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Amongs Physics, Chemistry, Biology. Mathematics is classified as 'pure science'. but it also has applications on its own.

part of Maths are discovered. (when mankind learns to counts). another part is invented. (Grecoroman, Renaissance, Age o' Reasons, and Napoleon days)

Dunno but its awesome!

Both. It is discovered, and varried methodes have been invented. But they could ofcourse be discovered too. You decide.

It's worth pointing out that I actually prefer 'constructed' to either 'discovered' or 'invented'. It's more accurate, IMO.

It's also worth pointing out that I didn't just bowl into this thread being rude, arrogant and dismissive. I posted my take on the issue, and Kovnik derided my points as 'completely false' and 'ridiculous', which isn't actually true - it's arguable. I'm a 'fight fire with fire' type. Always have been, always will be. Attack me, and I will attack you back, twice as hard. My only crime is being good at it.


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Monster Rain wrote:

Albatross wrote:I find it odd that you cling to absolutist statements about truth, and ignore the near-century of work that came after, pretty much destroying it.

If you're referring to quantum mechanics, I'm not convinced that the fact that we don't know what is going to happen by default makes them unknowable. We just haven't invented/discovered the maths (you guys are turning me British) to figure them out yet.

Hi MR, missed your post, as it was buried amongst all the rage!

I'm not talking about quantum mechanics, I'm talking about conceptualisation and construction. 'Truth' is held by some to be a construction, reliant upon the internal logic of logical systems. Yes, 2+2 will always equal 5, but not to an entity that has no ability to conceptualise 2, 5, addition, or amounts. To such an entity, it would be irrelevant. As an example, Kovnik offered the North American land-mass as an example of something that existed, waiting to be discovered. That's a view, certainly, but I would argue that without the ability to conceptualise a 'land-mass', a land-mass doesn't exist. Yes, the physical manifestations that allow the concept of 'land-mass' to exist in potentia are present, but without entities capable of organising the interpretations of these physical manifestations (and capable of conceptualising 'physical') into concepts such as 'land-mass' or 'ocean' (for example) then they don't exist as such, because they don't define themeselves as such. We (and other animals, arguably) define them.

Consider this, if there were no eyes, would the universe have a visual component? I would argue that no, it wouldn't. A visual component would exist in potentia, but without entities capable of 'seeing', there would be nothing to 'see', as 'seeing' would be meaningless, and thus, irrelevant. That's basically where I'm coming from. Without a brain capable of understanding maths, maths doesn't exist, because the perception of division into discrete amounts is not defined by the universe, it's defined by us. The universe doesn't know, or care, or even know that it is a universe waiting to be 'discovered'. It's all our construction, based on our limited biology.

I'm not talking about quantum mechanics, I'm talking about conceptualisation and construction. 'Truth' is held by some to be a construction, reliant upon the internal logic of logical systems.

Being an epistemological constructionist doesn't inherently justify deflationism (the devaluation of truth). That can only be argued if we consider that nothing is 'true' to those who do not conceptualize, which is, IMO, false. It's true for the dog that a plane is flying over his head, even tho he doesn't have a concept of it. It was true that the continental landmass of America was there, before it was named 'America', or that we figured out it was a landmass. Truth isn't relative to your capacity, but to the capacity of the objective standard (that of the being capable of perceiving the effect).

And I object to the representation of this century having proclaimed deflationism to be true.

Discovered, or rather... interpreted. Math is an absolute truth, but we put it into our own terms to make it comprehensible. The universe doesn't calculate things with equations and variables, nor does it analyse trends with the aid of interpretive graphs. Those are tools that we've developed to understand mathematics.

I don't think there's any way that math is "invented".

Just spitballin' here:

As the codification of consistent universal relationships, both known and unknown, mathematics as a system of codification was and continues to be invented by humankind.

This 'universal language' allows us to examine and hypothesize over the answer to 'What' and 'How' questions: What is it made of, How does it function?

In this manner mathematics facilitates discovery, but it still falls short of what is generally the ultimate goal of analysis; understanding the 'Why' questions and thereby having predictive power. One could argue that we simply haven't discovered "enough" math, but even then mathematics is simply secondary to our goal of understanding; the primer for the course text. This secondary function makes me believe that mathematics are primarily a human invention, a construct for quantifying greater-than-human phenomena.

I feel that the answer to this question will ultimately depend on what you define mathematics as.

Both, becuase if you invented something you have therefore discovered something new.

I see our math as an invention to make discoveries.
The underlying principles of math are universal, but requires an invented system to figure out.
I see it akin to creating a microscope to see germs. The germs were there and were only discovered because someone invented a microscope to see them.

Kovnik Obama wrote:

I'm not talking about quantum mechanics, I'm talking about conceptualisation and construction. 'Truth' is held by some to be a construction, reliant upon the internal logic of logical systems.

Being an epistemological constructionist doesn't inherently justify deflationism (the devaluation of truth).

Of course not, but it's a good position from which to justify deconstruction.

That can only be argued if we consider that nothing is 'true' to those who do not conceptualize, which is, IMO, false. It's true for the dog that a plane is flying over his head, even tho he doesn't have a concept of it.

Actually, it has been suggested that animals other than humans can produce culture, which in turn suggests that they are capable of conceptualising, albeit to a very, very, limited degree. Regardless, it's true that yes, for us, a plane flies over the dog's head regardless of his knowledge of it. It's not true for the dog. Saying that, I've seen my dog eat horse crap, so who the feth knows what they're thinking about!

It was true that the continental landmass of America was there, before it was named 'America', or that we figured out it was a landmass. Truth isn't relative to your capacity, but to the capacity of the objective standard (that of the being capable of perceiving the effect).

It's not about anything as banal figuring out that north America was there, or that it was a land-mass - what I'm getting at is that without a concept of 'land-mass' a land-mass can't exist, because it isn't defined by itself, but by entities capable of defining it.

And I object to the representation of this century having proclaimed deflationism to be true.

That's your right, of course. The real answer is that it's arguable, very arguable, so statements of the type you made when you first replied (unasked, I might add) to my post, such as 'absolutely false', or that my view points are 'ridiculous', are bound to come accross as arrogant and self-aggrandising, when the 'truth' is actually very much up for grabs. That was what I objected to. You belong to one school of thought, I another. I don't see why we have to be rude and disrespectful to each other, but let's be real here: You were the one who set the tone of how our exchanges were going to proceed, not me. Most here who know me (as much as anyone can in such an arena), know that I am capable of being VERY spiky, but generally meet politeness with politeness, friendliness with friendliness. I'm not the sort of chap who just jumps on people for no reason (and there are definitely some arounds these parts who do).

You seemed to have some pre-concieved notion of who I was, and had made up your mind that I was just some idiot to be dismissed with a string of terms you thought I wouldn't understand. I am not an idiot - I've just been offered a fee-waiver, a job and a post-grad position by my university, all before my final works have been submitted. I was invited to present a paper at an international postgrad symposium for my field (it was in South Africa - I couldn't afford to go, and because I was undergrad there was no funding available via my institution. Which sucked.) in the first year of my degree. I'm presenting this year because it's in the UK this time.

I'm just committed to plain-speaking, because that's just who I am. It's a consequence of my upbringing and field of study. If you're not speaking to your audience, who are you speaking to, and for what purpose? These are the types of questions I have to ask on a daily basis, and I guess I just applied them to you. If I got you wrong, then fair enough, my apologies. How about we start over?


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Da Boss has the right of it, incidentally.

This is like asking was language invented or discovered?

Pi is a 'fundemental' and is therefor 'discovered', but how we express that value has to be 'invented'.

So when you ask 'was maths discovered or invented', I would ask please define 'maths'?

Andrew

Albatross wrote:

Muhr wrote:
Actually, this is where I must come in. I for one have personally found Kovnik's addition to the thread to be one of the most interesting and thought provoking, but then again I understood him. Don't disparage somebody simply because what they say goes over your head. If he 'dummed' himself down then he would be guilty of patronizing you.

...aaaand, here comes the fan-club.

err I was the one who started this thread rolling. Kovnik and I have very similar beliefs and opinions and, to be honest, I think you put a good argument forward yourself, at least at the beginning of the thread anyway. It was only when you started to become abusive that my opinion of you changed slightly, there was just no need for it Albatross, you could have said exactly the same but used a less inflammatory approach.

I came to Koviks defence purely because of how nasty some of the posters were getting when he was simply putting a highly thought out argument forward. If someone really knows their stuff, they shouldn't be made to feel as though they are not wanted on the thread because someone doesn't like how intellectual they sound.

So peace dude allow folk to express themselves yeah?

Muhr wrote:

Albatross wrote:

Muhr wrote:
Actually, this is where I must come in. I for one have personally found Kovnik's addition to the thread to be one of the most interesting and thought provoking, but then again I understood him. Don't disparage somebody simply because what they say goes over your head. If he 'dummed' himself down then he would be guilty of patronizing you.

...aaaand, here comes the fan-club.

err I was the one who started this thread rolling. Kovnik and I have very similar beliefs and opinions and, to be honest, I think you put a good argument forward yourself, at least at the beginning of the thread anyway. It was only when you started to become abusive that my opinion of you changed slightly, there was just no need for it Albatross, you could have said exactly the same but used a less inflammatory approach.

I could have, but why should I? Go back and read the thread again. I posted my take on this issue, and was met with snorting derision by another poster. Not only that, he seemed like he was trying to cow me by using technical terminology he thought I wouldn't understand. Now, I'm not the sort to sit back and accept being insulted, so I let him have it, both barrels. If that wasn't what he was trying to do, then fair enough, it was an unfortunate misunderstanding, but I'm not sorry for my reaction - he was still pretty rude to me, in any case.

Nevertheless, I've offered an olive-branch by apologising. Whether or not he accepts it is up to him. I don't mind either way.

I came to Koviks defence purely because of how nasty some of the posters were getting when he was simply putting a highly thought out argument forward. If someone really knows their stuff, they shouldn't be made to feel as though they are not wanted on the thread because someone doesn't like how intellectual they sound.

OK, so you're impressed by him. Fine, that's understandable, but it isn't really about sounding 'intellectual' - as dogma rightly pointed out, he regularly uses technical language related to his field on here. I don't have a problem with that at all, because it's clear that he's not doing so purely to try and make someone else feel stupid. At least, not always!

I'm not anti-intellectual. It's how one uses such language that matters - I don't drop post-structuralist talking points or Marxist cultural theory into a thread about Justin Beiber, because it's alienating, and I have no burning desire to prove how smart I am by referencing it. I can form cogent arguments without it. I prefer an argument to be strong, not dense. I felt that Kovnik was grandstanding to make a point - he just happened to pick the wrong person, is all. Like I said, If that wasn't the case, then I apologise to him for the misunderstanding.

So peace dude allow folk to express themselves yeah?

Folk are free to express themselves however they want, as am I. Notwithstanding the MODs, that is...

AndrewC wrote:This is like asking was language invented or discovered?

Pi is a 'fundemental' and is therefor 'discovered', but how we express that value has to be 'invented'.

So when you ask 'was maths discovered or invented', I would ask please define 'maths'?

Andrew

Ok Andy, I see your point. Right, how to 'define' math? Hmmm, I'm not sure how I'm going to put but here goes.

A friend of mine has a degree in Mathematics and he told me that, for the final exam, they were given three hours to complete it. And the ENTIRE exam was just ONE problem!
Wow, one problem that was so complex that they were given three hours to solve it. He passed but what surprised him the most was that he had solved the problem in a different way to how the others that solved theirs. So, even though there was more than one way to solve it, it could still be done.

What's my point? Well the language of math is also an abstract one. To clarify my belief: I believe it is more accurate to say that math is both discovered AND invented, and here's why...

We could write an equation, any equation will do. It doesn't have to be true, it doesn't even have to mean anything. That kind of math would be invented but we then express another equation that reveals a fundamental, UNIVERSAL truth. If that same equation could then be applied to other systems in order to gain an accurate facet of truth then THAT math would be discovered. If another, intelligent alien species existed out there that gained that same piece of the puzzle by using their own form of equation, scribbling or what have you, no matter how much it differed from ours would have to arrive at the SAME conclusion as we did but expressed it DIFFERENTLY. Now, even though our mathematical systems could be radically different they would both, if they were correct, reveal the same truth. A clear example of a piece of universal math.

So, in short, any kind of math that deals with a fundamental truth would be discovered.

Also, having an instinctive appreciation of quantities (if I break my cats chew stick in half and give her one half and hide the other, she will know that I will have the other half) she will know this not because she has worked it out mathematically but rather she has a simple 'more or less' conclusion to come to. It comes more from instinct than any specific and focused thought process. Understanding the essence of quantity is an instinctive trait, NOT a mathematical one. If simple survival is going to be your concern and you are put in imminent danger then it's a safe bet that you will resort to simple 'more or less' conclusions, you wouldn't have the time to apply specific thought processes. If you ever applied real mathematics in order to improve your chances of surviving then that would only be because you had had the time beforehand to work it out when you were not in imminent danger.

So, to answer your question, the kind of mathematics that I believe is discovered are the equations that reveal a fundamental, universal truth. And if someone could think of an example of how a highly advanced alien species could become interstellar WITHOUT using math whatsoever then I would be happy to hear it but personally, I belief that only through the abstract language of math can we unlock the stars themselves. It simply cannot be done any other way.

In which case we agree that maths is both discovered and invented.

Cheers

Andrew