Unity+

Well, this is probably thought of already, but might as well give people the concept. This work is a small fraction of Collatz Theory So, basically, the idea is that it is an "equation" that lies on multiple dimensions(two dimensional). It is an evolving equation matrix, meaning on an infinite scale it involves infinitely. Here is the notation of a Collatz Matrix equation: [math]C(x)_{k\times d}\begin{Bmatrix}a_{f}&b_{f}\\u_{f}&v_{f}\end{Bmatrix},s(k_p,d_p) = A_{k\times d}[/math] In this case, the four variables that end with the subscript f are the formulas used in the equation to calculate the matrix. In each case, if the number were to be moved up the matrix, the original number stays at its coordinate while, when moving up the value, the number has to follow the rules of the [math]a_f[/math] variable formula. If the number is to be moved left, the value must follow the formula within the [math]b_f[/math] slot, if the number were to be moved right it must follow the rule or formula in the [math]u_f[/math] slot, and then when moving down the number must follow the rule or formula in the [math]v_f[/math] slot. The starting coordinate is the end coordinate in the notation. The x variable refers to the number being used in the whole entire Collatz Matrix equation. Now, the reason why I developed this is it originally was a game I made, where it follow the same rules. It used some of the rules of the Collatz Conjecture. http://en.wikipedia.org/wiki/Collatz_conjecture What I found interesting about the idea was the fact that within the Collatz Matrix equation the numbers next to a number in a slot(not in the diagonal directions) were approximately equal. I thought maybe a Collatz Perfect Matrix, which is a matrix following the Collatz Matrix Equation that has values working together equally being equal to the one that is either up, down,left, or right of it. I still have not answered the question, but the question is: Does a Collatz Perfect Matrix exist? This question probably isn't important, so I just want thoughts on this concept. If your a bit confused, here is a link to the game: http://www.thescienceforum.com/general-discussion/35844-collatzs-matrix-game.html The question or problem only applies for Collatz's rules, no other rules. [math]C(x)_{k\times d}\begin{Bmatrix}\frac{x}{2}&\frac{x-1}{3}\\3x+1&2x\end{Bmatrix},s(k_p,d_p)\ = A_{k\times d}[/math] X in the formula rules refers to the evolving x value, while the x next to the C refers to the initial x value. And the question also refers to a matrix that [math]k=d[/math] and [math]k > 2, d>2[/math] There are also Collatz Numbers, which are numbers that in all directions work for the Collatz Matrix Equation, though this does not mean that they are numbers that can form Collatz Perfect Matrices. Here are a few Collatz Numbers: [math]4,10,16,22...[/math] Here is a formula to find Collatz numbers if given a Collatz number: [math]C_{n} = c_{n} + 6[/math] Also.... [math]c_{n} = 6n-2[/math] Here are some conjectures that I put up about Collatz numbers. Collatz Number Conjecture: All Collatz Numbers are even Collatz Differential Number Conjecture: All Collatz Numbers can be found by adding 6 to another Collatz number. Collatz Sequence Number Conjecture: The Collatz Numbers will always be found when applying the Collatz Rules(Collatz Conjecture) to a Collatz Matrix Equation. Collatz Initial State Conjecture: For any number being processed through the Collatz Rules, the number as a result as the first step being an odd value will always be a Collatz Number. Collatz End Number Conjecture: For the first step value, if [math]C_{n} = x - 6,C_{n}\geq 4[/math] is done repeatedly until it equals 4, than the Collatz process will reach 1. Collatz Rule Perfect Matrix Hypothesis: If a Collatz Perfect Matrix can be formed, one can only be formed with the Collatz rules. Collatz 3x3 Perfect Matrix Conjecture(Questionable): A Collatz Perfect Matrix can only be formed in a 3x3 matrix Here is some Mathematica code(thanks to another user). Clear["Global'*"] out = "" up[x_] := If[Divisible[x, 2], x/2, 0]; left[x_] := If[Divisible[x - 1, 3], (x - 1)/3, 0]; right[x_] := 3 x + 1; down[x_] := 2 x; dimension = 4; x = 2; c = Table[0, {a, 1, dimension}, {b, 1, dimension}] MatrixForm[c] row = 2; col = 2 c[[row]][[col]] = x; MatrixForm[c] iterate[c_, row_, col_] := Module[{x, deadEnd, upM, downM, leftM, rightM}, x = c[[row]][[col]]; (*Print["here it is:",MatrixForm[c]];*) upM = c; downM = c; leftM = c; rightM = c; deadEnd = 1; If[row != 1 && c[[row - 1]][[col]] == 0 && up[x] != 0, (*If we're not at the top, and we haven't filled in the cell above, and the 'up' calculation gives an integer, construct the new matrix, and pass it recursively to the algorithm.*) upM[[row - 1]][[col]] = up[x]; deadEnd = 0; iterate[upM, row - 1, col]]; If[row != dimension && c[[row + 1]][[col]] == 0 && down[x] != 0, downM[[row + 1]][[col]] = down[x]; deadEnd = 0; iterate[downM, row + 1, col]]; If[col != 1 && c[[row]][[col - 1]] == 0 && left[t] != 0, leftM[[row]][[col - 1]] = left[x]; deadEnd = 0; iterate[leftM, row, col - 1]]; If[col != dimension && c[[row]][[col + 1]] == 0 && right[x] != 0, rightM[[row]][[col + 1]] = right[x]; deadEnd = 0; iterate[rightM, row, col + 1]]; (*If we were at a dead-end up, down, left, and right, then reveal the matrix*) If[deadEnd == 1, Print[MatrixForm[c]]; out = out <> "" ]; ]; iterate[c, row, col] out Thanks to the code, I made some fascinating findings. I made a Collatz-Matrix algorithm that can take a prime product and break it up into its two different factors. Right now, it is inefficient because there is currently no equation formed yet to retrieve the values of specific coordinates related to the value inputed. Also, the increase in the size of the prime product affects how large the matrix solutions must be in order to retrieve the prime factors involved in the prime products. Another inefficiency is the size of the matrix solutions at the moment. However, if the equations can be found to describe the values within the matrix solutions this maybe a new find of breaking down prime products. For example, for the sake of simplicity, let us take the two prime numbers 13 and 3 and multiply them together(the product is 39). Now, the algorithmic equation would look like the following: [math]C(39)_{5 \times 5}\begin{Bmatrix} \frac{x}{2} &\frac{x-1}{3} \\ 3x+1&2x \end{Bmatrix},s(3,3)[/math] In many of the solutions, one of the prime factors comes up once or twice. This means this will take less time to find the prime factor within the "jumble" of numbers that have resulted from the solutions. With my Collatz determinant equations, I may be able to form an equation that will predict the locations of the factors within the matrix solutions. If so, this may be revolutionary. Another thing to do to clean up the mess would be to set up a set that consists only one of each value from all the solutions(and then only include prime numbers into the set). And then you could eliminate all values that are not prime. Here would be the result: [math]S_{1} \left \{ 29,3,19,117,353,89,59,1423,157,13,229,119,79,241,11,103,7,101,67,17,709 \right \}[/math] Primes larger than the initial value also can be eliminated: [math]S_{2} \left \{ 29,3,19,13,11,7,17\right \}[/math] And one could run through these possibilities to test for the factors. There is also something I need to clarify. The zeros in the solutions do not necessarily mean they are 0(I know it is kind of paradoxical, but for the sake of argument). Though 0 can refer to the fact that element was a result of the parameters within the equations, the 0 can also mean a null-zero element(meaning it is non-existent as a part of the matrix solution). More definition will be provided later. Here is a file with mathematical properties of the concept: https://www.dropbox.com/s/n8o6dauuxq8i8s0/Collatz%20Theory.odf(requires Open Office Math). Here is another problem to be addressed by the Collatz-Matrix Prime Factorization algorithm. Since, by prediction, the size of the matrix solutions will increase as the size of the composite number gets larger the amount of matrix solutions that are produced by the Collatz-Matrix equation will increase because an increase in the size of the matrix solutions will bring a larger amount of solutions available(though there are exceptions). However, the problem is still pending because I haven't measured to a point where if the ratio of the size of the number to the size of the matrix solutions to the amount of matrix solutions will be linear, exponential, or a wave function. [math]C(p_{1} \times p_{2})_{k\times d}\begin{Bmatrix} \frac{x}{2} &\frac{x-1}{3} \\ 3x+1&2x \end{Bmatrix},s(k-3,d-3)[/math] [math]x=P=p_{1}\times p_{2}[/math] [math]k=d[/math] [math]A = k\times d=k^{2}=d^{2}[/math] [math]A:P[/math] [math]k^{2}: P[/math] [math]d^{2}: P[/math] [math]k^{2}:x[/math] [math]d^{2}:x[/math] [math]k^{2}: p_{1}p_{2}[/math] [math]d^{2}: p_{1}p_{2}[/math] [math]k:\sqrt{P}[/math] [math]d:\sqrt{P}[/math] [math]k:\sqrt{x}[/math] [math]d:\sqrt{x}[/math] [math]r=\frac{A}{P}=\frac{A}{p_{1}p_{2}}=\frac{k^{2}}{p_{1}p_{2}}=\frac{d^{2}}{p_{1}p_{2}}=\frac{k^{2}}{P}=\frac{d^{2}}{P}[/math] Where the function for these proportions is defined by [math]\Gamma (x) [/math] I am still working on the function, but this function is defined as such. One to keep in mind is this function does not refer to the proportion between the size of the matrix solutions and how many that will occur, but the composite and the minimal size of matrix solution needed, where k = d, to find the factors of the composite. Though, here are a few questions that must be asked: 1. Is the relation between the size of the matrix solution and the number of matrix solutions exponential, linear, wave-like, all, or none? 2. For the Collatz-Matrix Prime Factorization algorithm, is the relation between the size(or magnitude) of the composite number and the size of the matrix solution linear, exponential, wave-like, or neither?(If neither, then the function of [math]\Gamma (x) [/math] does not exist). Simply put, the question asks whether there is a function [math]\Gamma (x) [/math] to describe the relationship between [math]P[/math] and [math]A[/math]. 3. In relation with the first question, is growth dependent on the initial position of x? I forgot to mention that x refers to the size of the composite made up of two primes and two primes only, where a composite is referred to as [math]s_{n}[/math], where n is the index of the composite number made up of two primes. [math]C(2\times 2)_{2\times 2}\begin{Bmatrix} \frac{x}{2} &\frac{x-1}{3} \\ 3x+1 & 2x \end{Bmatrix},s(2,2)[/math] [math]\begin{bmatrix} 0 &2 \\ 0 &4 \end{bmatrix}[/math] [math]\begin{bmatrix} 0 &0 \\ 1 &4 \end{bmatrix}[/math] Now, using the proportions given above, here is the result: [math]P = 4[/math] [math]A = 4[/math] [math]r=\frac{4}{4}[/math] [math]r=1[/math] Here is another, which is 6: [math]C(2\times 3)_{2\times 2}\begin{Bmatrix} \frac{x}{2} &\frac{x-1}{3} \\ 3x+1 & 2x \end{Bmatrix},s(2,2)[/math] [math]\begin{bmatrix} 0 &3 \\ 0 &6 \end{bmatrix}[/math] Now, using the proportions given above, here is the result: [math]P = 6[/math] [math]A = 4[/math] [math]r=\frac{4}{6}[/math] [math]r=\frac{2}{3}[/math] Here is a problem, however, that arises from proving the second question, whether it is yes or no. Since with function [math]\Gamma (x) [/math] there requires an introduction of [math]s_{n}[/math] which represents a composite of two primes, where n represents the index of such a composite, and since there are infinite primes that exist, which is proven by Euler: Euler?s analytic proof of the infinitude of the primes | Beyond the Numbers(This is just a source out of many that give the article of his proofs), there would be no known way to make an analysis of the growth of the matrix solution sizes with the composite numbers of two primes. Since there are an infinitesimal set of prime numbers, [math]\Gamma (x) [/math] would be hard to be proven to exist because there is no known way(as I know of) to prove that an exponential, linear, or wave-like growth in the relationship between [math]P[/math] and [math]A[/math] exists. The only way to prove such a relationship would be to use Calculus(I think) and the concept of infinity in some fashion. Instead of looking at each semi-prime in order, it seems more consistent to observe each prime factor with another prime factor that is larger than it. For example, the first prime to analyze would be 2. Now, the tricky thing with this function is since there are infinite primes in analyze with the prime 2 this causes a problem with trying to analyze the primes precisely. Here is a graph of the ratios(not the function that I am looking for though). [math]P_n = \frac{1}{p_n},\frac{1}{p_{n+1}}, \frac{1}{p_{n+2}}, ...[/math] where [math](p)_\mathbb{N}[/math] is the normal sequence of prime numbers. Then [math]\Gamma: \mathbb{N} \to \mathbb{Q}^\mathbb{N}: x \mapsto \Gamma(x) = \frac{A}{p_x} P_{x}[/math]. [math]\Gamma(1) = \frac{A}{p_{1}p_{1}}, \frac{A}{p_{1}p_{2}}, \frac{A}{p_{1}p_{3}}, ...[/math] [math]\Gamma(2) = \frac{A}{p_{2}p_{2}}, \frac{A}{p_{2}p_{3}}, \frac{A}{p_{2}p_{4}}, ...[/math] If the [math]\Gamma (x)[/math] function can be found, an equation can be formed to predict the amount of solutions for the Collatz-Matrix Prime Factorization equation because the amount of matrix solutions is dependent on the size of the matrix solutions. This can also be used to predict the efficiency of the equation. The following, if this is true, would be the equation for finding the area of a matrix solution from a Collatz-Matrix equation(this only applies to Collatz-Matrix Prime Factorization equations). [math]A = \Gamma p_{x}p_{n}, x\geq n[/math] Which is also... [math]A = \Gamma P[/math] [math]P = \frac{A}{\Gamma}[/math] Here are a few more equations that can be formed, though they are irrelevant(at the moment). [math]p_{x} = \frac{A}{\Gamma p_{n}}, x\geq n[/math] [math]p_{n} = \frac{A}{\Gamma p_{x}}, x\geq n[/math] One thing I noticed while graphing this function is how as the semi-primes get larger for the Collatz-Matrix Prime Factorization equation the more primes that occur through out the matrix solutions that exist before the prime numbers that make up the semi-prime within the equation.

I just wanted to contribute to the debate. But I have to give you another +1 for that.

I would have to disagree with the idea that photons would have mass because it goes against the Higgs field's way of working. If photons had mass, they couldn't go faster than the speed of light, which is the irony. However, if the Higgsfield does not exist, I would only agree that photons have some sort of property similar to mass, but mass for a photon is farther out there to the explanations we have today. However, as any scientist would agree, nothing is impossible.

Can't tell if sarcasm or just being very, very....nevermind. Anyways, it seems like it could work, but you have to test it over and over to make sure it is a good process.

You make a great point here. +1 But yet we are to realize why this proportionality exists between the mass and the gravitational forces of the mass. There is still room for consideration.

All of them pretty much. And yes he did. Read the posts please.

Yes, but it that could account for varience in gravitational fields, for a gravitational field is not always constant, with very, very slight variance. For example, the Earth's gravitational acceleration could be at first 9.810000000000000 then it is 9.810000000000000000000000000001. Tell me if I misunderstood your point.

Maybe because particles spin proportional to their mass due to interaction between one mass and another?

I would like to see your sources. I am betting that it will be from a liberal media source. People still believe it was the video? Man we must still be in the Stone Ages(irony detected).

FYI, that isn't the point of this hypothesis if you even read the hypothesis in the first place. Thank you for not taking the time to read it.

Okay, I have no more questions right now. I will think of more if I can. [OFFTOPIC]Instead of me asking the questions here, maybe answer the PMs so this topic doesn't get overflown with questions[/OFFTOPIC]

This is the exact same theory I developed way before this one, and it didn't get much attention, so the likely hood of this one getting any attention is very slim(no offense, just the way things work).

Also, is this Inertia property a property of space? Sorry for such a small question.

Okay, here is another question(s): What causes the matter to emit this inertia field? How do Black Holes carry out the same inertia properties?

It says the space-time deformation phenomena occurs due to the mass of the object affecting the space-time fabric. It is just the property of matter and energy. Inertia properties would not be needed in this case.

Though I would have to say the Obama administration's actions towards this attack were totally out of line, where they did nothing for at least a month, there is no reason to call out a "Who really killed the ambassador?" card. There is a point being that the Obama administration isn't really that good at foreign policy(especially when they entered Pakistan's airspace and territory without due process as required by foreign policy). If they failed to acknowledge the fact that they did this, of course this situation was really likely to happen. People in the Middle East, especially Libya, were angered and are angered by what has been going on, which then leads to the Ambassador's death. In my opinion, Obama already knew that the Ambassador was facing some sort of threat. The commanders of the soldiers that went to Libya were interviewed and they even said that these Navy Seals had to volunteer because Obama refused to give support to the Ambassador. Well done Obama, you just killed off all these men. Now on to the other points. It was even said that the video wasn't EVEN close to the reason why they "outraged." The media even tried to "hide" the information due to their liberal mindedness(no offense to liberals). So, I would say it was the Obama administration's fault for all of this, but if there was a conspiracy behind all of this Obama would be heading towards a different direction. Obama isn't a conspirator, he is just not good at foreign policy as he says he is.

So you are saying that gravity does not affect space-time? This goes against what was recently tested, where they proved that Earth's gravity affects the space-time. Other than that, let me think of more questions to ask.

From what I can see, you just basically renamed gravity, which isn't a cause of gravity. By Albert Einstein's theory of relativity, Gravity is a force caused by a mass affecting the space-time area, like using the fabric analogy. When an object is on a space-time fabric, there is an indentation in the fabric. This indentation is the area of gravity. IF Inertia property is a cause gravity, here are the following questions: Does Inertia properties affect time as well? Is time the affect of inertia properties, where light photons are affected by this inertia property? I'll think up more questions later.

This is a paragraph from my latest manuscript of my new hypothesis. My hypothesis is dealing with the DNA language and the core of determining the interpretation of DNA. It goes out to explain how DNA is to be read in order to understand the language. This manuscript will go out to explain the hypothesis and how it is to be handled. I am open to debate, so I would love to have a healthy discussion about it. If you have any questions about the hypothesis, just let me now.Here are a few main points of the hypothesis: - DNA is to be read not from straight forward reading the code the way it is, but needs to go through an algorithmic process to be processed easier and be read the way it is supposed to be read. - The relation between this hypothesis and the new discovery that was released, where now scientists can easily determine DNA sequences using their Sudoku method. Source: Here - How to carry out the algorithm with a DNA sequence. Manuscript: Click here I am all ears(or eyes in this case).

I find it funny how people can fall for such alien "evidence". I remember one article about how a man was able to deceive these group of people to form a cult and commit suicide by just putting a trash can lid in front of a camera, photo-shopped it, and claimed he had evidence of extra-terrestrial. Seriously, if the government was hiding aliens from us, they would be proven to exist already. Unless you are implying that these "aliens" are invisible because we are brainwashed. I mean, it would be quite nice if there were aliens, but from evidence today there is no likely hood that we will see them any time soon.

First, if your going to complain about rights and government why are you doing it here? Second of all, was this supposed to make us feel bad for you? The users here came to talk scientifically with others to discuss science and related ideas, not to invoke our real-life problems on others, though if you want you can probably PM someone to see if they want to get involved. If your agenda coming here was to spread a political message you came to the wrong place. If you want to protest against government, go do so. Everyone comes here to NOT talk about politics unless in the right section. This section is labeled "Suggestons, Comments and Support" not "Politics".

One piece of evidence that could lead to the idea that homosexuality is a genetic disorder is the fact that there are more homosexual men than there are homosexual women. Genetically, this should be statistically correct because women are carriers while men are the ones who only have XY chromosomes that can cause the "gay" gene, but the problem with this issue is the fact that you can argue that men go through puberty longer than women(change in brain function more exactly), which leads to the point of whether this stage causes differences in sexual preferences. I mean, there seems to be no statistic to back up this claim so this can only by hypothesis, but the last one i mentioned can be backed up. In opinion, I feel that there is a genetic disorder, but it doesn't cause the homosexuality but can be the catalyst involved in having a man or woman decide whether they are homo or heterosexual.

I have been watching and reading up on the Higgs Boson, and I was wondering; if the Higgs Boson were to be discovered(it was supposedly found, but not confirmed yet), would it explain why on the quantum level electrons appear to be in two places at once while in the general physical world everything seems to have a specific location that it is located at? (I hope I posted this in the right section).