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Minato
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No, mathematics is not a science. The key to being a science is the "scientific method":

1) Observe a situation.

2) Create (many) hypotheses to explain the situation.

3) Extend the hypotheses to develop tests of each hypothesis.

4) Perform the tests to eliminate hypotheses.

 

Mathematics does not do that. It is true that mathematics can be used in (3).

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How can we exclude mathematics from the field of science? The techniques of mathematics are also based on the nature of observable features. For instance, vectors have been designed to meet the requirements of motion and quantities posing a definite direction.

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No, mathematics is not a science. The key to being a science is the "scientific method":

1) Observe a situation.

2) Create (many) hypotheses to explain the situation.

3) Extend the hypotheses to develop tests of each hypothesis.

4) Perform the tests to eliminate hypotheses.

 

Mathematics does not do that. It is true that mathematics can be used in (3).

I think I have to disagree there. as Srimann dutta said

 

How can we exclude mathematics from the field of science? The techniques of mathematics are also based on the nature of observable features. For instance, vectors have been designed to meet the requirements of motion and quantities posing a definite direction.

also there are other example like genetic algorithms and ant colony optimisation stuff like that was invented by observing nature.

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Well, we would be about three centuries behind where we are now in scientific knowledge without mathematics. So I would say that math is unavoidable in science. In most physics, you can only explain concepts so far until you have to get into some serious mathematics.

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Well, we would be about three centuries behind where we are now in scientific knowledge without mathematics. So I would say that math is unavoidable in science. In most physics, you can only explain concepts so far until you have to get into some serious mathematics.

I agree Math../ generate proof of an Event So ? Edited by Roger Dynamic Motion
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Even many physicists don't understand quantum mechanics on a practical level. They understand it mathematically, and can run the equations. But it's very hard to understand how the quantum world is.

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I think I have to disagree there. as Srimann dutta said

 

also there are other example like genetic algorithms and ant colony optimisation stuff like that was invented by observing nature.

 

Neither of you is talking about mathematics, you are talking about applications of mathematics.

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I find it very sad that something has to have an application for it to be of value.

The things you think are useful which you don't think have applications actually do have applications. If you do something merely because it brings you joy or pleasure, that's an application. To say something is "useful" is, by definition, to say that it has an application. Edited by Code42
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I think in this world anything that doesn't have use is simply of no value. But that's not the question here. Question is maths part of or not. We do use maths in science but is it as another entity or is it just integral part of science?

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  • 1 month later...
1 hour ago, Gratiano said:

Is this called self consistency?

Self Consistency is essential but not everything. There was (maybe still is) a hope to produce a mathematical system in which each of the axiomata are self-evident if the others are true - but in the end you need something which is just assumed to be true for your system 

 

Also complete self consistency is impossible - any sufficiently complex mathematical axiomatical system will eventually produce self-contradiction; but we tend to ignore this as you only get to those points with recursion and self reference.  A nice way of thinking about it in linguistic rather than mathematical terms is Epiminides paradox  -

Quote

Epimenides was a Cretan who made one immortal statement: "All Cretans are liars."

Douglas Hoffstadter - Godel Escher Bach

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9 hours ago, imatfaal said:

Self Consistency is essential but not everything. There was (maybe still is) a hope to produce a mathematical system in which each of the axiomata are self-evident if the others are true - but in the end you need something which is just assumed to be true for your system 

 

Also complete self consistency is impossible - any sufficiently complex mathematical axiomatical system will eventually produce self-contradiction; but we tend to ignore this as you only get to those points with recursion and self reference.  A nice way of thinking about it in linguistic rather than mathematical terms is Epiminides paradox  -

Douglas Hoffstadter - Godel Escher Bach

I am familiar with Epimenides paradox. Everything became clear to me about such paradoxa(including "inclusions" like all, uni, co) when I came across a story with uncle scrooge called "the collection of collections". Would the collection of all collection include itself? And of course when reading "logicomix". 

For all you said, I have fallen in love with mathematics. One can take something for granted(axiom) and build an entire entity on it. And it is equally valid to all, noone can defy it unless one changes the axiom. Philosophically speaking, the world seems to be like this, it started axiomatically from something... 

Give me an example where self-contradiction is produced.

 

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3 hours ago, Gratiano said:

...Give me an example where self-contradiction is produced.

 

 

In maths - too complex to do here.  In language - the paradox given above.  Read Godel Escher Bach by Doug Hoffstadter - it is completely bonkers but a modern classic

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3 hours ago, Gratiano said:

I am familiar with Epimenides paradox. ...

 

 

I have just seen your location - from that I really would hope that you are familiar with Epiminides; I also apologize for calling you a liar - even via a millennia old quote :)

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8 hours ago, imatfaal said:

I have just seen your location - from that I really would hope that you are familiar with Epiminides; I also apologize for calling you a liar - even via a millennia old quote :)

Hahaha!!! I am not cretan, I just reside here. Not many things have changed since though since the time of Epimenides especially here, on the western edge of the island! ;)

 

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Haven't been to Crete for many years - the whole island was pretty quiet when i was last there; apparently the area around Heraklion is quite ridiculously busy now.  When I was there it was mainly for people wanting to see Knossos - but now I hear awful stories; almost as bad as Rhodes  

I stayed (illiegally) for a week in a cave on the coast of Tilos (I think) that had been inhabited on and off for about 3000 years.  It was basically a hermit's cave  which had been walled in the 19th century; it was two hours hard hike from the nearest road and three hours to the nearest shops.   After a while the beauty , isolation, and utter tranquillity allowed the mind to really wander - it became clear how they came up with all these amazing ideas in classical times; space for the mind to be free. 

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5 minutes ago, imatfaal said:

Haven't been to Crete for many years - the whole island was pretty quiet when i was last there; apparently the area around Heraklion is quite ridiculously busy now.  When I was there it was mainly for people wanting to see Knossos - but now I hear awful stories; almost as bad as Rhodes  

I stayed (illiegally) for a week in a cave on the coast of Tilos (I think) that had been inhabited on and off for about 3000 years.  It was basically a hermit's cave  which had been walled in the 19th century; it was two hours hard hike from the nearest road and three hours to the nearest shops.   After a while the beauty , isolation, and utter tranquillity allowed the mind to really wander - it became clear how they came up with all these amazing ideas in classical times; space for the mind to be free. 

Around Heraklion things are better regarding lying... Epimenides would have to recall his statement! ;) The stories you hear probably have to do with Malia, I used to work as a lifeguard 12 years ago there and I can guarantee that the awful stories are true! :D Even during daylight... 

Why "illegally" stayef? What did you do? Were you condemned for any mathematical fault? ;) Classical era had a lot of land unoccupied, offering spectacular views and intriguing one's imagination, and too many slaves to take care of the boring "daily" matters and hard labour work... thus, ancient greeks had plenty of time to occupy themselves with philosophy and mental work... 

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29 minutes ago, Gratiano said:

Around Heraklion things are better regarding lying... Epimenides would have to recall his statement! ;) The stories you hear probably have to do with Malia, I used to work as a lifeguard 12 years ago there and I can guarantee that the awful stories are true! :D Even during daylight... 

Why "illegally" stayef? What did you do? Were you condemned for any mathematical fault? ;) Classical era had a lot of land unoccupied, offering spectacular views and intriguing one's imagination, and too many slaves to take care of the boring "daily" matters and hard labour work... thus, ancient greeks had plenty of time to occupy themselves with philosophy and mental work... 

Maybe not illegal - but dodgy; it was a bit of a shrine and place of pilgrimage for many years as the last hermit who lived there was very revered locally.  But it was clear that the locals had stopped coming regularly so I decided to use it.  Will see if I can dig out my snaps - unfortunately before digi-cameras so many fewer photos taken.

 

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29 minutes ago, imatfaal said:

Maybe not illegal - but dodgy; it was a bit of a shrine and place of pilgrimage for many years as the last hermit who lived there was very revered locally.  But it was clear that the locals had stopped coming regularly so I decided to use it.  Will see if I can dig out my snaps - unfortunately before digi-cameras so many fewer photos taken.

 

What is the name of this last hermit?

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