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The separation of math and physics is arbitrary at best and malicious at most. But the consequence of that separation is detrimental, logically invalid and physics controlled
Math, by definition, is not restricted or constrained by physical reality. Math is the studies of quantities, patterns and logical relationships, all of those are not restricted nor constrained by physical reality.
Physics are constantly being reshaped and advanced by mathematical developments/discoveries, as it's a specific application of math to the description of physical phenomena. But math goes necessarily beyond it.
You’re reversing cause and effect past addition of physical matter. You’re making assumptions and trying to get reality to fit inside those assumptions instead of making assumptions about reality. That’s a fallacy.. a closed loop trap that limits what physics can even ask
Physics and applied math can not ignore the ungrounded axioms of pure math because the entire system is build off of them. That bottlenecks, controls and limits physics. If you adopt a formal system, you automatically inherit every foundational rule that makes that system work
you’re committing serial reification and limiting/controlling physics through ungrounded axioms
You could be running in a trapped maze of a false axiom for thousands of years(it happened in history) and you wouldn’t even know because your axioms are untestable and protected by man made rules/dogma. This separation created a comical trap
Well, physics requires some sort of language that represents its own discoveries and relations. Math is exactly this. Since math is abstract, it necessarily precedes the application of a representational system derived from it, like physical descriptions.
See that I'm not saying that physical phenomena itself are preceded by math, but that physical descriptions must be preceded by the language that expresses them.
I don't concede that our understanding could ever be possibly changed in such a way that math becomes fundamentally different (1+1=2 will always be true, even if we find other symbols to use in the place of the symbols we currently use).
In any case, mathematics is discovered via physical reality, I agree, but that doesn't mean it is constrained by it. Only that physical reality operates via mathematically describable relations and operations.
Ok, see what you're saying. It becomes more of a philosophical preference, then, between saying that math is what it is because the physical reality exists as such, or that the physical reality is described as such because math couldn't possibly be different (which is my own position, as I lean into platonism).
There are forms of mathematics completely divorced from physical reality.
For example, 1+1=2 is defined such that it is conveniently aligned with physical intuition. However, you can define a field such that 1+1=0. This is a valid operation on a field defined over 0 and 1 but doesn't really make sense from a physical perspective.
This doesn't really clarify what you're trying to say. Are you saying that physicists shouldn't ignore the axioms of math that they apply to describe a physical system? If so, I don't think physicists really do that.
I’m saying physics is limited controlled and systematically trapped by definition from maths ungrounded axioms and arbitrary man made rules/ separation
Physics cant ignore maths ungrounded axioms
That bottlenecks, controls and limits physics. If you adopt a formal system, you automatically inherit every foundational rule that makes that system work
Ah, gotcha. Unfortunately, axioms are, by definition, untestable. The best that physics can do is test to see if the mathematics makes testable predictions, test those predictions, and see how they compare. That's good evidence that the math, including its axioms, are reasonable.
were not talking about proving axioms here though with absolute proof. Were talking about using reality to make an assumption(grounded) vs just an assumption (ungrounded)
grounded assumptions grant a conclusion you can eventually empirically test.
Ungrounded assumptions grant a conclusion you can’t even test empirically.
That’s a massive problem. You can’t even test an ungrounded assumptions conclusion. and again this controls and limits applied math & physics
youre acting as if youre forced to use ungrounded assumptions.. that is not the case
youre using utility and consitency as defense while consitency and utility can still work inside of a false axiom. You cant use utility as defense for this
theyre not grounded in reality because youre working with assumptions applied to reality instead using reality to make an assumption. Thats reversing cause and effect
There's no such thing as a true or false axiom. That's why they're called an axiom. They're just things we assume about the mathematical constructs we study and then deploy on physical problems.
The problem with using physical reality to drive assumptions is that you're ultimately limited to very basic models if you do that (if you can even generate a model at all).
I saw that you edited one of your comments earlier in this thread to give examples of ungrounded assumptions, which include 0 and infinity. It's pretty wild that 0 is included here, because it's literally the definition of nothing. You can have 0 apples, which I find is a pretty reasonable grounding for 0. While infinity isn't "real" (in fact no math is real), it is still extremely useful in physics as a limit for spatial or temporal dimensions. Use of this limit produces real, testable predictions from fluid mechanics to statistical mechanics and beyond.
If you have a rebuttal to anything said in this post state it if you don’t move on
So far we’ve only had derailments in this post (people trying to use utility and consistency as a defense, and using rules from inside the system as a defense against an audit of the system and it’s axioms) and it’s kind of scary that bullshit gets upvoted
We can't even do Newton's gravitational theory without calculus. And we can't do calculus without infinitesimals. Come back when you've found empirical evidence of an infinitesimal. Pics or it didn't happen.
Physics trumps theoretical mathematics every time. If the physics says “we can move a specific distance in a specific amount of time” then that’s what will happen. No math theorem will disprove that.
grounded assumptions grant a conclusion you can eventually empirically test.
Ungrounded assumptions grant a conclusion you can’t even test empirically.
That’s a massive problem. You can’t even test an ungrounded assumptions conclusion. This controls and limits applied math & physics. You cant ignore pure math axioms in applied math because the entire math is built on them.
If this was an honest system they wouldn’t funnel you into this system from birth without teaching you about grounding(whether your abstraction refers to objective observable reality, ie physical matter) or questioning its starting assumptions first
Now what is a grounded assumption? the abstraction must map back to objective observable physical matter not another mental concept. And all we have observed is physical matter as one unified thing. Absolute nothingness has never been observed in the history of man kind.
using observable objective reality to make assumption (grounded) vs just an assumption (ungrounded)
number of physical object: mental group of physical matter (grounded)
math group: mental group of mental group (ungrounded)
people dying in war: mental group of physical matter (grounded)
nationalism: mental group of mental group (ungrounded)
magical unicorn: mental group of mental group (ungrounded)
effects of gravity: mental group of physical matter (grounded)
The assumptions of 0 infinity and groups are logically the same as magical unicorns existing. A magical unicorn can provide utility and consistency. You have to completely change how you see these things. If this was an honest system they would first teach what is objective observable reality and what is a mental concept. They don’t
Moriturism | a day ago
Math, by definition, is not restricted or constrained by physical reality. Math is the studies of quantities, patterns and logical relationships, all of those are not restricted nor constrained by physical reality.
Physics are constantly being reshaped and advanced by mathematical developments/discoveries, as it's a specific application of math to the description of physical phenomena. But math goes necessarily beyond it.
[OP] Oreeo88 | a day ago
You’re reversing cause and effect past addition of physical matter. You’re making assumptions and trying to get reality to fit inside those assumptions instead of making assumptions about reality. That’s a fallacy.. a closed loop trap that limits what physics can even ask
Physics and applied math can not ignore the ungrounded axioms of pure math because the entire system is build off of them. That bottlenecks, controls and limits physics. If you adopt a formal system, you automatically inherit every foundational rule that makes that system work
you’re committing serial reification and limiting/controlling physics through ungrounded axioms
You could be running in a trapped maze of a false axiom for thousands of years(it happened in history) and you wouldn’t even know because your axioms are untestable and protected by man made rules/dogma. This separation created a comical trap
Moriturism | a day ago
Well, physics requires some sort of language that represents its own discoveries and relations. Math is exactly this. Since math is abstract, it necessarily precedes the application of a representational system derived from it, like physical descriptions.
See that I'm not saying that physical phenomena itself are preceded by math, but that physical descriptions must be preceded by the language that expresses them.
fudge_mokey | a day ago
> Math, by definition, is not restricted or constrained by physical reality.
Why is 1+1=2?
Because that's how physical reality works.
All of math is based on our understanding of physical reality.
If our understanding changed (or we went somewhere else with different laws of physics), then math would be different as well.
Moriturism | a day ago
>Why is 1+1=2?
Because that's that mathematics define as true.
I don't concede that our understanding could ever be possibly changed in such a way that math becomes fundamentally different (1+1=2 will always be true, even if we find other symbols to use in the place of the symbols we currently use).
In any case, mathematics is discovered via physical reality, I agree, but that doesn't mean it is constrained by it. Only that physical reality operates via mathematically describable relations and operations.
fudge_mokey | a day ago
> Because that's that mathematics define as true.
Sure, and why did they define it that way? Why not create a system of mathematics where 1+1=4 or 2*2=8?
Because then it would no longer correspond to our physical reality.
If our understanding of physical reality changes, then our understanding of the corresponding mathematics would necessarily change as well.
Since our understanding of physical reality is fallible, then our understanding of mathematics is fallible as well.
For more detail you can see Chapter 10 of Fabric of Reality by David Deutsch.
Moriturism | a day ago
Ok, see what you're saying. It becomes more of a philosophical preference, then, between saying that math is what it is because the physical reality exists as such, or that the physical reality is described as such because math couldn't possibly be different (which is my own position, as I lean into platonism).
darkerthanblack666 | a day ago
There are forms of mathematics completely divorced from physical reality.
For example, 1+1=2 is defined such that it is conveniently aligned with physical intuition. However, you can define a field such that 1+1=0. This is a valid operation on a field defined over 0 and 1 but doesn't really make sense from a physical perspective.
Thelonious_Cube | 11 hours ago
> All of math is based on our understanding of physical reality.
Math is not grounded empirically.
If I put a marble in an empty bag, then put in a 2nd marble and pour out three marbles, what would you conclude?
You would never conclude that "sometimes 1 + 1 = 3"
No empirical evidence would ever show that 1 + 1 = 3
[OP] Oreeo88 | a day ago
>past addition of physical matter
We are talking about past addition of physical matter. when ungrounded axioms and assumptions are introduced (0, infinity, groups)
darkerthanblack666 | a day ago
This doesn't really clarify what you're trying to say. Are you saying that physicists shouldn't ignore the axioms of math that they apply to describe a physical system? If so, I don't think physicists really do that.
[OP] Oreeo88 | a day ago
I’m saying physics is limited controlled and systematically trapped by definition from maths ungrounded axioms and arbitrary man made rules/ separation
Physics cant ignore maths ungrounded axioms
That bottlenecks, controls and limits physics. If you adopt a formal system, you automatically inherit every foundational rule that makes that system work
darkerthanblack666 | a day ago
Ah, gotcha. Unfortunately, axioms are, by definition, untestable. The best that physics can do is test to see if the mathematics makes testable predictions, test those predictions, and see how they compare. That's good evidence that the math, including its axioms, are reasonable.
[OP] Oreeo88 | a day ago
were not talking about proving axioms here though with absolute proof. Were talking about using reality to make an assumption(grounded) vs just an assumption (ungrounded)
grounded assumptions grant a conclusion you can eventually empirically test.
Ungrounded assumptions grant a conclusion you can’t even test empirically.
That’s a massive problem. You can’t even test an ungrounded assumptions conclusion. and again this controls and limits applied math & physics
youre acting as if youre forced to use ungrounded assumptions.. that is not the case
darkerthanblack666 | a day ago
Yeah, well, physics is interested in testable conclusions by and large. In which case, most axioms in physics are grounded by your definition.
[OP] Oreeo88 | a day ago
youre using utility and consitency as defense while consitency and utility can still work inside of a false axiom. You cant use utility as defense for this
theyre not grounded in reality because youre working with assumptions applied to reality instead using reality to make an assumption. Thats reversing cause and effect
darkerthanblack666 | a day ago
There's no such thing as a true or false axiom. That's why they're called an axiom. They're just things we assume about the mathematical constructs we study and then deploy on physical problems.
The problem with using physical reality to drive assumptions is that you're ultimately limited to very basic models if you do that (if you can even generate a model at all).
I saw that you edited one of your comments earlier in this thread to give examples of ungrounded assumptions, which include 0 and infinity. It's pretty wild that 0 is included here, because it's literally the definition of nothing. You can have 0 apples, which I find is a pretty reasonable grounding for 0. While infinity isn't "real" (in fact no math is real), it is still extremely useful in physics as a limit for spatial or temporal dimensions. Use of this limit produces real, testable predictions from fluid mechanics to statistical mechanics and beyond.
Thelonious_Cube | 11 hours ago
You keep repeating this, but it means nothing
[OP] Oreeo88 | 3 hours ago
youre saying nothing
If you have a rebuttal to anything said in this post state it if you don’t move on
So far we’ve only had derailments in this post (people trying to use utility and consistency as a defense, and using rules from inside the system as a defense against an audit of the system and it’s axioms) and it’s kind of scary that bullshit gets upvoted
onehasnofrets | a day ago
We can't even do Newton's gravitational theory without calculus. And we can't do calculus without infinitesimals. Come back when you've found empirical evidence of an infinitesimal. Pics or it didn't happen.
jeffcgroves | a day ago
The fact that math can exist without physical reality is what makes it superior, in my opinion
Alan_Watts_Gong | a day ago
Physics trumps theoretical mathematics every time. If the physics says “we can move a specific distance in a specific amount of time” then that’s what will happen. No math theorem will disprove that.
[OP] Oreeo88 | a day ago
grounded assumptions grant a conclusion you can eventually empirically test.
Ungrounded assumptions grant a conclusion you can’t even test empirically.
That’s a massive problem. You can’t even test an ungrounded assumptions conclusion. This controls and limits applied math & physics. You cant ignore pure math axioms in applied math because the entire math is built on them.
If this was an honest system they wouldn’t funnel you into this system from birth without teaching you about grounding(whether your abstraction refers to objective observable reality, ie physical matter) or questioning its starting assumptions first
[OP] Oreeo88 | a day ago
Now what is a grounded assumption? the abstraction must map back to objective observable physical matter not another mental concept. And all we have observed is physical matter as one unified thing. Absolute nothingness has never been observed in the history of man kind.
using observable objective reality to make assumption (grounded) vs just an assumption (ungrounded)
number of physical object: mental group of physical matter (grounded)
math group: mental group of mental group (ungrounded)
people dying in war: mental group of physical matter (grounded)
nationalism: mental group of mental group (ungrounded)
magical unicorn: mental group of mental group (ungrounded)
effects of gravity: mental group of physical matter (grounded)
The assumptions of 0 infinity and groups are logically the same as magical unicorns existing. A magical unicorn can provide utility and consistency. You have to completely change how you see these things. If this was an honest system they would first teach what is objective observable reality and what is a mental concept. They don’t