- #1
Icebreaker
Would you say it's discovered or invented?
Kerrie said:To say that Mathematics is discovered has the presumption that any form of intelligent life in our universe has the ability to understand Math also.
To say that Math is invented is doubting the existence of the reality we are a part of, which can be a disruptive thought to many.
cragwolf said:It presumes no such thing. Perhaps not all forms of intelligent beings are able to comprehend mathematics. Some intelligent beings might find it easy, some might find it hard (I think we fit in this category), and some might find it incomprehensible. Who knows?
Again, I don't see this as being necessarily so. There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws. Again, who knows?
Icebreaker said:Physics is the means to describe reality. You don't really need math in physics to actually describe it -- you can do it in english. It just happens that using math in physics is a lot more practical. Math wasn't invented/discovered with the sole purpose of describing reality.
Saying that math is "discovered", assumes that an answer exists whether we know it or not, and it is only a matter of time before we find it. Saying otherwise means that an answer may not exist... but what it means, I can't really interpret.
etc said:honestly, i don't understand why you equate the discovery of math with a logical universe.
Saying that math is "discovered", assumes that an answer exists whether we know it or not, and it is only a matter of time before we find it.
I'm currently writing on a book I call, Mathematics as a Concrete Abstraction that addresses this very issue. Which mathematical concepts have been discovered and which have merely been invented.Icebreaker said:Mathematics. Would you say it's discovered or invented?
Kerrie said:So, you have lent your constructive criticism on my answer, now where is yours?
Is math invented or discovered, and why do you think so?
cragwolf said:My answer is: I don't know.
It presumes no such thing. Perhaps not all forms of intelligent beings are able to comprehend mathematics.
There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws.
So crag, what is your criticism of this idea? And why?I lean towards the idea we invented the language of math once we discovered how it works.
cragwolf said:There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws. Again, who knows?
Les Sleeth said:Math is a language that corresponds to the order that exists in our universe. The more order there is in a situation, the better math works; the less order there is, the more one has to fall back on probabilities.
selfAdjoint said:True in general . . .
selfAdjoint said:. . . the amount of order required for math to get a grip is constantly being reduced
Les Sleeth said:What are you talking about? No proof? What kind of proof do you need before you accept that major aspects of physical reality, at least, can be mapped by math? That is either an incredibly ignorant statement or you are just being contrary.
cragwolf said:You do know the difference between proof and supporting evidence?
Icebreaker said:Would you say it's discovered or invented?
The whole idea of negative absolute numbers is an invention. In reality (that is to say that ontologically speaking) the universe never displays an absolute negative quantitative property. Negativity is actually a relative property between quantities. So on this point alone modern mathematics is grossly ontologically incorrect.Microburst said:X-RAy was discovered!
mathematics was definitely invented, don't forget the imaginary numbers..
square root of -1 i
In reality (that is to say that ontologically speaking) the universe never displays an absolute negative quantitative property.
Les Sleeth said:Absolutely, it is one of my favorite subjects. I think, however, you've chosen the wrong subject to be skeptical about. Order in this universe is likely more confirmed than any other single property.
yes maths is a language and the fact that some use it as a tool in other empiricial disciplines doesn't change the fact it's a language.vinter said:Is Math a language?
The fact that we write 33 as 33 and not as "-, is due to maths as a language. But the fact that 33 + 33 = 66 is a law of the universe.
Basically, I'm getting confused.
I fully accept the notion of negative numbers and imaginary numbers. I use them all the time. I just recognize that they aren't absolute or distinct ideas of quantity. They are always relative relationships between quantities. Yet the mathematical community has defined them as absolute or "stand-alone' concept. Like it's perfectly acceptable to talk about an absolute negative number. Like as if that concept has merit without any relation to anything else. That is simply incorrect. By that I mean it is ontologically incorrect. No quantity in the universe can have an absolute property of negativity. It just doesn't make any sense. It's a relative property between sets, it's not an absolute property of a set.Hurkyl said:
At least you've not ranting about zero this time. I'd respond in full, but I don't want to hijack the topic. You might want to check out some of the history of the cubic and quartic formulas, though, which forced the mainstream acceptance of negative and complex numbers.
NeutronStar said:I fully accept the notion of negative numbers and imaginary numbers. I use them all the time. I just recognize that they aren't absolute or distinct ideas of quantity. They are always relative relationships between quantities. Yet the mathematical community has defined them as absolute or "stand-alone' concept. Like it's perfectly acceptable to talk about an absolute negative number. Like as if that concept has merit without any relation to anything else. That is simply incorrect. By that I mean it is ontologically incorrect. No quantity in the universe can have an absolute property of negativity. It just doesn't make any sense. It's a relative property between sets, it's not an absolute property of a set. . . . Zero, for example, is not a number or quantity. . . Mathematics has zero incorrectly defined. Where I'm using "incorrect" here to mean "ontologically incorrect".
I too fully understand where the pure mathematicians are coming from. However, I also firmly believe that pure mathematics could be both, logically abstract, and ontologically correct. So I don't understand why mathematicians don't strive to make it both logically abstract, and ontologically correct.Les Sleeth said:I can see how such views might develop if one only works with numbers, and never has to verify predictions.
Icebreaker said:If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than hours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.
The difference between discovering and inventing math lies in the origin of the concepts and principles. Discovering math means that the concepts and principles already existed in nature and were simply observed and understood by humans. On the other hand, inventing math means that humans created the concepts and principles based on their own ideas and reasoning.
Yes, math can be both discovered and invented. Many mathematical concepts, such as the Pythagorean theorem, were discovered by ancient civilizations through observation and experimentation. However, humans have also invented new branches of mathematics, such as calculus, to solve specific problems and advance our understanding of the world.
This is a debated question among mathematicians, but most would agree that math is both a language and a tool. As a language, math is used to communicate and express complex ideas and relationships. As a tool, math is used to solve problems and make predictions about the world.
The concept of infinity is often used as evidence for the discovery of math. The idea of infinity has been explored by mathematicians for centuries, but it is still a concept that humans struggle to fully understand. This suggests that the concept of infinity is not something that was invented by humans, but rather something that has always existed and was discovered through mathematical exploration.
The debate between discovering and inventing math may seem like a philosophical question, but it has practical implications in the field of mathematics. Understanding the origin of mathematical concepts can help us improve our teaching methods and develop new ways of thinking about and applying math in various fields, such as science, engineering, and technology.