What is the purpose of Math

[fluffy]

I am not a maths wizard but I have a sense of what it is for and why it exists. Why so many kinds exist.

First of all why so many?

Because it's about relationships between mathematical objects we build up in our mental space.

Proofs formulas equations

They all are of matter of fact built up the way words in a story is. So you have begining middle endings. And vocabulary. Grammar. Syntax. Semantics.

All this is hard to know if you cannot read math. Math can fill libraries of books. Telling you how to get to a new placement in many domains.

It take practice and years of reading math books to get good just like any language you have thousands of subjects. You cannot just memorize math like a dictionary. You need to use it to understand.

To calculate you need symbols numbers and shapes. Operations and categories.

This is why it is so hard to grasp at first. Because we are exposed to math so little as children it's like not being spoken to as infants. We have very small vocabulary we barely can say thing in math like how you say "give food" or "give toy" this is not the same as Shakespeare (a highly advanced script writer).

As example, complex numbers are used in statistics to map out probabilities with samples in high dimensional space given some kind of fractal the data conforms too. Then you can make predictions with new data along some pathways as they are filled in.

What does this even mean unless you have done millions of calculations yourself over time. Mostly people can just do ten or so before giving up. You need big computers to even do something by hand would take years. People don't spend time on math that much. And new maths need years of new learning and research given you don't just read math you also communicate it to others like story books and on the playground with friends. Kids don't normally speak math to each other. It is very archain.

And not all math books are going to be written properly. You will get some that are totally crap. This makes it difficult to get somewhere as you will need to read hundreds of math books just to be literate. Even then it's the communication later on that is going to matter. To read math papers that don't have standard language in the math you know about.

I have this idea for the longest time I can not communicate in math but it is mathematical. I'm working on shapes and diagrams for it but it takes time to know what they are for forgetting why I did some part as I did or reinterpreting what I did. It's not fully explained. It takes tremendous amounts of work reviewing the process I have trains of thought that don't align and confuse them. (I still have trouble with principle components analysis without a computer)

 

[dr froyd]

the purpose of math is to arrive at logically provable statements about quantities, i.e. if certain assumptions are true then certain other things must be true.

that's why it's difficult for human brains to do math; we are mostly designed to reason in language, and language is noisy and inconsistent.

which is why i think people who call math a "language" have misunderstood what math is (it's a formal system, not a language)

 

[Hadoblado]

First of all why so many?

QED

 

[sushi]

measurement

calculation

count

there is a whole theory of math called measurement theory

 

[nobody]

I don't know. Math is a formal language, but in Physics it seems to create a layer of frustrating abstraction when it isn't well explained or becomes overly complex and convoluted.

For example, the famous F=ma is easy enough to understand, but if you didn't know what each variable was and no one showed you the causal geometry it represents, unless you relate it to geometry, it's just an abstraction to you. Something you could potentially calculate, but not truly understand.

This is a problem and endless debate of Modern Physics, where many people feel Quantum Physics is relying on mathematics without causal geometry. To them it feels 'incomplete', like we lost the plot of the geometry. To others, they like the thought of God collapsing wavefunctions or there being Many-Worlds. A lot of Unified Field Theories seem to rely on connecting Math, instead of determining geometry, as if the Math is what's more important.

But I've been wondering if the Riemann Hypothesis is also true, but possibly unproveable. Mathematics seems weird when you start considering infinite series, as if it all has to represent something geometric, but it just seems beyond our comprehension.

 

[fluffy]

The density of where things happen or might be is not real in a hard sense. It's more of a prediction. Like what is the likelihood of finding high IQ people in Harvard vs a gas station in the desert. This but with many times the sample discrepancy.

I get that math can be used for things.

Many kids in class said: why study math, when am I ever going to use it?

I was looking for something like this also.

I thought more about algorithms than math because I never could do all the calculations myself. But I understand computers do this better. I just cannot buy the software yet.

 

[kuoka]

Mathematics is a language used to describe the world, but not only that.

The world has several "ontological" layers:
- The actual reality, how the universe really works and what it is
- The perception of reality, how humans and other living beings see the world through our senses
- The models of reality, how humans try to describe reality using logic, observed patterns and rules they create. Those rule sets become frameworks, branches of mathematics, physics theories and so on

Mathematics is a modelling language that can approach a partial simulation or a partial explanation of reality.

Then there's mathematics that isn't applicable to reality. Maybe there is a different universe where that part of mathematics would describe it, but not ours. We are discovering, making rules in an infinite space of logic and solutions, it makes sense that most of the elements drawn from the space of mathematical constructs would be useless to us.

 

[nobody]

The density of where things happen or might be is not real in a hard sense. It's more of a prediction. Like what is the likelihood of finding high IQ people in Harvard vs a gas station in the desert. This but with many times the sample discrepancy.

Yeah. I totally understand statistics in that way. But it's odd to see it being used in quantum mechanics as if it represents absolute reality. For example, probability distributions of hydrogen atoms show a clear geometry, but I haven't seen anyone attempt to explain this geometry in causal terms.

What's most peculiar is QFT induces eigenstates in order to measure these densities clearly. But the reality is perhaps more dynamic. You end up only looking at atoms in stable states and ignoring transitions. Transitions instead are often quantized to make them easier to calculate, such as what appears to be bosons, despite the fact that they exist for a very short period of time and seem to be hinting at something more dynamic and complex than the calculations want to show.

But there's another problem in that the scale of things seems to lead to the Uncertainty Principle. Photons just need to be higher frequency to interact with an electron and bring it to a higher energy state. But on the quantum level nothing exists independently, because of Bells Theorems and superposition, so effecting an electron also effects the rest of the entangled atom, so potentially everything in the nucleus. Further photons have variable wavelengths that are much greater than the size of a fermionic particle (and even an electron is thought to be 'pointlike'). Geometrically, you could interpret that as blasting an atom with a vortex of energy and somehow expecting to quietly observe what's there. You can't and so you end up with deducing things from effects and not causes and instead have to infer things through probability and statistics (which is fine). But again, it might mislead from the actual geometry. The problem is this leads to a paradox where we assume there is no transition between when something is a particle or a wave because we designed the math to ignore or exclude dynamic states because we can't look at them directly. So you get hazy, contradictory, and hand-wavy answers to the problem of collapsing the wavefunction.

And when it comes to gravity, which is a macro phenomena, that might mean that thinking we can 'quantize' gravity is misguided. So far, no one has been able to do it. It might be that we need to bring back relativity to quantum mechanics fully, not just in QCD.

But I want to point out I don't have a problem with using what we have to and what works. Nor do I think Physics is "wrong" in that sense. It does work for prediction, so that's fine. I just have a problem with how people are interpreting these things to represent reality.

 

[fluffy]

Back in the old days all you had was pen and paper. In school when they had us memorize times tables that was the last time I had full instructions on what to do. In the time period before I got to school a new philosophy of teaching came into being called constructivism. Just give the student problems and they figure it out themselves.

This worked a little bit for me. I figured out algebra but I never learned long division or decimal multiplication/division.

In calculus to do allot of it requires adding and substraction in an algorithm. But they never told me how to draw a basic circle in calculus.

I have something like a 135 spatial IQ but terrible processing speed and working memory. I remember I did allot of projects, they just did not involve math. Supposedly in the 1950s the average highschool student can do calculus but then why was I held back? Because I was supposed to figure it out myself do to "constructivism". I was smart enough?

Well if I don't have books or school I can at least try something I am interested in. Which is why I am collecting data. Not much you can do without it. My coin collection in one and I began collecting aluminum cans.

I am getting a new computer soon. I think if I get the right software I can create simulations. If not I think I will try and learn java again. Python I just cannot create algorithms in it. It's not meant to be object oriented in the way Java is. And C++ is, can break things bad and is to low level even if it's highly efficient.

I think I can afford some books, they just need to be more college level. My local library has math books but I like practical math. Math to get projects done.