (yet) know about all the confounding factors - like intermolecular forces for example. We assume that NG/GR applies everywhere and that therefore there has to be dark matter!

This is a very perverse way of looking at the problem. I chose PV=nRT (I'll include the n if you like, PR=RT implicitly relates to 1 mole of gas) because we can look back on all the complications which prevented that beautiful equation, among others, applying universally. When it comes to cosmology we can't do the analogous extreme experiments, so we don't know what complications exist when we scale up from the solar system (where I believe there are already hints at complications coming from the motion of the Voyager spacecraft as they fly away from the solar system) to the scale of even one galaxy - so conventional science has blithely assumed that nothing will complicate this massive extrapolation.

David

Exactly, now do you see the analogy with what has happened cosmology. The only real difference is that we don't (yet) know about all the confounding factors - like intermolecular forces for example. We assume that NG/GR applies everywhere and that therefore there has to be dark matter!

This is a very perverse way of looking at the problem. I chose PV=nRT (I'll include the n if you like, PR=RT implicitly relates to 1 mole of gas) because we can look back on all the complications which prevented that beautiful equation, among others, applying universally. When it comes to cosmology we can't do the analogous extreme experiments, so we don't know what complications exist when we scale up from the solar system (where I believe there are already hints at complications coming from the motion of the Voyager spacecraft as they fly away from the solar system) to the scale of even one galaxy - so conventional science has blithely assumed that nothing will complicate this massive extrapolation.

David

As stated earlier I share your suspicision that Big Bang didn't happen for the same reason you mention here regarding the "extrapolation fallacy". This is not the same as stating that "there is zero evidence for the Big Bang".