Is science invented or discovered?

[danzibr]

Topic. This is a question I've been thinking about lately. Take math, for example. Is all math already out there and we as humans just discover it? Or do we just make all sorts of wacky stuff?

[AsteriskAmp]

It starts with a concrete reality and then we start building abstract models and testing them against observable reality, when this is no longer possible we keep on modelling and hope for better instruments to measure.

[big teej]

Topic. This is a question I've been thinking about lately. Take math, for example. Is all math already out there and we as humans just discover it? Or do we just make all sorts of wacky stuff?

2 + 2 is still four whether someone knows it or not.

ergo.
discovered

inventions would be the application of a discovery, such as a toster oven.

[Artemis97]

I'd say it's all out there and we just have to figure it out. Chemical reactions and things like gravity have all existed long before people figured out chemistry or physics. Science is just our way of cataloguing and understanding it all.

[AsteriskAmp]

2 + 2 is still four whether someone knows it or not.

ergo.
discovered

inventions would be the application of a discovery, such as a toster oven.

But is 6/9 - 8 part of our observable reality?
Also, we have another thing pop-up, math helps us understand our universe yet it's not necessary for it to work, the peruvian indians don't know anything about math and yet they can produce music with their quenas. This however doesn't means there is no math there.


I'd say it's all out there and we just have to figure it out. Chemical reactions and things like gravity have all existed long before people figured out chemistry or physics. Science is just our way of cataloguing and understanding it all.

Math has long departed from cataloguing. Quantum physics may say that we actually generated the past by collpasing past wave functions.

[golentan]

Science is discovered. The underlying principles of the universe exist, and are uncovered and modeled through experimentation rather than written from whole cloth. Math is invented, though the principles which compose it are not (from first principles, whatever they are, the rest can be deduced). Since much of math that we used (almost all) is based on first principles found in the universe, it can be argued that basic math is discovered rather than invented, but since those principles are not the only math systems explored math as a whole is not.

[AsteriskAmp]

Science is discovered. The underlying principles of the universe exist, and are uncovered and modeled through experimentation rather than written from whole cloth. Math is invented, though the principles which compose it are not (from first principles, whatever they are, the rest can be deduced). Since much of math that we used (almost all) is based on first principles found in the universe, it can be argued that basic math is discovered rather than invented, but since those principles are not the only math systems explored math as a whole is not.
Math it's by principle axiomatic, so it's kinda more invented to be able to understand something, not really discovered.

[thubby]

science is a verb now, you do it :smallamused:

[AsteriskAmp]

science is a verb now, you do it :smallamused:

Which is its past tense?

[golentan]

Scienced.

Also, I said I considered math invented. I'm all confused now.

[erikun]

Science would probably be best described as the action of discovering, rather than the discoveries themselves. For that matter, science isn't supposed to be reality, it's supposed to be a model of reality - because we can't objectively tell the way things "really" are, we are best at coming up with a description that allows for what we can see and what we can expect.

[RebelRogue]

Those principles (edit: of math) are hardly arbitrary, though; they're heavily inspired by intuition about how collections of things behave (i.e. sets). In short, they are based on the world around us to some degree.

[Telonius]

Pure math (the a priori stuff) is discovered. It would be correct whether or not humans ever existed, in this or any other universe.

Equations with "universal constants" are also discovered, though they might only be correct in this universe. E equalled mC^2 (or whatever more precise equation accounts for the universe, was correct) for millions of years before Einstein realized it did. But there's nothing saying that in another universe, the speed of light has to be 299,792,457 m/s^2. It might be 300 million even, or seventeen, or anything else for that matter.

The particular methods people use to discover what those equations are - that is, the actual conduct of science - are invented. If you had full knowledge of the laws of physics a million years ago, and somebody explained to you the idea behind an internal combustion engine, or a microscope, or any other tool, you could say whether or not it would work. But you still have to build the thing in order for it to exist.

[erikun]

Those principles (edit: of math) are hardly arbitrary, though; they're heavily inspired by intuition about how collections of things behave (i.e. sets). In short, they are based on the world around us to some degree.
True, which is why I specified science rather than other fields (assuming you were talking to me).

The question of "Is math invented or discovered?" is a bit trickier - you could say that concepts like 1+1 and pi are discovered, but specific formula to determine mathematical answers are invented. The Pythagorean Theorem isn't a universal truth, it's a mathematical equation that someone came up with which relates three properities of a right triangle.

[AsteriskAmp]

Pure math (the a priori stuff) is discovered. It would be correct whether or not humans ever existed, in this or any other universe.

Equations with "universal constants" are also discovered, though they might only be correct in this universe. E equalled mC^2 (or whatever more precise equation accounts for the universe, was correct) for millions of years before Einstein realized it did. But there's nothing saying that in another universe, the speed of light has to be 299,792,457 m/s^2. It might be 300 million even, or seventeen, or anything else for that matter.

The particular methods people use to discover what those equations are - that is, the actual conduct of science - are invented. If you had full knowledge of the laws of physics a million years ago, and somebody explained to you the idea behind an internal combustion engine, or a microscope, or any other tool, you could say whether or not it would work. But you still have to build the thing in order for it to exist.

E=m22c4+p2c2
Is the correct ecuation for things which don't have rest mass.
Yet still, we don't discover the ecuations, we invent them and hope that they correctly model the universe, otherwise, REDO.


True, which is why I specified science rather than other fields (assuming you were talking to me).

The question of "Is math invented or discovered?" is a bit trickier - you could say that concepts like 1+1 and pi are discovered, but specific formula to determine mathematical answers are invented. The Pythagorean Theorem isn't a universal truth, it's a mathematical equation that someone came up with which relates three properities of a right triangle.
I would say Euclidian geometry further supports the invented proposition. Even though the margin of error is nanoscopic, a right triangle does not exist outside our heads.

[danzibr]

Those principles (edit: of math) are hardly arbitrary, though; they're heavily inspired by intuition about how collections of things behave (i.e. sets). In short, they are based on the world around us to some degree.

How sets behave?

In any case, thank you all for your answers. I recently got my Master's in Mathematics (2 more years until PhD). I probably should have been a bit more specific in my original post (but I didn't want to scare anyone way). Is more modern, abstract mathematics discovered or invented? I agree not many would debate 2+2=4, but does the same hold true for things which don't have such concrete physical meanings?

And golentan, I'm confused by science is discovered but math is invented. Math is a science.

[AsteriskAmp]

How sets behave?

In any case, thank you all for your answers. I recently got my Master's in Mathematics (2 more years until PhD). I probably should have been a bit more specific in my original post (but I didn't want to scare anyone way). Is more modern, abstract mathematics discovered or invented? I agree not many would debate 2+2=4, but does the same hold true for things which don't have such concrete physical meanings?

And golentan, I'm confused by science is discovered but math is invented. Math is a science.

I would like to debate 2+2=4. It is based on an axiom, it is invented by definition. You cannot prove it through reality, we invented math to quantify stuff, and then we discovered its model fitted reality. But even though it represents reality it is a model that is invented, not discovered.

Or are you going to argue that you can pull a Banach Tarski on a football?

[RebelRogue]

How sets behave?
Well, for instance, the axiom of pairing is inspired by the fact, that if you have an apple and an orange, it makes sense, that a collecion of the apple and the orange exists too. Similar for axion of unions. As a mathematician, of course you know that we will get in trouble if we just follow our noses too far like this, but at least some of the axioms comes from such common sense arguings.


I would like to debate 2+2=4. It is based on an axiom, it is invented by definition. You cannot prove it through reality, we invented math to quantify stuff, and then we discovered its model fitted reality. But even though it represents reality it is a model that is invented, not discovered.

Or are you going to argue that you can pull a Banach Tarski on a football?
But which axioms? You can actually define what '2' and '4' means using set theory and the prove 2+2=4, but then you need the axioms of set theory.

But counting stuff and finding that 2 apples combined with 2 more apples results in 4 apples is indeed discovered!

[danzibr]

I would like to debate 2+2=4. It is based on an axiom, it is invented by definition. You cannot prove it through reality, we invented math to quantify stuff, and then we discovered its model fitted reality. But even though it represents reality it is a model that is invented, not discovered.

Or are you going to argue that you can pull a Banach Tarski on a football?

Ahh, you're getting into axioms, which is more philosophy than I want to get into.

Supposing we all accept reasonable axioms (whatever reasonable is), we can deduce things. We can make more definitions and deduce more things. After a certain point of abstractness, when we're off in la-la land, when objects don't have any reasonable physical interpretation (or perhaps just something we can't imagine), are new results discoveries or inventions? Were they just sitting around waiting to be found, or is it something like a microwave oven?

EDIT: And RebelRogue, I was just wondering about your choice of the word set. They're really fundamental, of course, but I don't work with sets at all, unless you just consider everything as elements in some random set. Oh, and thanks for calling me a mathematician, but I still have a ways to go :P. I only have one publication.

[Flame of Anor]

I would like to debate 2+2=4. It is based on an axiom, it is invented by definition. You cannot prove it through reality, we invented math to quantify stuff, and then we discovered its model fitted reality. But even though it represents reality it is a model that is invented, not discovered.

What? That's ridiculous. If there are two planets orbiting one star, and two planets orbiting another star, there are four planets total no matter if humans ever existed.

[AsteriskAmp]

What? That's ridiculous. If there are two planets orbiting one star, and two planets orbiting another star, there are four planets total no matter if humans ever existed.

What are numbers to begin. Also, if you want to talk about a lack of humans, we also are stemming somewhat into quantum mechanics and the concept of observer. Sciences stem from philosophy, when they get somewhat precise and exacts answers they get separed. However, there is also the issue that some of their principles stem from it, which eventually leads us to the age old elementary school paradox.

An element is anything inside a set.
A set is a gathering of elements.


Ahh, you're getting into axioms, which is more philosophy than I want to get into.

Supposing we all accept reasonable axioms (whatever reasonable is), we can deduce things. We can make more definitions and deduce more things. After a certain point of abstractness, when we're off in la-la land, when objects don't have any reasonable physical interpretation (or perhaps just something we can't imagine), are new results discoveries or inventions? Were they just sitting around waiting to be found, or is it something like a microwave oven?
But axioms are just defined as correct and useful. Sure, we can deduce things, but the fact that the base is an assumed truth and that we have no way of proving means that it is not discovered but invented to create a model of reality. It fits reality, but whatever we do there is invented, it just fits reality because it was invented to do so.

[Flame of Anor]

What are numbers to begin. Sciences stem from philosophy, when they get somewhat precise and exacts answers they get separed. However, there is also the issue that some of their principles stem from it, which eventually leads us to the age old elementary school paradox.

Well, what are planets to begin with? They exist even if we don't perceive them. So do numbers. Any conceivable rational being, seeing two planets, would have some concept of "two", and those concepts are fundamentally identical. Any one being's concept is not a priori, but the fundamental two-ness that all these concepts refer to is.


An element is anything inside a set.
A set is a gathering of elements.

That's not a paradox, it's just stated badly. Say rather:

A set is a gathering of items.
An element is an item within a set.

Now you have to define item, true, but it's not a paradox.

[RebelRogue]

From a more technical viewpoint, it is customary to deal with only sets. Sets can be elements in another set, but in the end everything is sets. In fact, everything is build from the empty set.

[Weezer]

It's invented. Science is merely a model to understand the universe. The universe has always been there, we humans are the ones who create the modeling system.
Let's try an analogy: You're walking down the beach and find a rock. You want to recreate the rock so you make a mold of it to the best of your abilities. At first its a really ****ty mold, but it works. As you keep making more and more molds they come closer and closer to being perfect, but never quite reach it and even the perfect mold will not be the rock. That's what science is, a continually recreated mold that describes the universe.

[AsteriskAmp]

Well, what are planets to begin with? They exist even if we don't perceive them. So do numbers. Any conceivable rational being, seeing two planets, would have some concept of "two", and those concepts are fundamentally identical. Any one being's concept is not a priori, but the fundamental two-ness that all these concepts refer to is.



That's not a paradox, it's just stated badly. Say rather:

A set is a gathering of items.
An element is an item within a set.

Now you have to define item, true, but it's not a paradox.
See a mushroom cluster, count them, you may say 20, I may say one interconnected fungi system, someone could say derp, which is a numbering system based on some random variables. Natural numbers are the only ones that could hold some slight basis to reality, but still, they as language are invented and developed, not discovered. One is not part of nature, the semantic behind one is in a way part of reality as in it represents a concept of it in the sense that it's meant to model it.

Does it need to be items? Aren't there empty sets?

[DraPrime]

Hmmm, time to throw in Augustinian philosophy.

Now fundamental laws of matter existed before we did. However, since we're on mathematics, I'd like to make an argument for the idea that we discover everything mathematical, rather than inventing it. Now, how do we acquire knowledge that we do not have? Through the senses of course. I figure out what the taste of a drink is by putting it in my mouth. I figure out what a cow is by looking at it. However, what about something like math? That really doesn't come in through any of the senses. Instruction on math certainly does, via hearing. I'd cover mathematical ability that doesn't require instruction, but to be honest I'm not knowledgeable enough in psychology to know how the human's ability to do math develops. Anyways, once you have been instructed in something, you suddenly have a whole new realm opened up to you. If you know how to do 2+2, you will suddenly be able to do 20+20. However, no one taught you what 20+20 is. You just innately know. It would seem as if you already knew this, you just didn't know how to get at that knowledge.

Despite this, I am not arguing that we simply have everything mathematical memorized, and we just remember it (I'm not Plato), it seems that the knowledge of all math is already there in some way, even if we do not have every eventuality exactly memorized. So what does this mean? Well, since this seems to be inherently ingrained in our psychology, it's not something we could make for ourselves. It would seem that we evolved with this, so this predates us. Since the question was whether or not humans have invented or discovered it, I would say that humans no more invented math than they did opposable thumbs. Therefore, it would seem that we discovered it in the depths of our a priori knowledge.

Also, there are singular units of stuff. I'm not going with big things like planets, since one could argue that their being a "thing" is only a status conferred by humans (although I'd disagree). I'll simply point to subatomic particles. One electron is one electron, and chemical reactions are based around numbers of electrons and how they are moved between atoms. Hooray, numbers exist!

There is one thing that we do invent, which is how we represent these universal truths. That is technically a part of science so I guess you could say that it is in fact both invented and discovered.

[rayne_dragon]

I think it is a combination of discovery and invention. Certain parts of math are fairly concrete: 2 + 2 = 4 for example or that the number pi is required to calculate the area of a circle. Then we get into stranger extrapolations that require invention. For instance the number i.

For science, the concepts exist independant of the theories, those theories are just codifying such things in a way that we can understand. But then there are things such as theoretical physics where the ideas are not yet proved and disproven ideas like the concept of aether. These things are invented and represent things that may or may not actually exist (or have been proven not to exist). Plus even our description of things is an invention, as often it turns out that as theories evolve and become better understood the concepts become more and more refined to be more and more accurate descriptions of the forces at work; just look at the differences between Newton's physics and Einstien's physics - while Newton wasn't wrong, Einstien's descriptions are more accurate and detailed. He discovered new aspects of existence and invented terminology and theories that described things better.

[HalfTangible]

Science is invented. The things it catalogues are discovered.

[danzibr]

But axioms are just defined as correct and useful. Sure, we can deduce things, but the fact that the base is an assumed truth and that we have no way of proving means that it is not discovered but invented to create a model of reality. It fits reality, but whatever we do there is invented, it just fits reality because it was invented to do so.

So you're saying axioms are invented and so everything we do with them is an invention. I see.

I was taking the viewpoint of considering a collection of axioms as accepted basic truths. Rather than inventing the axioms we accept some facts (I'm kind of using the word fact as truth here). We label them with words, but I don't think of axioms as creations.

Personally, I believe all Mathematics is discovered. Same with Physics. I'm not sure about Biology yet.

[danzibr]

Science is invented. The things it catalogues are discovered.

Ahh that was good for a laugh. Unless you were being serious, in which case, sorry for laughing.

[RebelRogue]

Science is invented. The things it catalogues are discovered.
That seems accurate, yes. At least for empirical disciplines. Math is harder to classify.

[AsteriskAmp]

Hmmm, time to throw in Augustinian philosophy.

Now fundamental laws of matter existed before we did. However, since we're on mathematics, I'd like to make an argument for the idea that we discover everything mathematical, rather than inventing it. Now, how do we acquire knowledge that we do not have? Through the senses of course. I figure out what the taste of a drink is by putting it in my mouth. I figure out what a cow is by looking at it. However, what about something like math? That really doesn't come in through any of the senses. Instruction on math certainly does, via hearing. I'd cover mathematical ability that doesn't require instruction, but to be honest I'm not knowledgeable enough in psychology to know how the human's ability to do math develops. Anyways, once you have been instructed in something, you suddenly have a whole new realm opened up to you. If you know how to do 2+2, you will suddenly be able to do 20+20. However, no one taught you what 20+20 is. You just innately know. It would seem as if you already knew this, you just didn't know how to get at that knowledge.

Despite this, I am not arguing that we simply have everything mathematical memorized, and we just remember it (I'm not Plato), it seems that the knowledge of all math is already there in some way, even if we do not have every eventuality exactly memorized. So what does this mean? Well, since this seems to be inherently ingrained in our psychology, it's not something we could make for ourselves. It would seem that we evolved with this, so this predates us. Since the question was whether or not humans have invented or discovered it, I would say that humans no more invented math than they did opposable thumbs. Therefore, it would seem that we discovered it in the depths of our a priori knowledge.

Also, there are singular units of stuff. I'm not going with big things like planets, since one could argue that their being a "thing" is only a status conferred by humans (although I'd disagree). I'll simply point to subatomic particles. One electron is one electron, and chemical reactions are based around numbers of electrons and how they are moved between atoms. Hooray, numbers exist!

There is one thing that we do invent, which is how we represent these universal truths. That is technically a part of science so I guess you could say that it is in fact both invented and discovered.
Prior issue, it is not necessarily true that a Universe existed before us, it gets really weird but it's part of one the four main interpretations of quantum physics. That aside:

However, the issue comes when you factor in the fact that math is not a biological process, math is by definition an abstraction of reality through numbers, and abstraction is something humans aren't built to do and they pretty much force it into their systems to cope with the systems they've built. However, it's possible to develop abstraction through the evolution of the brain, the ability to create new things, invent means we could have tried to understand our medium and finally abstract things from it and employ a system to understand them, even on a primitive level, were they would be no different from reality since they were based on it. Next, we did not discover nor invent opposable thumbs, we developed them through a biological process, math got there because a biological process made possible a mental process, and this mental process allowed us to produce something not part of nature, something that was split from our observable reality yet still modelled after it, ergo, it was not part of it, so we invented it. Also, one electron is a lot more complex in reality than it seems on models. and everything could be made of strings, which are one dimensional, this is not me, this is string theory and it's insane.


So you're saying axioms are invented and so everything we do with them is an invention. I see.

I was taking the viewpoint of considering a collection of axioms as accepted basic truths. Rather than inventing the axioms we accept some facts (I'm kind of using the word fact as truth here). We label them with words, but I don't think of axioms as creations.

Personally, I believe all Mathematics is discovered. Same with Physics. I'm not sure about Biology yet.
Axiom of choice vs determinacy.
We invent them based on the enviroment and hope they model it correctly. They are not merely a label for a set of facts, they are the set of facts we have to assume to try to further progress a set model. Sure, they are developed through observation of reality, but we are not discovering it, we are modelling it to try to discover things from the model we couldn't otherwise assume from the place we took it.


That seems accurate, yes. At least for empirical disciplines. Math is harder to classify.

I heard Quantum Mechanics knocking on the quantum door between empirical and theoretical.

[Flame of Anor]

See a mushroom cluster, count them, you may say 20, I may say one interconnected fungi system, someone could say derp, which is a numbering system based on some random variables. Natural numbers are the only ones that could hold some slight basis to reality, but still, they as language are invented and developed, not discovered. One is not part of nature, the semantic behind one is in a way part of reality as in it represents a concept of it in the sense that it's meant to model it.

Does it need to be items? Aren't there empty sets?

You're sidetracking the issue by calling into question the definition of an item. I already said that was unimportant to the definition of sets per se. If it's a set of mushrooms, then it has 20 elements. If it's a set of fungal clusters, it has one element. If it's a set of herp, it has derp elements. That does not mean that numbers or sets are undefined.


Hmmm, time to throw in Augustinian philosophy.

Now fundamental laws of matter existed before we did. However, since we're on mathematics, I'd like to make an argument for the idea that we discover everything mathematical, rather than inventing it. Now, how do we acquire knowledge that we do not have? Through the senses of course. I figure out what the taste of a drink is by putting it in my mouth. I figure out what a cow is by looking at it. However, what about something like math? That really doesn't come in through any of the senses. Instruction on math certainly does, via hearing. I'd cover mathematical ability that doesn't require instruction, but to be honest I'm not knowledgeable enough in psychology to know how the human's ability to do math develops. Anyways, once you have been instructed in something, you suddenly have a whole new realm opened up to you. If you know how to do 2+2, you will suddenly be able to do 20+20. However, no one taught you what 20+20 is. You just innately know. It would seem as if you already knew this, you just didn't know how to get at that knowledge.

Despite this, I am not arguing that we simply have everything mathematical memorized, and we just remember it (I'm not Plato), it seems that the knowledge of all math is already there in some way, even if we do not have every eventuality exactly memorized. So what does this mean? Well, since this seems to be inherently ingrained in our psychology, it's not something we could make for ourselves. It would seem that we evolved with this, so this predates us. Since the question was whether or not humans have invented or discovered it, I would say that humans no more invented math than they did opposable thumbs. Therefore, it would seem that we discovered it in the depths of our a priori knowledge.

Also, there are singular units of stuff. I'm not going with big things like planets, since one could argue that their being a "thing" is only a status conferred by humans (although I'd disagree). I'll simply point to subatomic particles. One electron is one electron, and chemical reactions are based around numbers of electrons and how they are moved between atoms. Hooray, numbers exist!

There is one thing that we do invent, which is how we represent these universal truths. That is technically a part of science so I guess you could say that it is in fact both invented and discovered.

I love Augustine! He just makes so much sense... :smallsmile:



Science is invented. The things it catalogues are discovered.
Ahh that was good for a laugh. Unless you were being serious, in which case, sorry for laughing.

Well, it was a witty way to put it, but it's entirely correct, assuming you define "science" properly.

[AsteriskAmp]

You're sidetracking the issue by calling into question the definition of an item. I already said that was unimportant to the definition of sets per se. If it's a set of mushrooms, then it has 20 elements. If it's a set of fungal clusters, it has one element. If it's a set of herp, it has derp elements. That does not mean that numbers or sets are undefined.
I'm targeting the issue toward the fact that we depend on definitions, and a different definition means a different structure to work upon.

The concept of two, expressed as two units of something depends on the definition of unit, which will eventually make a chain around since definitions pretty much allude other concepts. This tells us we are interpreting reality through our means, we are inventing a model that maps it, what we discover is on the models, the models are human inventions made to map a reality.

I think of it as a Scale Model, like the ones used by architecture students. Assume the house is already built, you make a perfect model of it in the human sense of the word perfect. It is not the house, it is a model of it, pretty darn close but not it, ergo, anything you take from it is discovered from an invention used to represent something.

[golentan]

OP: Math is not a science. Math is not a science at all. It does not rely on experimentation (much less statistical rigor) to advance itself. Demonstrations of logical consistency just aren't the same, and the falsifiables work differently than those used in experimentation. It's arguably more similar to philosophy than science, but I find it infinitely more useful. And it's a "hard" discipline, I grant, and certainly the most useful tool in the arsenal. I'm not trying to disparage it, it's just not science by itself, just as a wrench is not a mechanic's shop (being both more generally useful and a small piece of the whole).

[danzibr]

Axiom of choice vs determinacy.
We invent them based on the enviroment and hope they model it correctly. They are not merely a label for a set of facts, they are the set of facts we have to assume to try to further progress a set model. Sure, they are developed through observation of reality, but we are not discovering it, we are modelling it to try to discover things from the model we couldn't otherwise assume from the place we took it.

This topic strayed a bit from what I intended. Personally, I don't really think of axioms as invented or discovered.

I'll refer to an earlier post to get back to my real question.
After a certain point of abstractness, when we're off in la-la land, when objects don't have any reasonable physical interpretation (or perhaps just something we can't imagine), are new results discoveries or inventions? Were they just sitting around waiting to be found, or is it something like a microwave oven?

[Weezer]

This topic strayed a bit from what I intended. Personally, I don't really think of axioms as invented or discovered.


What are they if they aren't either of those things?

[danzibr]

OP: Math is not a science. Math is not a science at all. [...]

Whoa, what? I mean, I did read the rest of your post, but I absolutely disagree. Our definitions of science must be different.

[Lord Raziere]

Both of course.

Since science would not exist without us inventing it, and science is made up for things we discovered and is the art of discovering, we invented science by discovering it and discovered it by inventing it, because we invented discovery and discovered invention by inventing invention and discovering discovery, and therefore we both discovered and invented the universe for it would exist without us to observe that it exists and say that it exists because we discovered it and through discovering it we invented it.

Therefore we both discovered and invented the universe and we continue to do so every time we experiment, come, let us invent and discover reality by dropping an apple on an orange and seeing what happens. :smallbiggrin:

[danzibr]

What are they if they aren't either of those things?

Accepted. Something inherent, maybe. As opposed to something which has a proof. When I talk about discovered v. invented I'm referring to results. Axioms aren't results and so, to me, the words discovered and invented don't apply.

[AsteriskAmp]

This topic strayed a bit from what I intended. Personally, I don't really think of axioms as invented or discovered.

I'll refer to an earlier post to get back to my real question.
After a certain point of abstractness, when we're off in la-la land, when objects don't have any reasonable physical interpretation (or perhaps just something we can't imagine), are new results discoveries or inventions? Were they just sitting around waiting to be found, or is it something like a microwave oven?

Sorry for kinda derrailing it.
When you reach La La Land they are an invention (and before that too, but I'm willing to drop this statement since it is not part of the question).
Otherwise, I want my Pentachoroidal plushy of a Pentachoron now!

[Flame of Anor]

Accepted. Something inherent, maybe. As opposed to something which has a proof. When I talk about discovered v. invented I'm referring to results. Axioms aren't results and so, to me, the words discovered and invented don't apply.

Well, if they're inherent, and we didn't know them at some earlier time, and we do know them now, I'd say that's a pretty good case for "discovered".

[golentan]

Whoa, what? I mean, I did read the rest of your post, but I absolutely disagree. Our definitions of science must be different.

You may be using the term in the manner of aristotle. (http://en.wikipedia.org/wiki/Science) But I hold that my version is the currently accepted definition. In part, it's because math is not externally testable in the same way as, say, gravity, or allele propagation in fruit flies. All you can do is hold it up and ask if it's internally logically consistent, and if you are for one reason or another incapable of properly spotting a fallacy that's that. Some really, really crazy things have been logically consistent internally and most decidedly unscientific by virtue of being untestable or ignoring the results of contradictory tests (I'm sure you can think of your own examples here). If we get into a definition argument, though, neither of us will win because that's the point at which argumentation breaks down, so I'm going to leave it at that.

[Weezer]

Whoa, what? I mean, I did read the rest of your post, but I absolutely disagree. Our definitions of science must be different.

Then whats your definition of science? Because from the discussions I've had with people it seems pretty accepted that math is not a science, primarily because it doesn't rely on empirical data or the scientific method.

[danzibr]

Well, if they're inherent, and we didn't know them at some earlier time, and we do know them now, I'd say that's a pretty good case for "discovered".

Eh I dunno... I could just refer to the second part of my argument. I just wouldn't use the words for axioms. Anyways, some things are inherent. I'm a new father, too. I totally think some things are inherent. ZF axioms are kinda advanced, so maybe that's a bad comparison. Yeah, I'll stick with the second part.

And araveugnitsuga, I wasn't trying to complain about the topic straying. I should have been clearer. Still, all the talk of axioms (and the other talk) is interesting. I'm surprised at how much of a response I got, to be honest. In the 3.5 forums I don't get neaaaarly as much feedback.

[danzibr]

Then whats your definition of science? Because from the discussions I've had with people it seems pretty accepted that math is not a science, primarily because it doesn't rely on empirical data or the scientific method.

Oh I dunno, something like the first hit from dictionary.com.

[Yanagi]

Inventing suggests coming up with something new--a primarily conceptual process--with no semantic marker about the validity of the thing invented. Discovering suggests confirming the existence of something with no semantic implications about it novelness.

Generation of theory is an act of invention basic to natural philosophy and underpinning scientific postulation; however--the "scientific method"--the construct of how ideas are agreed upon as empirically valid--concerns itself with confirmation of truth. Semantically, the scientific method has greater intersection with discovery than invention because of its pursuit of confirmation.

[AsteriskAmp]

Oh I dunno, something like the first hit from dictionary.com.

Why not try Webster or Oxford?


Definition of SCIENCE

1
: the state of knowing : knowledge as distinguished from ignorance or misunderstanding
2
a : a department of systematized knowledge as an object of study <the science of theology>
b : something (as a sport or technique) that may be studied or learned like systematized knowledge <have it down to a science>
3
a : knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method
b : such knowledge or such a system of knowledge concerned with the physical world and its phenomena : natural science
4
: a system or method reconciling practical ends with scientific laws <cooking is both a science and an art>

the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment:
the world of science and technology
a particular area of science:
veterinary science
[count noun] :
the agricultural sciences
a systematically organized body of knowledge on a particular subject:
the science of criminology
archaic knowledge of any kind.
Math COULD be a science by some definitions.

[Ravens_cry]

Discovered. We invent theories to explain the discovered phenomena, we invent technology that takes advantage of the discovered phenomena and we can use the principles of science to help in engineering, but science is about the discovery itself. Making up a theory to explain it all comes after.

[Catch]

The Latin origin of "discover" means to expose or lay bare.
The Latin origin of "invent" means to come upon or to find.

Is science invented or discovered? Both.

Concisely:
The universe exists.
It has constants and variables.
These have structure and behaviors.

Humans observe the universe and ask questions: How? Why?
Humans create tools to answer to these questions.
Sciences are sets of tools to answer questions.
New tools enable new observations, which raise new questions to be answered, which require new tools.

Science is composed of observation (discovery) and explanation (invention). So, returning to the Latin, science exposes the properties of the universe and comes upon ways to define them.

[Ravens_cry]

Eh, screw what I said, Catch is right, it's both.

[Flame of Anor]

Catch, your description is good, but didn't you use to have a different username?

[Brother Oni]

Science is composed of observation (discovery) and explanation (invention). So, returning to the Latin, science exposes the properties of the universe and comes upon ways to define them.

And sometimes science invents new things. The higher number elements which mostly exist for fractions of a second in the heart of particle accelerator chambers are a good example, as are any synthetic drug molecule.

I agree that it is both - science discovers new things, then invents ways to make use of them.

[Kislath]

Mathematics is a science, the science of studying Math.
Math, though, is simply an underlying fundamental truth of the universe which applies to and governs all else. It's the programming language of reality and beyond.
Deep or shallow? Profound or insipid?

[Yora]

After 5 years of economics, cultural studies, social geography, and linguistic, I am now confident to say that all social sciences are completely invented. In most cases they still conform to the standards of scientific research, but nothing social scientists describe does really exist. All social science studies always only describe what the scientists did percieve, usually followed up with a rough general system how they suppose such things usually behave.
Historians and linguists often claimed that they are stating facts, but thankfully that bad habbit has been decreasing in the last decades. They still create stories that do not contradict the evidence, but still most stuff is just made up in a way that fits their views. But when a scientists is aware of that, social sciences are still valuable and provide knowledge and understanding.
The worst offenders are econimic sciences, which love to use charts and number and complex calculation, which creates the appearance that they are working with hard facts. But since the numbers are all made up based on educated guesses, it's still a social science and doesn't have anything to do with math.

[drakir_nosslin]

Talking about math I'd say that the axioms are invented and the result these produces are discovered.
There's nothing that says that we couldn't use a wholly different set of axioms for our math, but it would probably turn out to be pretty much useless in physics and stuff, so we don't.

[Serpentine]

Probably already been said, and with a lot more words, but anyways:
Science is the process by which we discover things about our universe.
Technology is the application of those discoveries to practical purposes.
My housemate, who has a Bachelor in Pure Mathematics, Honours in Astrophysics, Diploma of Mathematics Teaching, and is undergoing a Masters in Pure Mathematics, says mathematics is discovered, not invented.

[PirateMonk]

Also, there are singular units of stuff. I'm not going with big things like planets, since one could argue that their being a "thing" is only a status conferred by humans (although I'd disagree). I'll simply point to subatomic particles. One electron is one electron, and chemical reactions are based around numbers of electrons and how they are moved between atoms. Hooray, numbers exist!

No, things which can be described perfectly or near-perfectly with numbers exist. When we say "three is a prime number," we are not actually talking about electrons. As far as I can tell, we are not actually talking about anything.

[Science Officer]

I would agree that math is discovered.
At least, after some few axioms (http://en.wikipedia.org/wiki/Godel%27s_incompleteness_theorem) are invented/discovered/intuited/enter-the-mind-and-gain-widespread-knowledge-through-some-method-which-is-not-invention-or-discovery.

After those, the process is to discover that more things are logically consistent with those axioms. I think.


Seems relevant, but not entirely:
There was a bit that I really liked in the A Very Short Introduction to Mathematics about the black king.
In chess, it doesn't make very much sense to ask if the black king exists. It is represented on the gameboard by a piece, its behaviour and effects are modelled by the rules.
Likewise, in mathematics, it makes little sense to ask if, say, the number i exists, it only matters what can be done with it.
Sort of an instrumentalism for mathematics.

[Trog]

Science is neither invented nor discovered.

Science is awesomed.


For example:

Scientist: "Whoa! I totally awesomed a time machine!"
Bystander: "Really? ...Awesome!"

or

Scientist: "Whoa! I awesomed a cure for cancer!"
Bystander: "Wait... didn't you like... just awesome some other invention just like a second ago." :smallconfused:
Scientist: "uhhh... yeah... Time Machine?!"
Bystander: *blinks* "Oh yeah!
...
... Awesome!"

[AsteriskAmp]

Science is neither invented nor discovered.

Science is awesomed.


For example:

Scientist: "Whoa! I totally awesomed a time machine!"
Bystander: "Really? ...Awesome!"

or

Scientist: "Whoa! I awesomed a cure for cancer!"
Bystander: "Wait... didn't you like... just awesome some other invention just like a second ago." :smallconfused:
Scientist: "uhhh... yeah... Time Machine?!"
Bystander: *blinks* "Oh yeah!
...
... Awesome!"

Look for Ferrofluids to be awesomed in their termination of cancer (experimental treatment for the time being).

[Toastkart]

I lean more on the side of invented. Although it does depend a lot on exactly what is meant by discovered and invented. I think someone earlier actually said science is just a model of reality, however imperfect, and that's as close as we can get, which I think is pretty accurate.

My field of study is psychology, so I may be a little biased. Here's some thoughts to keep in mind.

Operationalization: Operationalization of a concept is a way of narrowing its definition so that it can be empirically studied. Through this process the operationalization of a concept becomes the concept. Invented.

Variables: Controlling for variables is the cornerstone of being able to do empirical research. Unfortunately, the real world doesn't exist in a vacuum, and even in a laboratory setting you will never control every variable. In fact, the manner in which you control variables can greatly influence the outcome. Invented.

Samples: This may be less important in some fields, but it is very important in mine. It is assumed that a random sample of a group is representative of the whole, but that's just an assumption because the whole is a nebulous concept. Invented.


I am now confident to say that all social sciences are completely invented. In most cases they still conform to the standards of scientific research, but nothing social scientists describe does really exist.

Glad to know that people who exhibit various behaviors don't exist.:smalltongue: I've always thought of it sort of the other way around. That empirical scientific methods are ill-suited to describe complex interactions of intelligent beings. More or less for the reasons that I already outlined. You can't work with whole concepts, you can't control all variables, and your sample isn't necessarily representative of your population.

“The facts of nature are settled within the field of human argument.” ~ The Golem- What Everyone Should Know about Science by Harry Collins and Trevor Pinch.


Math, though, is simply an underlying fundamental truth of the universe which applies to and governs all else. It's the programming language of reality and beyond.
Deep or shallow? Profound or insipid?

I could say the same about language and it would be just as true.

[Flame of Anor]

Science is neither invented nor discovered.

Science is awesomed.


For example:

Scientist: "Whoa! I totally awesomed a time machine!"
Bystander: "Really? ...Awesome!"

or

Scientist: "Whoa! I awesomed a cure for cancer!"
Bystander: "Wait... didn't you like... just awesome some other invention just like a second ago." :smallconfused:
Scientist: "uhhh... yeah... Time Machine?!"
Bystander: *blinks* "Oh yeah!
...
... Awesome!"

What genius! Trog, you have just awesomed a totally new and, er, awesome way of perceiving science! :smallbiggrin: