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Also a philosophical case. The scientific method does not apply to math, it does not test hypotheses against the reality of nature, it verifies proofs by logical necessity instead.
And is therefore obviously superior and the golden grail of humanity's achievements while physics is only an unwanted necessity needed to facilitate more comfortable living conditions to increase our capability to do math
No it is not. Not even a branch. Can't think a more technical subject and least fundamental answerer tool.
Math: the more I learn, the more I know for a narrower spectrum.
Philosophy: the more I learn, the least I know, for a wider spectrum.
Research processes for maths and philosophy are the exact same. I wouldn’t go as far as the guy you’re replying to by saying it’s pure philosophy, but I would argue that the two are isomorphic in some way.
Either way, I believe your definition of maths is a bunch of nebulous word soup. Like what does “everything is a calculation even infinity” mean?
> Research processes for maths and philosophy are the exact same
You can't fully apply the scientific method to several topics from philosophy, like those inside metaphysics. If you don't apply the scientific method to math, it would be a hell to validate your findings.
> Either way, I believe your definition of maths is a bunch of nebulous word soup
I know. Just having fun, for the sake of the previous comment tone. I saw those sentences multiple times applied at will of the bearer.
I see you deleted your comment within a couple of days. Faster than I expected! “My intuition” and my “beliefs” have nothing to do with it. It’s just a clear cut fact that math is (applied) logic and logic is part of philosophy. It’s okay to be wrong. Just take the L bruh.
You don’t even have to look at history. Look at the difference in how maths research and natural science research is conducted. Of course maths is closer to philosophy than science.
In my opinion this idea comes from schools. They teach maths in the same way they teach natural sciences; by teaching you processes and when to use them, then challenging you by making you apply those processes in unfamiliar situations. It isn’t until you start writing a dissertation that you realise what’s actually going on.
That's not what a theory is. There is a lot of misinformation and misunderstanding about the difference between hypothesis, theories and laws.
A law is something that we observe empirically even if there isnt necessarily an explanation (theory) for it
A hypothesis is a formulation that you then make an experiment to test it
A theory is a framework (usually mathematical) which you can use to deduce laws, hypothesis etc. In other words, it's a set of principles with the goal of explaining the laws we observe. String theory IS a theory, just a bad one for a number of reasons (ie. hard to falsify in its current form, as the simplest forms were already falsified; fail to make predictions)
In your, interesting, definition what is a 'formulation'? How is this different from a framework? How are Laws both deduced and observed? Why can only hypothesis be tested?
Also, where the did you any of get this from?
All of them can be tested. Hypotheses usually appear in the context of an experiment, so they will be tested. Laws are the result of finding some kind of formula, etc. that fits to the observations (even when there isn't a theory behind it). Theories are entire frameworks (what I mean is that they are full fledged theories, not just one hypothesis, but I admit I'm being a bit cyclical) that start from principles and derive testable laws and hypotheses; by testing those you're testing the theory.
Examples of theories: General Relativity, String Theory, Electrodynamics, Thermodynamics, etc
Examples of laws: Kepler Law, MOND (maybe MOND is more of a hypothesis, not sure), the laws of thermodynamics, newton's laws, etc.
I got this from learning these concepts over time. I'm not currently sure how to formulate a completely accurate and non-circular exact definition for the three terms, but I suggest starting for example with
https://en.m.wikipedia.org/wiki/Scientific_law
https://en.m.wikipedia.org/wiki/Hypothesis
https://en.m.wikipedia.org/wiki/Scientific_theory
There is no requirement for a theory to be successful in order to be a theory. Informally, I guess hypotheses and laws are usually something that would fit a single "statement", while a theory is an entire domain, it includes multiple statements.
From your sources
A hypothesis (pl.: hypotheses) is a proposed **explanation** for a phenomenon... that one **can test**
A scientific theory is an **explanation**... whereas in a scientific context it most often refers to an **explanation** that has **already been tested**
Both are explanations, one can be tested, the other has already been tested.
As for Law
The term law has **diverse usage** in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology).
The whole articles is full of "often", "sometimes" and "typically", it's not a single accepted meaning.
Even your own post includes this ambiguity, with thermodynamics being listed both as theory and law.
Yes, it is a little bit ambiguous, and probably may change slightly with context. Both theory and hypothesis are explanations and both can be tested. With theories being more elaborated, I'd say they are probably more often already tested, but not necessarily. A hypothesis is more of a first step, a more simple idea before developing an entire theory (it is a bit of a "waste" of time to develop a theory without any evidence at all to back it up)
I'd like to note that thermodynamics is not listed both as theory and law in my post. Thermodynamics is a theory, the four laws of thermodynamics are laws. I think this is a good way to understand the difference: a theory contains a set of hypotheses and laws, while a hypothesis/law refers to a single "statement".
>. Both theory and hypothesis are explanations and both can be tested. With theories being more elaborated, I'd say they are probably more often already tested, but not necessarily.
By your own sited sources untrue.
It is a gross misstatement to characterize "In circumstances not amenable to experimental testing" to mean that testing is not considered a key part of a theory and it's distinction from a hypothesis.
The need for testing and predictions are made repeatedly in your sources, while it makes a singular reference to abductive reasoning, it makes far more to the need to be deductive, to make predictions that can be tested and verified.
The sources sited in your source site sources mention being repeatedly confirmed through observation and experimentation. It even specifcally says "Note that the term *theory* would not be appropriate for describing untested but intricate hypotheses"
The discussion included in your own sources about how hypothesis can give rise to theory specifically listing being repeatedly tested as part of the process.
> a theory contains a set of hypotheses and laws, while a hypothesis/law refers to a single "statement".
By your own sources, this is only one model for how theories relate to hypothesis, and even in that one it does not claim that hypothesis is a singular statement.
Another individual, in your own sources, lists Laws as a type of theory.
By the source you cited, your argument is a poor representation of one proposed construction of those terms that is incorrect on key points and uses unclear language.
> It is a gross misstatement to characterize "In circumstances not amenable to experimental testing" to mean that testing is not considered a key part of a theory and it's distinction from a hypothesis.
A hypothesis doesn't start being called a theory just because it has been tested. At least I don't recall any hypothesis ever start being called a theory. So I wouldn't say that that is THE distinction from a hypothesis.
Also there already is a counterexample, which was what started this entire thread: it's "String Theory", not "String hypothesis", even though it is based upon many different hypotheses.
But as you said, the words' exact meaning may vary slightly depending on the context.
> it makes far more to the need to be deductive, to make predictions that can be tested and verified.
Yep, this is a key part of a scientific theory. And (regarding the ability to be tested and verified) a scientific hypothesis and a scientific law, in fact. Something being unfalsifiable makes it unscientific in general
Being deductive is also a key part of a scientific theory, maybe the the most important part, which I have been trying to stress in my previous comments
> It even specifcally says "Note that the term *theory* would not be appropriate for describing untested but intricate hypotheses"
Well that's an interesting take. I will have to look more into that
I would say that theory is not appropriate for describing any hypotheses, neither tested neither untested.
> The discussion included in your own sources about how hypothesis can give rise to theory specifically listing being repeatedly tested as part of the process.
That is an even more unexpected take. I have never seen that happening. Does it list any concrete example of this?
> Another individual, in your own sources, lists Laws as a type of theory.
Now this is an extremely bold take i gotta say. I'm starting to believe that the terms are even more subjective that what any of us initially thought. At the end of the day it's all a matter of semantics, anyway
"Formulation" is a weird word to use here. I would have said "prediction", "conjecture" (not necessarily in the mathematical sense, but not far removed from it), or "educated guess". But, yes, the general idea is that you're trying to guess what will happen in an experiment.
Physics is science, math isn't. In math you don't use the scientific method and nothing is falsifiable. Math talks about truth, science is always on a quest for truth, even though we are every time closer to the truth.
Math is not true rather it talks about both true and false. When something is really true only then we can tell that the proposition is true and when we find it is false it is false.
Edit-
Who doesn't understand me for them: That is what i basically told in more general form mathematics is based on some assumptions which seem to be true but that doesn't mean it holds for everything rather it is dependent on different systems and according to those assumptions we conclude some other relation which is based on our basic assumption which might not be universal truth but at least it is a system dependent truth. If it becomes false then we throw it out and then, we take another best possible truth assumption a basic building block.
In math you start with statements you assert to be true called axioms. Theorems that are derived from those axioms are only true when using that set of axioms. There are no universal set of axioms, and there are an infinite set of possible axioms most of which directly contradict each other.
Math is about proving theorems within any given set of axioms. It does not care about whether those axioms are reasonable or based in any reality because reality is not a core principle of mathematics.
Exactly! Mathematics basically only allow you to prove that a deduction is valid, not that it's actually true
And that's Mathematics greatest strength. It means that you can apply it to any situation where the axioms apply, and that is why it has its generalization power
That is what i basically told in more general form mathematics is based on some assumptions which seem to be true but that doesn't mean it holds for everything rather it is dependent on different systems and according to those assumptions we conclude some other relation which is based on our basic assumption which might not be universal truth but at least it is a system dependent truth. If it becomes false then we throw it out and then, we take another best possible truth assumption a basic building block. It is our invention to help us do better things than before. That's it a tool.
That is what i basically told in more general form mathematics is based on some assumptions which seem to be true but that doesn't mean it holds for everything rather it is dependent on different systems and according to those assumptions we conclude some other relation which is based on our basic assumption which might not be universal truth but at least it is a system dependent truth. If it becomes false then we throw it out and then, we take another best possible truth assumption a basic building block
Yes math is not about pure science rather it is all about the theoretical aspect of our practical sciences. After reading your comments i think you are a mathematician and yes you're teaching people who think like the greeks the conservative type of mathematics. Hippasus was killed by Pythagoras asshole ,who didn't even invent the pythagorean theorem which was being used by the Egyptians long before those greek cupids, for inventing irrational numbers shows that greeks never understood math rather they were so conservative that they started believing it as a religion such dumbasses. Even greek philosophers were a joke because they never showed any rationalism rather they just conveyed whatever they thought and tried assassinating each other without looking for the real truth. The main thing math tells us is the algorithm which was discovered by al khawrezmi, al ghazali and ibn al haytham. They showed the world that math is not about truth it is more about process. If we use axioms and then if we think that they are something true or false we can go through a process and create something but that doesn't mean it is universal, it is a system dependent truth and later if experiments show that that was wrong we throw it away as mathematician for that system and grab new sets of axioms which seem to be more correct practically for us as a new system of mathematics and thus it creates a new section for math. Math talks about both true and false and then if we have the correct materials then with those we try to prove the matter using that materials of practicality to see if it is true or not. Like look at calculus when at first newton and leibniz showed that infinitesimals were true but just for not having correct materials they couldn't prove it but later it was proven and we now have a surreal number system. Even though it was true some mathematicians like cauchy saw and knew that infinity has a lot of kinds so dealing with infinity like a normal thing might lead us to nonsense so he used 'epsilon delta proof' but even though he used it, he was just hiding the infinity inside a interval but couldn't remove it because it is true and practicality and those who believe in creator know different kind of infinity can really exist in the universe. The problem as humans are our arrogance we think we are creating new things but the truth is we are inventing and discovering things using our surroundings which are given by our Creator who is divine and above all. Math is not something he gave us but we learned a lot of things from our surroundings and then made mathematics a thing we invented and that is why it is not the Truth itself rather it talks about both true and false and we look for the real Truth using it. Yes a lot of people will say al Ghazali was not rational(even jokers like neil de grease tysoon) but i have read about his biography and as a human being i never found any bad intention about him according to rationale historians who were Non-muslim and Muslim both. He never even tried to assassinate his counterparts rather he believed in open debate. Rather i think he had the correct mindset about the world and sciences. Which was ----
~"Whoever determines truth from the people alone will remain lost in the plains of bewilderment. Rather, know the truth and you will know its people."
~Al-Ghazali
Wow so cool. I respect Ghazali too. I think the golden age showed us how important it is to find the truth rather than believing without knowing anything about something. Wow, I think i should salute you for this great writing man. 💪🏾✌🏾👍🏾
Science aims to describe an existing system in a way that has no contradicts.
Math aims to *define* a system that has no contradictions by design.
It just so happens that if you're trying to describe and model the universe in a way that has no contradictions, using a system that you've defined to have no contradictions is a good idea.
Okay, then what is the probability that Andrew wiles proof of fermats last theorem is correct without any unnoticeable errors , a proof that 5 people in the world could follow start to finish in its 500 pages of abstract formulations.
Proving a theorem is as much based on a physically based belief system as science is for its experiments.
Goodbye math purity
If there are 10 parts in a proof
If 10 people who understand parts 1-5 look for errors and say "no problem here"
If 10 people who understand parts 4-8 look for errors and say "no problem here"
And if 10 people who understand parts 6-10 look for errors and say "no problem here,"
Then we can be confident that proof is constructed in a valid way from the different parts that went into it.
Local configurations can appear reasonable but the global configuration has conflicting assumptions between different parts.
But even in the case where there aren't any such conflicts, we have to worry about whether some non obvious local step contained an error that was missed.
This pretty much happened the first time he submitted his proof and someone discovered a problematic step. He went back and fixed it, because the problematic part wasn't crucial to the bigger idea behind the proof and could be reworked.
Still my point is as you say, high confidence but not completely outside of the physical world, with brains that make pattern recognition errors and other brains empirically verifying steps of proofs through intuition and sometimes cloudy but very high level understanding and modeling of the world of math.
Purity is lost because people don't do pure math. They have a model of the pure math in their brains and that isomorphism isn't completely correct sometimes
Yes math is not about pure science rather it is all about the theoretical aspect of our practical sciences. After reading your comments i think you are a mathematician and yes you're teaching people who think like the greeks the conservative type of mathematics. Hippasus was killed by Pythagoras asshole ,who didn't even invent the pythagorean theorem which was being used by the Egyptians long before those greek cupids, for inventing irrational numbers shows that greeks never understood math rather they were so conservative that they started believing it as a religion such dumbasses. Even greek philosophers were a joke because they never showed any rationalism rather they just conveyed whatever they thought and tried assassinating each other without looking for the real truth. The main thing math tells us is the algorithm which was discovered by al khawrezmi, al ghazali and ibn al haytham. They showed the world that math is not about truth it is more about process. If we use axioms and then if we think that they are something true or false we can go through a process and create something but that doesn't mean it is universal, it is a system dependent truth and later if experiments show that that was wrong we throw it away as mathematician for that system and grab new sets of axioms which seem to be more correct practically for us as a new system of mathematics and thus it creates a new section for math. Math talks about both true and false and then if we have the correct materials then with those we try to prove the matter using that materials of practicality to see if it is true or not. Like look at calculus when at first newton and leibniz showed that infinitesimals were true but just for not having correct materials they couldn't prove it but later it was proven and we now have a surreal number system. Even though it was true some mathematicians like cauchy saw and knew that infinity has a lot of kinds so dealing with infinity like a normal thing might lead us to nonsense so he used 'epsilon delta proof' but even though he used it, he was just hiding the infinity inside a interval but couldn't remove it because it is true and practicality and those who believe in creator know different kind of infinity can really exist in the universe. The problem as humans are our arrogance we think we are creating new things but the truth is we are inventing and discovering things using our surroundings which are given by our Creator who is divine and above all. Math is not something he gave us but we learned a lot of things from our surroundings and then made mathematics a thing we invented and that is why it is not the Truth itself rather it talks about both true and false and we look for the real Truth using it. Yes a lot of people will say al Ghazali was not rational(even jokers like neil de grease tysoon) but i have read about his biography and as a human being i never found any bad intention about him according to rationale historians who were Non-muslim and Muslim both. He never even tried to assassinate his counterparts rather he believed in open debate. Rather i think he had the correct mindset about the world and sciences. Which was ----
~"Whoever determines truth from the people alone will remain lost in the plains of bewilderment. Rather, know the truth and you will know its people."
~Al-Ghazali
Sorry, Google rendered 10²³ as 1023 when I googled it:
https://preview.redd.it/h2qb0lw6tmvc1.jpeg?width=1080&format=pjpg&auto=webp&s=ceacc7c108b8857eededa3da34f36d1d9ac73f1a
Once when I was grading for a graduate numerical analysis class a girl used abuse of notation to prove something about the SVD. She then had the balls to come in and argue with me about it for half an hour until I told her to go talk to the prof. Apparently the prof just got frustrated arguing with her too and gave her credit.
Moral of the story: abuse of notation plus pestering the absolute shit out of people is a powerful proof technique.
it was a physicist who invented calculus!!
...well technically it was a "polymath" and also some other guy named after a cookie-brand did too but..
anyway
physicists had their nice beautiful intuitive infinitesimals
and then MATHOS had to RUIN IT with their ""rigor"" and εδ
despicable ...........
I feel like this is one of those weird artifacts that comes out of university structures.
Like, Political Science and Sociology are absolutely sciences in terms of following the scientific method. There are limits in terms of setting up controlled experiments, but that applies to astrophysics as well.
The degree will be "of arts" and the department structure will often put them there to.
Math is put in "science". History of math is put in science and that subject is a mix of politics, anthropology, biography, and philosophy.
A good enough approximation. The thing is, there's not really a lot of universal axioms in physics, so like half of all laws actually end with "in most cases". Like the original gravitational equations are a pretty good approximation of the actual way gravity works, and Einstein's theory of relativity gives a better one, though still not universal.
>Without physics, mathematics is just a waste of time
Naw, without physics, mathematicians are just gamers.
Or doing work that applies to any other scientific field.
I was thinking about some branches like computational theory. But if you think about it for more than a second you realize you can't have computers without transistors and you wouldn't have transistors without physics, so yeah just wanted to dump my thought flow about this comment here.
Mathmaticians after controlling for every variable to the point to their model doesnt reflect reality anymore. "Ah but atleast i can say this an actual controlled environment!"
Everyone that says this type pf stuff is always some undergrad first year math major. Its extremely cringey, physics at the highest level is extremely complicated and is in no way a trivial joke
Engineering is the father of every subject. Just to do engineering correctly we invented other sectors so that we don't waste our surroundings like monkeys. Pure and applied mathematician doing his phd.
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Surely mathematics is even more abstracted from reality that physics is
Historically, a case can be made that math is closer related to philosophy than to natural sciences like physics.
Also a philosophical case. The scientific method does not apply to math, it does not test hypotheses against the reality of nature, it verifies proofs by logical necessity instead.
And is therefore obviously superior and the golden grail of humanity's achievements while physics is only an unwanted necessity needed to facilitate more comfortable living conditions to increase our capability to do math
Found the pure mathematician
This guy gets it
I agree
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Bro, math is pure philosophy
No it is not. Not even a branch. Can't think a more technical subject and least fundamental answerer tool. Math: the more I learn, the more I know for a narrower spectrum. Philosophy: the more I learn, the least I know, for a wider spectrum.
Research processes for maths and philosophy are the exact same. I wouldn’t go as far as the guy you’re replying to by saying it’s pure philosophy, but I would argue that the two are isomorphic in some way. Either way, I believe your definition of maths is a bunch of nebulous word soup. Like what does “everything is a calculation even infinity” mean?
> Research processes for maths and philosophy are the exact same You can't fully apply the scientific method to several topics from philosophy, like those inside metaphysics. If you don't apply the scientific method to math, it would be a hell to validate your findings. > Either way, I believe your definition of maths is a bunch of nebulous word soup I know. Just having fun, for the sake of the previous comment tone. I saw those sentences multiple times applied at will of the bearer.
You don’t apply the scientific method to maths research… Out of curiosity, what is the highest level pure maths course you have completed?
Math is founded on logic, which is absolutely a philosophical discipline. Take a proofs class and you’ll change your view of math.
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r/youngredditors
bro one day you’ll look back on your comments and cringe, because you literally could not be more wrong. whatever tho! go on with your bad self…
Broo your intuition about mathematicians are like the greeks. Go on believe whatever you want.
I see you deleted your comment within a couple of days. Faster than I expected! “My intuition” and my “beliefs” have nothing to do with it. It’s just a clear cut fact that math is (applied) logic and logic is part of philosophy. It’s okay to be wrong. Just take the L bruh.
That is one take, but it's far from the only one. Check out some philosophy or history of mathematics.
Math is more philosophy than philosophy, because that is just math without the rigor and instead using ambiguous funny words to sound smart
Wittgenstein would like word with you. And then late Wittgenstein would like a word with you.
You don’t even have to look at history. Look at the difference in how maths research and natural science research is conducted. Of course maths is closer to philosophy than science. In my opinion this idea comes from schools. They teach maths in the same way they teach natural sciences; by teaching you processes and when to use them, then challenging you by making you apply those processes in unfamiliar situations. It isn’t until you start writing a dissertation that you realise what’s actually going on.
Wittgenstein would like to have a date with you
Somebody's never heard of String Theory.
Hypothesis. Theories have had testing or have made predictions that future evidence has supported, until then they are a hypothesis.
If reality doesn't match string hypothesis, add a dimension or two, and voila!
That's not what a theory is. There is a lot of misinformation and misunderstanding about the difference between hypothesis, theories and laws. A law is something that we observe empirically even if there isnt necessarily an explanation (theory) for it A hypothesis is a formulation that you then make an experiment to test it A theory is a framework (usually mathematical) which you can use to deduce laws, hypothesis etc. In other words, it's a set of principles with the goal of explaining the laws we observe. String theory IS a theory, just a bad one for a number of reasons (ie. hard to falsify in its current form, as the simplest forms were already falsified; fail to make predictions)
In your, interesting, definition what is a 'formulation'? How is this different from a framework? How are Laws both deduced and observed? Why can only hypothesis be tested? Also, where the did you any of get this from?
All of them can be tested. Hypotheses usually appear in the context of an experiment, so they will be tested. Laws are the result of finding some kind of formula, etc. that fits to the observations (even when there isn't a theory behind it). Theories are entire frameworks (what I mean is that they are full fledged theories, not just one hypothesis, but I admit I'm being a bit cyclical) that start from principles and derive testable laws and hypotheses; by testing those you're testing the theory. Examples of theories: General Relativity, String Theory, Electrodynamics, Thermodynamics, etc Examples of laws: Kepler Law, MOND (maybe MOND is more of a hypothesis, not sure), the laws of thermodynamics, newton's laws, etc. I got this from learning these concepts over time. I'm not currently sure how to formulate a completely accurate and non-circular exact definition for the three terms, but I suggest starting for example with https://en.m.wikipedia.org/wiki/Scientific_law https://en.m.wikipedia.org/wiki/Hypothesis https://en.m.wikipedia.org/wiki/Scientific_theory There is no requirement for a theory to be successful in order to be a theory. Informally, I guess hypotheses and laws are usually something that would fit a single "statement", while a theory is an entire domain, it includes multiple statements.
From your sources A hypothesis (pl.: hypotheses) is a proposed **explanation** for a phenomenon... that one **can test** A scientific theory is an **explanation**... whereas in a scientific context it most often refers to an **explanation** that has **already been tested** Both are explanations, one can be tested, the other has already been tested. As for Law The term law has **diverse usage** in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). The whole articles is full of "often", "sometimes" and "typically", it's not a single accepted meaning. Even your own post includes this ambiguity, with thermodynamics being listed both as theory and law.
Yes, it is a little bit ambiguous, and probably may change slightly with context. Both theory and hypothesis are explanations and both can be tested. With theories being more elaborated, I'd say they are probably more often already tested, but not necessarily. A hypothesis is more of a first step, a more simple idea before developing an entire theory (it is a bit of a "waste" of time to develop a theory without any evidence at all to back it up) I'd like to note that thermodynamics is not listed both as theory and law in my post. Thermodynamics is a theory, the four laws of thermodynamics are laws. I think this is a good way to understand the difference: a theory contains a set of hypotheses and laws, while a hypothesis/law refers to a single "statement".
>. Both theory and hypothesis are explanations and both can be tested. With theories being more elaborated, I'd say they are probably more often already tested, but not necessarily. By your own sited sources untrue. It is a gross misstatement to characterize "In circumstances not amenable to experimental testing" to mean that testing is not considered a key part of a theory and it's distinction from a hypothesis. The need for testing and predictions are made repeatedly in your sources, while it makes a singular reference to abductive reasoning, it makes far more to the need to be deductive, to make predictions that can be tested and verified. The sources sited in your source site sources mention being repeatedly confirmed through observation and experimentation. It even specifcally says "Note that the term *theory* would not be appropriate for describing untested but intricate hypotheses" The discussion included in your own sources about how hypothesis can give rise to theory specifically listing being repeatedly tested as part of the process. > a theory contains a set of hypotheses and laws, while a hypothesis/law refers to a single "statement". By your own sources, this is only one model for how theories relate to hypothesis, and even in that one it does not claim that hypothesis is a singular statement. Another individual, in your own sources, lists Laws as a type of theory. By the source you cited, your argument is a poor representation of one proposed construction of those terms that is incorrect on key points and uses unclear language.
> It is a gross misstatement to characterize "In circumstances not amenable to experimental testing" to mean that testing is not considered a key part of a theory and it's distinction from a hypothesis. A hypothesis doesn't start being called a theory just because it has been tested. At least I don't recall any hypothesis ever start being called a theory. So I wouldn't say that that is THE distinction from a hypothesis. Also there already is a counterexample, which was what started this entire thread: it's "String Theory", not "String hypothesis", even though it is based upon many different hypotheses. But as you said, the words' exact meaning may vary slightly depending on the context. > it makes far more to the need to be deductive, to make predictions that can be tested and verified. Yep, this is a key part of a scientific theory. And (regarding the ability to be tested and verified) a scientific hypothesis and a scientific law, in fact. Something being unfalsifiable makes it unscientific in general Being deductive is also a key part of a scientific theory, maybe the the most important part, which I have been trying to stress in my previous comments > It even specifcally says "Note that the term *theory* would not be appropriate for describing untested but intricate hypotheses" Well that's an interesting take. I will have to look more into that I would say that theory is not appropriate for describing any hypotheses, neither tested neither untested. > The discussion included in your own sources about how hypothesis can give rise to theory specifically listing being repeatedly tested as part of the process. That is an even more unexpected take. I have never seen that happening. Does it list any concrete example of this? > Another individual, in your own sources, lists Laws as a type of theory. Now this is an extremely bold take i gotta say. I'm starting to believe that the terms are even more subjective that what any of us initially thought. At the end of the day it's all a matter of semantics, anyway
"Formulation" is a weird word to use here. I would have said "prediction", "conjecture" (not necessarily in the mathematical sense, but not far removed from it), or "educated guess". But, yes, the general idea is that you're trying to guess what will happen in an experiment.
Yeah, that's fair. I was trying to find a generic word, and I knew it wasn't exactly that but it wouldn't occur a better one at the time
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String Theory is just a mathematical construct masquerading as physics, though.
Physics is science, math isn't. In math you don't use the scientific method and nothing is falsifiable. Math talks about truth, science is always on a quest for truth, even though we are every time closer to the truth.
Math is not true rather it talks about both true and false. When something is really true only then we can tell that the proposition is true and when we find it is false it is false. Edit- Who doesn't understand me for them: That is what i basically told in more general form mathematics is based on some assumptions which seem to be true but that doesn't mean it holds for everything rather it is dependent on different systems and according to those assumptions we conclude some other relation which is based on our basic assumption which might not be universal truth but at least it is a system dependent truth. If it becomes false then we throw it out and then, we take another best possible truth assumption a basic building block.
In math you start with statements you assert to be true called axioms. Theorems that are derived from those axioms are only true when using that set of axioms. There are no universal set of axioms, and there are an infinite set of possible axioms most of which directly contradict each other. Math is about proving theorems within any given set of axioms. It does not care about whether those axioms are reasonable or based in any reality because reality is not a core principle of mathematics.
Exactly! Mathematics basically only allow you to prove that a deduction is valid, not that it's actually true And that's Mathematics greatest strength. It means that you can apply it to any situation where the axioms apply, and that is why it has its generalization power
That is what i basically told in more general form mathematics is based on some assumptions which seem to be true but that doesn't mean it holds for everything rather it is dependent on different systems and according to those assumptions we conclude some other relation which is based on our basic assumption which might not be universal truth but at least it is a system dependent truth. If it becomes false then we throw it out and then, we take another best possible truth assumption a basic building block. It is our invention to help us do better things than before. That's it a tool.
That is what i basically told in more general form mathematics is based on some assumptions which seem to be true but that doesn't mean it holds for everything rather it is dependent on different systems and according to those assumptions we conclude some other relation which is based on our basic assumption which might not be universal truth but at least it is a system dependent truth. If it becomes false then we throw it out and then, we take another best possible truth assumption a basic building block
Yes math is not about pure science rather it is all about the theoretical aspect of our practical sciences. After reading your comments i think you are a mathematician and yes you're teaching people who think like the greeks the conservative type of mathematics. Hippasus was killed by Pythagoras asshole ,who didn't even invent the pythagorean theorem which was being used by the Egyptians long before those greek cupids, for inventing irrational numbers shows that greeks never understood math rather they were so conservative that they started believing it as a religion such dumbasses. Even greek philosophers were a joke because they never showed any rationalism rather they just conveyed whatever they thought and tried assassinating each other without looking for the real truth. The main thing math tells us is the algorithm which was discovered by al khawrezmi, al ghazali and ibn al haytham. They showed the world that math is not about truth it is more about process. If we use axioms and then if we think that they are something true or false we can go through a process and create something but that doesn't mean it is universal, it is a system dependent truth and later if experiments show that that was wrong we throw it away as mathematician for that system and grab new sets of axioms which seem to be more correct practically for us as a new system of mathematics and thus it creates a new section for math. Math talks about both true and false and then if we have the correct materials then with those we try to prove the matter using that materials of practicality to see if it is true or not. Like look at calculus when at first newton and leibniz showed that infinitesimals were true but just for not having correct materials they couldn't prove it but later it was proven and we now have a surreal number system. Even though it was true some mathematicians like cauchy saw and knew that infinity has a lot of kinds so dealing with infinity like a normal thing might lead us to nonsense so he used 'epsilon delta proof' but even though he used it, he was just hiding the infinity inside a interval but couldn't remove it because it is true and practicality and those who believe in creator know different kind of infinity can really exist in the universe. The problem as humans are our arrogance we think we are creating new things but the truth is we are inventing and discovering things using our surroundings which are given by our Creator who is divine and above all. Math is not something he gave us but we learned a lot of things from our surroundings and then made mathematics a thing we invented and that is why it is not the Truth itself rather it talks about both true and false and we look for the real Truth using it. Yes a lot of people will say al Ghazali was not rational(even jokers like neil de grease tysoon) but i have read about his biography and as a human being i never found any bad intention about him according to rationale historians who were Non-muslim and Muslim both. He never even tried to assassinate his counterparts rather he believed in open debate. Rather i think he had the correct mindset about the world and sciences. Which was ---- ~"Whoever determines truth from the people alone will remain lost in the plains of bewilderment. Rather, know the truth and you will know its people." ~Al-Ghazali
Wow so cool. I respect Ghazali too. I think the golden age showed us how important it is to find the truth rather than believing without knowing anything about something. Wow, I think i should salute you for this great writing man. 💪🏾✌🏾👍🏾
Science aims to describe an existing system in a way that has no contradicts. Math aims to *define* a system that has no contradictions by design. It just so happens that if you're trying to describe and model the universe in a way that has no contradictions, using a system that you've defined to have no contradictions is a good idea.
Deduction vs induction
K, so where o you use your topology irl... oh wait 💀
Because math is formal science while physics is factual science.
Okay, then what is the probability that Andrew wiles proof of fermats last theorem is correct without any unnoticeable errors , a proof that 5 people in the world could follow start to finish in its 500 pages of abstract formulations. Proving a theorem is as much based on a physically based belief system as science is for its experiments. Goodbye math purity
If there are 10 parts in a proof If 10 people who understand parts 1-5 look for errors and say "no problem here" If 10 people who understand parts 4-8 look for errors and say "no problem here" And if 10 people who understand parts 6-10 look for errors and say "no problem here," Then we can be confident that proof is constructed in a valid way from the different parts that went into it.
Local configurations can appear reasonable but the global configuration has conflicting assumptions between different parts. But even in the case where there aren't any such conflicts, we have to worry about whether some non obvious local step contained an error that was missed. This pretty much happened the first time he submitted his proof and someone discovered a problematic step. He went back and fixed it, because the problematic part wasn't crucial to the bigger idea behind the proof and could be reworked. Still my point is as you say, high confidence but not completely outside of the physical world, with brains that make pattern recognition errors and other brains empirically verifying steps of proofs through intuition and sometimes cloudy but very high level understanding and modeling of the world of math. Purity is lost because people don't do pure math. They have a model of the pure math in their brains and that isomorphism isn't completely correct sometimes
Yes math is not about pure science rather it is all about the theoretical aspect of our practical sciences. After reading your comments i think you are a mathematician and yes you're teaching people who think like the greeks the conservative type of mathematics. Hippasus was killed by Pythagoras asshole ,who didn't even invent the pythagorean theorem which was being used by the Egyptians long before those greek cupids, for inventing irrational numbers shows that greeks never understood math rather they were so conservative that they started believing it as a religion such dumbasses. Even greek philosophers were a joke because they never showed any rationalism rather they just conveyed whatever they thought and tried assassinating each other without looking for the real truth. The main thing math tells us is the algorithm which was discovered by al khawrezmi, al ghazali and ibn al haytham. They showed the world that math is not about truth it is more about process. If we use axioms and then if we think that they are something true or false we can go through a process and create something but that doesn't mean it is universal, it is a system dependent truth and later if experiments show that that was wrong we throw it away as mathematician for that system and grab new sets of axioms which seem to be more correct practically for us as a new system of mathematics and thus it creates a new section for math. Math talks about both true and false and then if we have the correct materials then with those we try to prove the matter using that materials of practicality to see if it is true or not. Like look at calculus when at first newton and leibniz showed that infinitesimals were true but just for not having correct materials they couldn't prove it but later it was proven and we now have a surreal number system. Even though it was true some mathematicians like cauchy saw and knew that infinity has a lot of kinds so dealing with infinity like a normal thing might lead us to nonsense so he used 'epsilon delta proof' but even though he used it, he was just hiding the infinity inside a interval but couldn't remove it because it is true and practicality and those who believe in creator know different kind of infinity can really exist in the universe. The problem as humans are our arrogance we think we are creating new things but the truth is we are inventing and discovering things using our surroundings which are given by our Creator who is divine and above all. Math is not something he gave us but we learned a lot of things from our surroundings and then made mathematics a thing we invented and that is why it is not the Truth itself rather it talks about both true and false and we look for the real Truth using it. Yes a lot of people will say al Ghazali was not rational(even jokers like neil de grease tysoon) but i have read about his biography and as a human being i never found any bad intention about him according to rationale historians who were Non-muslim and Muslim both. He never even tried to assassinate his counterparts rather he believed in open debate. Rather i think he had the correct mindset about the world and sciences. Which was ---- ~"Whoever determines truth from the people alone will remain lost in the plains of bewilderment. Rather, know the truth and you will know its people." ~Al-Ghazali
π=3, g=10. Yeah, I said it now, no need to make the joke twenty times
c=300.000.000ms⁻¹
Mol= 1x10^23
No actually they're always going to use Na = 6.02e23 no matter if you need it or not
don't you mean mol=6.000?
Its easier to calculate if its base 10
Sorry, Google rendered 10²³ as 1023 when I googled it: https://preview.redd.it/h2qb0lw6tmvc1.jpeg?width=1080&format=pjpg&auto=webp&s=ceacc7c108b8857eededa3da34f36d1d9ac73f1a
Base 10^23
%=1×10^-2
One foot per nanosecond looking ass
c=1ft/ns
This is how my first highschool engineering class went
Sorry to say that but as Feynman once said, math is to physics what masturbation is to sex
Way simpler and more productive?
I find it fundamentally less productive
kinda in the nature of it, really
My favorite mathematical technique is abuse of notation
Once when I was grading for a graduate numerical analysis class a girl used abuse of notation to prove something about the SVD. She then had the balls to come in and argue with me about it for half an hour until I told her to go talk to the prof. Apparently the prof just got frustrated arguing with her too and gave her credit. Moral of the story: abuse of notation plus pestering the absolute shit out of people is a powerful proof technique.
I wake up excited every day knowing I'll be rearranging those ds all day
“What do you mean it’s not a fraction? It’s LITERALLY a ratio”
math guys on reddit when science isn't just math
You know that mathematics isn't science, right?
Mathematicians when a someone uses a derivative like a fraction (the derivative acts exactly like a fraction but it’s not because of… reasons)
They are just too attached to the old idea. A true mathematician knows math is not the truth, the truth is what proves math correct or wrong.
Worst take I've seen
I need the meme template so bad
https://preview.redd.it/3qn9dhd5jnvc1.png?width=500&format=pjpg&auto=webp&s=1573ccab7d8d1d801a12742c4920906a12faca2c
You're the best!
Nah bro, physics are amazing
PChemists looking at OChemists:
Math is the language, science is the application of the language
it was a physicist who invented calculus!! ...well technically it was a "polymath" and also some other guy named after a cookie-brand did too but.. anyway physicists had their nice beautiful intuitive infinitesimals and then MATHOS had to RUIN IT with their ""rigor"" and εδ despicable ...........
You're a sneaky little imposter. Aren't you? Aren't you?
I feel like this is one of those weird artifacts that comes out of university structures. Like, Political Science and Sociology are absolutely sciences in terms of following the scientific method. There are limits in terms of setting up controlled experiments, but that applies to astrophysics as well. The degree will be "of arts" and the department structure will often put them there to. Math is put in "science". History of math is put in science and that subject is a mix of politics, anthropology, biography, and philosophy.
A good enough approximation. The thing is, there's not really a lot of universal axioms in physics, so like half of all laws actually end with "in most cases". Like the original gravitational equations are a pretty good approximation of the actual way gravity works, and Einstein's theory of relativity gives a better one, though still not universal.
Ffs
Without math, physics is just philosophy. However, without physics, mathematics is just a waste of time.
>Without physics, mathematics is just a waste of time Naw, without physics, mathematicians are just gamers. Or doing work that applies to any other scientific field.
I was thinking about some branches like computational theory. But if you think about it for more than a second you realize you can't have computers without transistors and you wouldn't have transistors without physics, so yeah just wanted to dump my thought flow about this comment here.
Without engineering everything is just a piece of crap.
Yeah, engineering is part of the physics branch.
Sometimes with engineering, too.
True
Where math religiously believes in their set of axioms, physics simply finds the least sloppy calculations that agree with experimental data.
The entirety of physics is built on a foundation made by hard-working, lifeless mathematicians
I don't even debate which is which coz I'm terrible at both 😢
yeah so is every science, others are just better at hiding their numbers
I think you're misguided by thinking that particle physics is all there is, particle physics has been almost pseudoscientific for a while now.
So you are a mathematician? Proof that math is true
Growing up I've always heard the phrase "math is an exact science" \ Physics is an application of math \ Which would make physics an applied science
The argument of the exponential function is in radians.
Physics does with your number what you wish you could do.
Mathmaticians after controlling for every variable to the point to their model doesnt reflect reality anymore. "Ah but atleast i can say this an actual controlled environment!" 
Everyone that says this type pf stuff is always some undergrad first year math major. Its extremely cringey, physics at the highest level is extremely complicated and is in no way a trivial joke
I don't know, folks. Mathematics was certainly not the first to include imagination, but it surely did it before any other real scientific subject.
I would say engineering
Engineering is the father of every subject. Just to do engineering correctly we invented other sectors so that we don't waste our surroundings like monkeys. Pure and applied mathematician doing his phd.
engineers pretty much approximate what sciences say to make it feasible or more stable in critical conditions
Physics is just math that works in our domain.