What Actually Is Mathematics ??!!!

[harisankartj]

Numbers and shapes are helpful since we can navigate the world based on certain models of reality. But doesn't that mean math is biased towards human need ? I don't see numbers anywhere .... and shape ? Forget square, rectangle,circle ....What the actual heck is a shape ?????

What are we ACTUALLY DOING when we say we wanna know the math of the world ?? Is it a pattern seeing stuff ? Cus lately i have been wondering about the role of what they call "math" ... in my direct actual experience.

[Lorcan]

I do not understand the full function of mathematics. To me it is an entirely relative function trying to measure things in the universe that itself are relative.

 

How much different would mathematics be if I simply added another number after 9?

The current numbers are.    0, 1, 2 ,3, 4, 5, 6, 7 ,8 ,9

All other numbers are made from combining these number. What if I added to more numbers?

Who said there only had to be 10 numbers.

0,1,2,4,5,6,7,8,9,P,X

Now how much would mathematics change by simply adding more numbers? Would calculus still work? I do not know. And surely if calculus does still work then the amount of numbers available in the number alphabet is irrelavent. It then would appear that mathematics is some form of logic to do with the measurement of defining of what is relative in relative way?

[ajasatya]

@Lorcan https://en.wikipedia.org/wiki/Numeral_system

binary system: 0, 1
hexadecimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

when we state a mathematical truth like a²+b²=c², it doesn't depend on the numerical system. it will be true no matter what basis you use to represent the numbers you plug in the formula. so calculus, geometry, linear algebra etc do still work.

Edited August 10, 2017 by ajasatya

[harisankartj]

@Lorcan 

 

4 hours ago, Lorcan said:

I do not understand the full function of mathematics.

That was what i was pointing out too . What confused me is the realization that Mathematics was not founded in ANY ASPECT of direct experience aka reality . For physics, chemistry  and biology we can at least say that something "of substance" is witnessed and we are conceptualizing it on paper, in form of field report or something. 

But math is the only field of study that is heavily biased to aid human need of measurement and NOT actually occurring in reality . 

The only form of math I see in the world are symmetry. Besides that ALL math seem to be putting "our twist on the world".

 

[harisankartj]

Hey guys I found a cool video on the topic I posted! 

 

 

[nick96]

@harisankartj

When speaking of maths referred to just as arithmetics, then the question about defining numbers with an empirical link to reality arises. 

I remember that in my first year at University the professor of mathematical analysis 1 ( calculus ) was very clear at the beginning of the course stating that we wouldn't focus on defining what a number is. This field is studied in https://en.m.wikipedia.org/wiki/Philosophy_of_mathematics . Still nobody seems to agree on an answer to that .

But other fields of mathematics ( analytical geometry, linear algebra, abstract algebra , real analysis, complex analysis ) in a lot of areas aren't less linked to experience than physics or chemistry are . These fields don't just work with numbers but with wider sets. 

They infact have a lot to do with parts of reality that we usually take for granted. 

Linear algebra with vector spaces creates a model of what we perceive as space.

Mathematical analysis ( calculus ) studies all the properties that arise when making an infinite subdivision of a dense object . This includes continuous change. 

The mental concepts that arise from this are very connected to our perceptions of space and time . In this way ,mathematics can be a deep field that creates a model of very fundamental parts of reality.

The concepts of continuity , continuos change and derivatives relate a lot to creating a model of the present moment, or rather moving "deeply" into the present moment . They are also connected with constant changing in the present.  If you have studied the concepts you can look at their definitions and see for yourself .

The concept of infinite in calculus can be a model for our perception of infinity ( for who has been able to experience it... ) .

So, maths deals with concepts connected to our experience as deep as space, time ( even if we don't actually experience it ) , present moment, constant change !!

[harisankartj]

@nick96  I have not yet studied aspects of mathematics that deep. So my reasoning here will look amateur,pardon me.

7 hours ago, nick96 said:

I remember that in my first year at University the professor of mathematical analysis 1 ( calculus ) was very clear at the beginning of the course stating that we wouldn't focus on defining what a number is.

See that is exactly what led me to put up this topic in the first place. I tried to "define" a number by attempting to see "where actually the number is " in empirical reality, which confused me a lot.

 

7 hours ago, nick96 said:

But other fields of mathematics ( analytical geometry, linear algebra, abstract algebra , real analysis, complex analysis ) in a lot of areas aren't less linked to experience than physics or chemistry are . These fields don't just work with numbers but with wider sets.

Hmmm...now that you mention it,that is quite true. But if that is the case doesn't the entire field of science purport to model reality without tackling epistemology of how scientific modeling is done ? ( Phy, chem, math , bio ) .If so are the kids in our school studying something that doesn't ACTUALLY exist in empirical reality?

7 hours ago, nick96 said:

Linear algebra with vector spaces creates a model of what we perceive as space

'....creates a model ...' . I agree that mathematics make accurate models that other aspects of reality seems to confirm. What I am saying is "math is a human creation" and not actually what IS in direct experience.

 

 

7 hours ago, nick96 said:

Mathematical analysis ( calculus ) studies all the properties that arise when making an infinite subdivision of a dense object . This includes continuous change. 

The mental concepts that arise from this are very connected to our perceptions of space and time . In this way ,mathematics can be a deep field that creates a model of very fundamental parts of reality.

The concepts of continuity , continuos change and derivatives relate a lot to creating a model of the present moment, or rather moving "deeply" into the present moment . They are also connected with constant changing in the present.  If you have studied the concepts you can look at their definitions and see for yourself .

The concept of infinite in calculus can be a model for our perception of infinity ( for who has been able to experience it... ) .

So, maths deals with concepts connected to our experience as deep as space, time ( even if we don't actually experience it ) , present moment, constant change !!

 

IT'S too remarkable how models seem to confirm reality but .... ahhh. I still have a nagging sense of "this is not it" . Not cus your arguments "aren't strong enough" or something but I personally have a hard time grasping of the essence of "math". Will it exist devoid of human need of modelling? It seems so constant ...TO US. If our visual field was circular instead of flat we would have different concepts of modeling space right?  

I guess what I was trying to figure out is the "actual foundation" for math....the epistemological grounds for math.Mathematics seem to be "catered to us" instead of the "actual structure of direct experience".... know what I'm saying..?

Edited August 14, 2017 by harisankartj

[Joseph Maynor]

It's a set of loosely-related but not foundationally unified theories about numbers, logic, sequences, series, sets, relations, geometry, and inqualities -- and corresponding numerous applications of these concepts.

Mathematics is thoughts.  Lots of thoughts.  Thoughts that have nice application in the Physical Sciences, Engineering, and elsewhere.  

Edited August 14, 2017 by Joseph Maynor

[harisankartj]

@Joseph Maynor

2 hours ago, Joseph Maynor said:

 

Mathematics is thoughts.  Lots of thoughts.  Thoughts that have nice application in the Physical Sciences, Engineering, and elsewhere.  

So it IS THOUGHT! That's what I wanted to hear to be honest ( yh validation of belief is frowned upon I know ) but that's what I feel.They don't have any ACTUAL foundation in reality.

[nick96]

@harisankartj

ALL sciences are thought. All sciences create a mental model of some part of reality.

Even if you fully understand intellectually the most recent and complex theory of physics you will not have understood reality directly but you will have understood your mental model of it. 

What is particular with maths is that in a lot ( but not all ! ) areas it does not have any kind of FOUNDATION with something that we can DIRECTLY CONNECT with our experience of reality ( as in what numbers are ).

But the vector space R3 in linear algebra is as much a good model of the part of reality we percieve as space as the model of an object falling described in physics is. 

7 hours ago, harisankartj said:

@nick96  But if that is the case doesn't the entire field of science purport to model reality without tackling epistemology of how scientific modeling is done ? ( Phy, chem, math , bio ) .If so are the kids in our school studying something that doesn't ACTUALLY exist in empirical reality?

The question you are asking is a very deep and important question that has been the object of study by lots of people during a lot of centuries . https://en.m.wikipedia.org/wiki/Scientific_method

@harisankartj

7 hours ago, harisankartj said:

@nick96  If our visual field was circular instead of flat we would have different concepts of modeling space right?

Yes. Enlightenment experiences can shift your perception of reality to something that appears more like a 180 degrees sight.

And this makes me think now that a lot in maths could have a lot of do with our dualistic perception of reality .  

Bcuz with so many advanced concepts it gets very very close to understanding deep parts of reality that can only be really understood experiencially.

Also, in a non- dualistic perception of reality , would it have any sense (or would it even be possible ) to count ??

Maths could be a serious attempt of the human mind to grasp what cannot be grasped with the mind.

Quite cool stuff !!

Edited August 14, 2017 by nick96

[harisankartj]

3 hours ago, nick96 said:

 

Quite cool stuff !!

Hell yeah it's cool !!

[Joseph Maynor]

On 8/14/2017 at 3:23 AM, harisankartj said:

@Joseph Maynor

So it IS THOUGHT! That's what I wanted to hear to be honest ( yh validation of belief is frowned upon I know ) but that's what I feel.They don't have any ACTUAL foundation in reality.

Mathematics doesn't have a foundation in reality, but it has correlation with theories about reality.  Or, more importantly, theories can be framed within the theories of Mathematics.  But notice that any practical application of a mathematical idea is no longer the pure mathematical idea.  It is now a new thought.  A different thought.  One way to think of Mathematics is it is the theoretical residue that remains after the mechanical-mind abstracts the content out of its mechanical theories, especially physical or scientific theories of external reality.  When that content falls away, what is left is the abstract structures of Mathematics, the scaffolding of the probing-mind facing outwards on physical reality.  But this is a story, don't cling to this as a truth.  It's just an idea to goose the intuition a little bit.  We call these intuition-pumps in Philosophy.   Talking about Mathematics as one thing is a bullshitting exercise, but it can be useful as a training-wheels theory to get your gears-turning as you explore more on your own.   At some point you gotta kick the training-wheels off though.

Mathematics also comes from quantizing, individuating, drawing analogies to geometry, consideration of groups or sets in the abstract of what's actually in them, or the consideration of relations or functions between variables that can be represented in mathematical structures.  But notice that X = YZ has a different meaning from F = MA, although F = MA is influenced on the pure mathematical form of X = YZ.  F = MA is force is equal to mass times acceleration, a principle of Newtonian Physics.

Remember this, Mathematics is more like a bush than a tree.  Don't think of Mathematics as a single thing reducing-down to a foundation in logic or set theory, but as a loose connection of theories with a certain resemblance.  Set theory or symbolic propositional logic is no more foundational than the theory of ratios or the theory of integral equations.  Mathematics has no center or foundation.  The expectation that Mathematics should have a center or a foundation is a theory that WE overlay on top of Mathematics.  Each theory in Mathematics is of-a-piece and has a unique history of relation, influence, and interconnection with other "mathematical theories" or other concepts and metaphors (some existing outside of Mathematics).  Think of Matrices.  Do they exist in Nature?  No, we made them up to solve certain problems.  Each Mathematical theory or structure has a history behind it.  If you really want to learn the Philosophy of Mathematics, learn about the History of Mathematics and new doors will open for you.  The a-historical way that Mathematics is taught in schools where all the theories are bunched-together in a nifty, tidy book, is a convenience that textbook authors created, they made it up.  Mathematics didn't come into being that way.  Mathematics evolved in a more piece-meal, messy, creative, and exploratory way, one little step at a time, each step standing on the shoulders of prior work done in the field of Mathematics (and Mathematical Physics especially).

Here's a great book to read which I read and loved every page.

The Story of Mathematics by Lloyd Motz.  (If you like this read his The Story of Physics too, it is excellent.)

https://www.amazon.com/Story-Mathematics-Lloyd-Motz/dp/0380724588/ref=sr_1_2?s=books&ie=UTF8&qid=1502931087&sr=1-2&keywords=the+story+of+physics+motz

https://www.amazon.com/Story-Physics-Jefferson-Weaver-Paperback/dp/B010WF6JRA/ref=sr_1_4?s=books&ie=UTF8&qid=1502931123&sr=1-4&keywords=the+story+of+physics+motz

Edited August 17, 2017 by Joseph Maynor

[harisankartj]

@Joseph Maynor

10 hours ago, Joseph Maynor said:

Each Mathematical theory or structure has a history behind it.  If you really want to learn the Philosophy of Mathematics, learn about the History of Mathematics and new doors will open for you.  The a-historical way that Mathematics is taught in schools where all the theories are bunched-together in a nifty, tidy book, is a convenience that textbook authors created, they made it up.  Mathematics didn't come into being that way.  Mathematics evolved in a more piece-meal, messy, creative, and exploratory way, one little step at a time, each step standing on the shoulders of prior work done in the field of Mathematics (and Mathematical Physics especially).

IKR ! The way they teach math in school is just so robotic that no wonder most kids grow up to despise the subject of math.They don't understand the essence of it! How it came to be! 

The Story of Mathematics by Lloyd Motz.  (If you like this read his The Story of Physics too, it is excellent.)

https://www.amazon.com/Story-Mathematics-Lloyd-Motz/dp/0380724588/ref=sr_1_2?s=books&ie=UTF8&qid=1502931087&sr=1-2&keywords=the+story+of+physics+motz

https://www.amazon.com/Story-Physics-Jefferson-Weaver-Paperback/dp/B010WF6JRA/ref=sr_1_4?s=books&ie=UTF8&qid=1502931123&sr=1-4&keywords=the+story+of+physics+motz

Will put it on my "to read" list. Thanks for the suggestion!

[Nahm]

@harisankartj it's a creation of the one, like everything and nothing else.It's imagination. It's a dream. It's other-than-alone. It's fuckin awesome!