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Old 14th September 2012
Ninguem Ninguem is offline
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Default HIgher math

What's your take on it?
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Old 15th September 2012
ocicat ocicat is offline
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Quote:
Originally Posted by Ninguem View Post
What's your take on it?
Your question is rather vague & open-ended.

If the underlying question you are really asking is whether higher mathematics is useful and/or necessary as a consumer of the digital age, it all depends upon what are your goals. What do you want to understand?

Higher mathematics is critical to understanding the guts of cryptography, graphics, compression, & search, & here are a few reasons/examples why:
  • A number of arguments made in cryptography are based on inductive proofs, discrete statistics, all mixed in with some emerging ideas coming from abstract algebra. Each one of these disciplines is covered in advanced undergraduate courses, but true mastery only comes in post-graduate work.
  • Graphics (as does neural networks...) attempts to do very smart things in the smallest number of processor cycles. Although the code which will be executed may seem exceedingly simple, it is based on increasingly sophisticated calculus & physics.
  • Historically, compression came as a end result of the work pioneered by Claude Shannon in information theory. From an educational perspective, this material isn't typically seen until graduate school.
  • Search used to be based on databases & fast string comparisons. Now, it is using some leading edge research done in machine learning -- teaching machines algorithmically how to discern if any particular solution is more efficient than another, & letting them figure out themselves what data really answers any particular question. The mixture of statistics with linear algebra to deal with millions of variables at the same time is cutting edge research.
This obviously is not meant to be a comprehensive list. It only begins to attempt to tie topics back to their theoretical underpinnings.

Personally, I find this stuff fascinating, but this material isn't learned merely from Wikipedia pages; rather, Wikipedia articles will give only a very high-level summary. To master & understand the underlying theory takes years. Shortcuts don't exist. Patience, tenacity, & curiosity are required.
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Old 15th September 2012
Ninguem Ninguem is offline
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Thanks, man.

I was curious as to how my mind works with pattern recognition and came to the conclusion that Fourier systems are the closest.
How does one properly say, "I understood some of the concepts of higher math before I studied the subject"?
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Old 20th September 2012
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Daisuke_Aramaki Daisuke_Aramaki is offline
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Agree with ocicat. Higher Math could mean a lot of things and ocicat has mentioned a few. Let me add a couple of points. Broadly speaking, math development takes place in two areas - Pure Math and Applied Math. Most of my personal experiences have been with applied math. All through my studies and research career, I have worked on diverse areas, such as, Recurrent neural nets, Global optimization problems, pattern recognition, artificial intelligence, multivariate statistical analysis, combinatorial game theory and stochastic methods. I have also had the pleasure of having worked in the core mathematical areas of non-linear equations, chaos and deterministic differential equations. At one point, I was totally obsessed with a problem in infinite partial differential equations. Thankfully, it is beyond me.

If you are in engineering, then, numerical analysis and optimization problems are extremely important. In Physics and in particular, theoretical physics, the importance of math, be it elementary or complex is a no brainer.

Coming to your question, are you telling us that you are like a clairvoyant and can know something before understanding about it. Some people can grasp complex concepts much better than others. Apart from that, I don't know how to answer your question. But I can tell you this, you probably know Ramanujan, whose contributions in number theory has been tremendous. Too bad he died very young. He is very famous for writing clumsy proofs of his theorems and making a lot of mistakes. Thankfully, the English mathematician, Hardy helped him a lot. But, the validity of his theorems could never be questioned. Once asked, how he is able to construct such theorems, Ramanujan replied that it was his Goddess who provided him the ideas.

I had to slow down a bit on my math work a bit right now, since my obsession pushed me to the brink of madness. Started seeing mathematical objects suddenly everywhere and started talking in math. This led to a strong psychotic episode that eventually led to being diagnosed as a paranoid schizophrenic. But, once I feel better, I will immediately go back.
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Old 20th September 2012
Ninguem Ninguem is offline
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No, I am not a clairavoyent of any sort. Pattern recognition and manipulation to create a new pattern and then to test that against the original.
Maybe you should write down the formulas next time you start seeing them; it could give you something to solve in the mean time. Either they will make sense or be gibberish.
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Old 5th February 2013
Ninguem Ninguem is offline
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A few questions and opinions that may be without any logic or reason:
1. A point is a one dimensional object in space; yet, would a point also be a four dimensional object if it exists for more than one moment in time? I see time as the fourth dimension and not the tesseract example so commonly referred to.
2. It seems that some believe that a point is both a one dimensional and zero dimensional object while others believe that a zero dimensional object has no mass. I can understand why an object would be one/two/three dimensional and four dimensional at the same time- along with other factors- but not as zero and one simultaneously. On the latter group, what would light be considered as or even other wave-energy forms? These would still need a fourth dimensional property- the same for higher dimensional values- to exist or even be observed in our plane.
3. Higher math uses the concept of division by zero in infinity. Why isn't this implemented in computer programming? Is the difficulty in setting a character value or in separating the function i.e. to prevent a system crash?
4. One of the basic concepts of string theory is that all things occur at the same moment. Now this brings up the idea that everything is a single moment and a single instance. Is it possible that the uni(multi)verse is but one in an infinite series and that the process is repeating itself infinitely? (Ha ha! I made a joke.)
5. A circle has 1,296,000 points if you include all minutes, degrees and seconds. Yes, I am aware if you do not overlap 0 and 360 then the total can be 1,295,999. Would these points also have a negative value? If the circle is large enough that the area between seconds is one foot or greater- let's say a meter- then what would be the value of those points in between each two seconds? Would the exist as micro, nano, etc or would the vale be one of infinity plus X?
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Old 5th February 2013
ocicat ocicat is offline
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Quote:
Originally Posted by Ninguem View Post
A point is a one dimensional object in space; yet, would a point also be a four dimensional object if it exists for more than one moment in time?
You are mixing metaphors.
  • If discussion is limited to a line, then a point position along that line has only a single dimension because the line itself is one-dimensional.
  • A position on a plane has coordinates in two different dimensions because the plane itself is two-dimensional.
Yes, a two-dimensional plane can exist in 3-space, but in this system, points will have three coordinates -- one for each dimension considered in the entire system under consideration.
Quote:
It seems that some believe that a point is both a one dimensional and zero dimensional object while others believe that a zero dimensional object has no mass.
Pure mathematics is not concerned with physical interpretation. A point can have coordinates in n-dimensions if discussion is allowing for n dimensions.
Quote:
I can understand why an object would be one/two/three dimensional and four dimensional at the same time- along with other factors- but not as zero and one simultaneously.
It appears you are changing the definition of a system midstream.
Quote:
Higher math uses the concept of division by zero in infinity. Why isn't this implemented in computer programming?
Study how division is implemented in hardware.
Quote:
A circle has 1,296,000 points if you include all minutes, degrees and seconds. Yes, I am aware if you do not overlap 0 and 360 then the total can be 1,295,999. Would these points also have a negative value?
Can one go outside and count -3 cars? Physically, no. Yet, there are times when negativity is added to conversation to describe direction. This is usually done relative to Greenwich, England -- both in terms of timezones and direction east & west.

Last edited by ocicat; 5th February 2013 at 02:37 PM. Reason: spelling
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