Omega constant?

Post Reply New Topic

I've been working on this model/theory thing that I started around a month ago to help me understand logarithmic equations in chemical kinetics. Anyway, the idea has developed A LOT and something that was very encouraging happened last night as I was trying out different idea's as to how the " shapes " would interact. I then noticed the significance for the first few digits of the Omega constant when considering the natural logarithmic constant 'e'. So I spent the next few hours crunching the hell out of it until finally I got it down to 14 decimals (my calculator wouldn't let me go any further). Then got pretty excited about it, played around with it and was blown away by some of the results, but really couldn't figure out why I was getting said results.

Anyway, I started to search google after I realized how significant a number it seemed to be... and at first the only thing I could find was Omega to like ten decimals in some Spanish ( I think ) book that only brought up the numbers once, and seemed to give no significance to it. A few hours later I found the wiki-page with all the mathematical constant and of course, at the very bottom was my wasted little discovery.

Now it seems, after scouring the internet, that all I can find are long equations which mean nothing to me. This could be explained by how I realized around the time that I started on logarithms that I never really actually KNEW what math was really doing or representing outside of fundamental arithmetic like addition, subtraction, multiplication and division. My math background was just trying to remember how the equations worked and interacted with each other in a, " If I put the number five into these curves ( parenthesis ) which is over a line (division) with a one underneath it the result will be a five." And if asked why any of that was as it was, I would have no idea how to answer you outside of saying that it's just what happens when a number is over a one. I'm starting to think this was attributed to the fact that I never actually attended sixth, seventh, or eight grade.

So please try to stay away from long equations. If you have to use equations, please try to break it down for me. Metaphors and analogies would be great. Thanks.

This sounds rather interesting. Please provide an abstract definition of Omega, since the symbol is widely used in different contexts. Also provide some references in the scientific or mathematical literature.

The Omega I have heard of is a tensor related to Einstein's correction to his field equations which measure how curved or bent the cosmos is globally. Is this the Omega to which you refer?

ruveyn

Well for me the constant as of now, and at first glance, seems to be (obviously) highly related to the constant e for natural logarithms. And my measurements have been strictly expressed as what I could best describe as ratios of the Sierpinski Pyramid with it's inverse, and also as a simple method to express the concept involving graph paper and the division of fraction percentages using graph paper. Where a single cube will represent the shape of the molarity number in aqueous reaction much in the sense of cm^3 would in a small container, the container metaphorically being e. With that you make a continually smaller shape within the shape ( I won't try to explain the math just yet, it's fairly long ) ... and at a certain point these percentage numbers, at an incredibly small fraction of the natural logarithmic " shape " constant can be applied to find the inverses of other shapes in a process that I can't fully ' see ' or understand.

So one possibility seems to be that Omega could represent a point B to cross reference and increase calculation accuracy for the rate reactions which for some reason disregard the cube fraction's method, which only works for a percentage of equations, and varies in approximate rate reaction percentage correlation.

As for references ... I suppose there have been very little. For the most part my book started it, as I was having trouble understanding how to visualize or understand the math for chemical kinetics. From there it went from understanding how the typical log equation ' flowed ', then to graph paper where I recognized the ladder like sequence, then I noticed how a cone like shape would be a fair way to represent what was happening visually. Then I googled something like eulers pyramid and eventually found the Sierpinski pyramid.

From there I used molarity as a logic point to understand the math and ended up with the graph paper cubes as a logical choice. The cone/triangle idea was from a large collection of memories, and a basic theory of gravity based on how I think thermodynamics works... which is something I thought up a few months prior when faced with the blimp equation and my need to totally understand what it happening visually before I feel comfortable with going on. Other than that... I also got the initial triangle idea for the logarithms from this really old idea I had roughly two years ago where I thought of the ' big bang ' theory as an expanding and contracting thing, then drew an hourglass like shape to represent it to my friends.

As far as mathematical references ... I don't really have any besides the natural log constant, initial logarithmic concept, and the Sierpinski pyramid ... where the pyramid was mostly a visual aid. An example of how minimalist like the math is = A ' coach ' like student teacher I know at the chemistry learning center, who is very good with chemistry/math, helped me put a portion of the cube concept into an equation, which ended up being both totally confusing for me, and fairly large considering how little of the idea it was representing. However, page to page ratio wise... his equation took up about 1/6th of what my math did.



I really don't know ... all I can find are things related to Lambert and whatever W represents. It took me long enough to even find the number at all, to the point where I figured I had discovered a new constant. Only to find it at the bottom of a wiki-mathematical constant list.

Try to keep in mind that before this semester I had never read more than a section of a paragraph from a chemistry 2 high-school book roughly five years ago. I've never taken geometry, never taken physics, never taken calculus... I also took algebra three times in high-school. It was never hard for me, I just loathed being forced to sit and remember things that they wouldn't explain to me, and which fade from memory and meaning months later.

Could you provide the link to the Wikipedia page with your constant please? I'm finding myself curious. (I just spent the past two hours working with equations that deal with the physical properties of polymer/fiber composites for a homework assignment)

http://en.wikipedia.org/wiki/Omega_constant ... also, not my constant, but it would be if this were a hundred years earlier. :\



Me too

Ah yeah, no worries. I've had that feeling before, I get a sudden idea in the middle of the night, spend hours scribbling down things on paper, then I go online to look stuff up and lo-and-behold, there's the work I just did. Don't be too disheartened by things like this, just realize that there are millions of scientists constantly working on their own little niches, leaving you to find it very hard to come up with original, unique work. We had a speaker come in to one of my undergraduate engineering classes, he started up a fairly successful pharmaceuticals company nearby, and he said something that's so very true: "As science progresses, the studies of individual scientists has to be more and more of a narrower and narrower subject, or less and less about more and more subjects. We'll soon reach the point where, to be successful, you have to know either everything about nothing or nothing about everything."

Yeah I've definitely noticed that pattern throughout my life. My main theme with this isn't to solve the singularity thing with black holes... but more so to prove that A: The educational system is horrendously flawed. and B: I'm not as dumb as my grades would suggest.

A: Is a fairly distant work in progress ... however my transition into B this semester has reminded me a lot of the movie Phenomenon. However, I know what I can and can't do ( I count on my fingers for s*** sake ) ... and I'm also not anywhere near as good as John Travolta magically gets throughout that movie. Just somehow, out of nowhere, this semester, especially chemistry, suddenly started exposing faculty to my odd way of doing things whose unconventional factor has had and probably will still have people constantly attacking me ... but at least now I know that my imagination is applicable to something other than daydreaming, cool dreams, video games, and writing fiction in short bursts.

P.S. Is it normal for high level math students to not have a clue as to what the equations actually apply to outside of more equations and more numbers? I've been stumping calc 1 and 2 students with what I consider to be a fairly simple calculation sequence ... which is great for my ego ( if I cared about it at all) but horrible for my aspirations of developing more efficient teaching methods.

Wow, Ntstanch, your thought and my thought are so much alike it is kind of scary. I think you might be a little more advanced in your classes than I am in my classes. Anyway. I no longer believe the universe is going to collapse back in on itself. I know that is physics heresy, especially when you are a physics major like me. But it kind of seems like zero point energy makes it impossible for the universe to collapse back in on itself. At zero point energy, the quantum particles begin to vibrate. This kind of seems like the property of a solid. IF the quantum phase into a solid state, it kind of seems like the universe will not have the ability to collapse back in on itself. So the rubber band thing is no longer working for me.

I have been very deeply in thought about several different topics, most of which my Mom has made me promise not to write out loud about until I am far enough advancd in my studies to be able to substantiate them. However, I too have been considering the e constant, mostly from a how everything works point of view.

The e constant has a number assigned to it. The pi constant has a number assigned to it. The K constant does NOT have a number assigned to it. So I became sort of fascinated in the differences between them and how they move. The ln e constant moves in a spiral shape. It occurs naturally in nature. (so when you have plasma circuling a magentic field line ejected from the sun, it probably takes a natural e spiral shape.) The pi constant has a number assigned to it. This number stays the same no matter what size the circle is....and the shape is a circle. The K constant has no shape, it represents movement (decay and other things) and it seems in order for us to track it, we are dependent on time. WOW do I have a lot of thought about time....you just would not believe.

Anyway. I think in images and I have always had this large image of math all connected. I still do not have all of the math pieces, so there are large gaping holes in my images, but when you started talking about how the numbers "connect" I am amazingly fascinated.

Thanks for posting it.