Unity+

He feels guilty because he is eating a turtle? Or it could be he feels guilty about a previous event that occurred involving the eating of turtle soup.

Because he felt guilty when he tasted it?

Because that taste was the whole turtle soup.

Here is an extension of the Collatz-Raymond Hailstone Conjecture: Iff C is a Collatz number and A is the identity 2, here would be the equation: [math]2\left \{ \right \}^{1}_{0} \times B\left \{ \right \}^{H_{2}}_{n_{2}} = C_{n}\left \{ \right \}^{H_{2} + n_{1}}_{H_{1}+ n_{2}}[/math] Here is an equation for division: [math]\frac{A\left \{ \right \}^{H_{1}}_{n_{1}}}{B\left \{ \right \}^{H_{2}}_{n_{2}}} = C\left \{ \right \}^{H_{1} \times n_{2}}_{H_{2}+ n_{1}}[/math] And this is the equation for powers so far: And for square roots: [math]\sqrt{A\left \{ \right \}^{H}_{[\frac{n}{2}]}} = B\left \{ \right \}^{H}_{[\frac{n}{2}]+[\frac{n}{2}]}[/math]

Instead of looking at all of the numbers as if they are all part of the same group(though they are), look at them individually. This will help in the development of an equation. Ask questions if needed. And notice how the order seems to correlate with each other. n+4: 1-> 6/2 = 3, 10/2 = 5, 14/2 = 7, 18/2 = 9... n+8: 2-> 12/4 = 3, 20/4 = 5, 28/4 = 7, 36/4 = 9... n+16: 3-> 24/8 = 3, 40/8 = 5... n+32: 4-> 48/16 = 3...

How did a crackpot paper get published on a credible publisher(unless of course it isn't)? Also, isn't it obvious that a photon cannot have mass because of the Higgs field(which has recently been confirmed) and how it reacts with other particles within the Higgs field? If the photon did have mass that would ruin the whole point of what the Higgs field partially was trying to explain.

http://en.wikipedia.org/wiki/Scientific_evidence And don't be the user that says the crackpot concept that the scientific community has had it wrong, that Galileo is an example of this, the Catholic church hid the truth kind of thing. It will definitely hurt your reputation here. This isn't meant to be an insult in any form. We encounter this kind of thing a lot on scientific forums, especially with me going around science forums, and there are users who constantly sign up to say they have the truth and that the government is after your work and all that. Look around at what we have here, post about questions. Then, from there, you can maybe start making threads about articles you found that may be interesting. Scientific ideas take a long time to make that are sound and work around current models. Be patient and work slowly up to a point where you can make a sound speculative idea and then form a hypothesis. Follow the scientific method. Once you do, people will listen.

Well, here is how I would answer your question(though the moderators would probably answer better). In one section about asking the question of "Was the Law of Conservation of Energy ever proven for electricity?" which was then responded by a user which stated: In which, in reply, you stated: That is the trigger button of getting your threads locked. Speculation is not another word for "Denying the observable facts". It is creating an idea that does NOT contradict any other model that exists and adding onto the ideas of today.

That is probably either because they are posted in the wrong sections, there are duplicates, or other reasons that violate the forum board guidelines. Maybe you should private message the moderators instead of posting this question in the wrong section.

Here is a conjecture to present for Set-Sequence arithmetic. Collatz Number Hailstone Conjecture: For all Collatz numbers, defined by 6n - 2, H of a Hailstone sequences will always be equal to 1. Disproven at 22. Rewritten Collatz Number Hailstone Conjecture: For any Collatz number that has an index within the sequence of Collatz numbers of a Collatz number, the Hailstone sequence will have an HE bigger than 1. Collatz-Raymond Hailstone Conjecture: For any Hailstone equation, iff C is not a Collatz number.

Ill actually check that site out. Thank you for the recommendation. I know the full blame is not on the education system, but it just goes to show how spending so much money on a failed education system can be quite inefficient.

I teach myself most of the time, so the system doesn't effect me as much with my ability to comprehend mathematical concepts. But, the problem with that kind of ideal is that our current education system produces small amount of successful students as there are in other countries. Accepting our current way of presentation will lead down the same road and will be unsuccessful. If the point of the education system is to produce as many successful engineers and scientists then the system is doing a poor job of it.

Well I guess the point I am getting at is I feel the American education system is "wrong" and needs working on with teaching topics such as mathematics. EDIT: Either that I really do suck at math and should head down another field. EDIT2: I am truly devoted to mathematics and I find many of the concepts fascinating, however with such a low point within the education system I would not be able to contribute to mathematical concepts(of course I can, but people willing to listen to them would be unlikely, though that isn't my main point).

Well, here is the common question(or so I think) about the American education system and whether it is doing the right thing. Let me expand the question, however. I am normally the rebellious(lack of term) person who with mathematical courses in schools I fail at(or get below average) the class and I always feel like I am a failure at math and I will never be able to understand it no matter how they seem to teach it in the classroom, yet on my free time I do math and I always find interesting things within mathematical concepts such as number theory and the relationships between different types of numbers, such as primes, and I enjoy taking a look into set theory and such. What strikes me funny is how the top students in the classroom, when I begin to talk to them about these kind of subjects, clearly have no idea what I am talking about. For some reason, I am able to understand subjects within mathematics that even the top students in my classroom seem to have no clue(I am not bragging, but if you know what i am getting at). I mostly do research on number theory and applied mathematics on my own time(in fact it consumes my time). In a summarized sentence, the reason why I can't comprehend the subjects within my math class is due to the fact that I can only understand something if I see why something is the way it is. I have to be able to see the core equations behind a specific law in mathematics in order to be able to accept that law. For example, in geometry I have a hard time accepting specific geometric laws because I always have this small feeling that it could be wrong. Even if I tell myself I accept the geometric law I still have this skeptical feeling of it(keeping an open mind that something could be right or wrong). It could either be my paranoid feelings or skepticism, I don't care how someone puts it. I have to develop my own ways of understand the inner workings of a specific mathematical law or equation by trying to find the core equations behind it. Without it, I either don't understand it or I become "skeptical" of it. Does anyone else have these thoughts on the American education system? Or is it just me?

Based on my analysis of numbers within Set-Sequence arithmetic, there are some special properties that need to be addressed. Identity numbers: These are numbers like 1 and 2. Within Set-Sequence, they would be addressed as [math]1\left \{ \right \}^{1}_{1}[/math] and [math]2\left \{ \right \}^{1}_{0}[/math]. Identity numbers are what give other numbers their identity as Hailstone sequences. In fact, if A or B is equal to 1, then multiplication applies differently, where the following would occur. Non-Communicative: All numbers within this arithmetic are not flexible as they are in regular multiplication. There are unique factors for unique values. Property of powers: If one is to increase a value A by the power of n, here would be the following equation to represent the change in B, being the resulting value: . However, this specific equation of the property only applies to the identity of 2. More to come.

Well it isn't frustrating me at all... Just as a suggestion, keep scientific discussions from swerving to a really bad direction of trying to disprove anything of the religious sense with science because it ain't going to work(that is just the way it is). Ultimately it will lead to a hole of insanity and evil(meaning the discussion won't end well).

Though this is work-in-progress, there is a new development called Set-Sequence Mathematics(Collatz-Raymond(since it was inspired by Daedalus) Arithmetic). Here are some findings from the use of Hailstone sequences. Here are some examples: {2, 1} -> 0 HE: 1 {4, 2, 1} -> 1 HE: 1 {6, 3, 10, 5, 16, 8, 4, 2, 1} -> 3 HE: 2 {8, 4, 2, 1} -> 1 HE: 1 {10, 5, 16, 8, 4, 2, 1} -> 3 HE: 1 {12, 6, 3, 10, 5, 16, 8, 4, 2, 1} -> 3 HE: 2 {14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}-> 7 HE: 2 {16, 8, 4, 2, 1}-> 2 HE: 1 {18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 } -> 8 HE: 3 {20, 10, 5, 16, 8, 4, 2, 1} -> 3 HE: 1 Let us say we have two sequences: A{} and B{} Now, formatting the sequences for Hailstone equations: Where H represents the amount of hailstone remainders or hailstone exceptions within a given sequence and n represents the amount of Collatz numbers within a given sequence. Now, let us compare this to normal multiplication: [math]A \times B = C[/math] Now make this for sequences: Here is what it would look like: For example: Now carry out the operations: And this statement is true: {12, 6, 3, 10, 5, 16, 8, 4, 2, 1} -> 3 HE: 2 Here's another example: {2} = {1} -> 0 HE: 1 {9, 28, 14} [math]\rightarrow[/math] {7, 22, 11, 34, 17, 52, 26}[math]\rightarrow[/math] {13, 40, 20, 10, 5, 16, 8, 4, 2} = {1} -> 8 HE: 3 {18} [math]\rightarrow[/math]{9, 28, 14} [math]\rightarrow[/math]{7, 22, 11, 34, 17, 52, 26}[math]\rightarrow[/math]{13, 40, 20, 10, 5, 16, 8, 4, 2} = {1} -> 8 HE: 3 This mathematical construct, however, is incomplete because there are still some loops that need to be filled with the arithmetic form. These Hailstone equations are a predictive concept to the Hailstone formulas as shown in the previous post. This ability to predict Hailstone formulas with Hailstone equations shows that there are specific sequences known as identity sequences that are located in all Hailstone sequences. This ability to predict them would give a better understanding of the Collatz conjecture.

Here is a more precise graph to replace the graph above: Though it seems as if y is approaching 0 and that there is a function to describe the slope as seen in the graph, there is still no proof of whether this will continue onto infinity. This proof would include a function that would describe this graph. The one problem with developing this function of [math]\Gamma (x)[/math] is being able to describe the exception of the prime number 2, which is described by [math]p_{x}[/math], where [math]x=1[/math]. Now, one could argue that the reason for the exception of 2 is due to the parameters given by the Collatz-Matrix equation, which is that there is a parameter for [math]\frac{x}{2}[/math]. Though this is a simple explanation, I still find it quite interesting as it being the exception. Here is something Daedalus brought into mind, which sparked an idea with Hailstone sequences. Here are examples: {1, 4, 2, 1} -> 1 HE: 1 {2, 1} -> 0 HE: 1 {3, 10, 5, 16, 8, 4, 2, 1} -> 3 HE: 1 {5, 16, 8, 4, 2, 1} -> 2 HE: 1 {6, 3, 5, 16, 8, 4, 2, 1} -> 2 HE: 2 {7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 7 HE: 2 {9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 8 HE: 3 {11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 6 HE: 2 {13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 4 HE: 1 {15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 8 HE: 1 {17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 5 HE: 2 {19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 9 HE: 2 {21, 64, 32, 16, 8, 4, 2, 1} -> 3 HE: 1 {23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 9 HE: 1 {25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 10 HE: 3 {27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, } -> 49 HE: 12 {29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} -> 8 HE: 2 (HE: Hailstone Exceptions, Hailstone remainders) Now, notice here that each Collatz number is placed on an even number element within each Hailstone sequence, though there are some that are placed on odd elements. Each Collatz element has a pattern(where a Collatz number will be found next to another number that is next to a Collatz number). However, there are what are known as Hailstone exceptions, which are sequences of two numbers that break the sequence pattern. For example, {26, 13} is a Hailstone exception. Hailstone exceptions will always be located in sequences that have an odd number length. That is one property of Hailstone sequences(of course this set of Hailstone sequences are prime numbers). These Hailstone exceptions are important because they do something interesting with the placement of Collatz numbers within these sequences. For example, {7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} has an odd number of elements, therefore the Hailstone exception {26, 13} is found(there is currently no equation to predict the elements of the Hailstone exceptions). Collatz numbers, before a Hailstone exception, will always be located on even numbered indexes. However, after an exception there is a switch. Collatz numbers will begin to be located on odd-numbered placements while the other numbers are located on even numbered placements. If another Hailstone exception occurs within the sequence then the properties are flipped again. Here is dealing with Hailstone exceptions: {25, 76, 38} [math]\rightarrow[/math] {19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26} [math]\rightarrow[/math] {13, 40, 20, 10, 5, 16, 8, 4, 2} = {1} HE: 3 {9, 28, 14} [math]\rightarrow[/math] {7, 22, 11, 34, 17, 52, 26} [math]\rightarrow[/math] {13, 40, 20, 10, 5, 16, 8, 4, 2} = {1} HE: 3 {27, 82, 41, 124, 62}[math]\rightarrow[/math]{31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242} [math]\rightarrow[/math]{121, 364, 182, 91, 274, 137, 412, 206}[math]\rightarrow[/math]{103, 310, 155, 466, 233, 700, 350}[math]\rightarrow[/math]{175, 526, 263, 790, 395, 1186, 593,1780, 890} [math]\rightarrow[/math]{445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850} [math]\rightarrow[/math]{425, 1276, 638}[math]\rightarrow[/math]{319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154}[math]\rightarrow[/math]{577, 1732, 866}[math]\rightarrow[/math]{433, 1300, 650}[math]\rightarrow[/math]{325, 976, 488, 244, 122}[math]\rightarrow[/math]{61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2} = {1} HE: 12 The Hailstone remainder determines how many sub sequences exist within a Hailstone sequence.

Thank you for commenting, I thought no one was paying attention to it. Collatz Theory(or this part of it) was originally meant to try to solve the Collatz Conjecture, but once I found more there seemed to be more relationships between primes and other types of numbers that it expanded.

Is anyone going to comment? More work coming.

It still de[ends on your point of view.

The reason why it doesn't seem novel is the fact that ideas now days grow slowly instead of just instantly come out with all these new ideas and people are saying "Whoa, this is new." When information slowly comes out of the blue we are less excited about the new pieces of information. This presented only a stepping stone in the knowledge of evolution. Though, simply to say that this information isn't a novel is quite ignorant(not in an offensive way, but you get what I mean). If you don't get the meaning of the information of course it isn't novel. However, to some who understand the implications are flabbergasted by the information.

Fair enough.

There are many views of Creationism, which one are you referring to? If you are referring to the most stereotypical version of it then okay, but there are many views of creationism that you would have to specify the specific on you are referring to.

I would have to say that the professor makes great points about the fallacies(well, not in a negative connotation, but in a way to express the mistakes that Dawkins has made) on how Richard Dawkins seems to make an incorrect image of genetic material. One great point is how Richard Dawkins seems to credit DNA for the production of organisms, but DNA is not functional without the organism itself. This is important to bring to attention because an experiment done within the 19th century produced results that stated that within heated environments and with the existence of water that genetic material could be produced, however this is irrelevant to the existence of life because the genetic material would not form an organism and would stay inactive unless within organisms. I also find another point important about how genetic material is random in formation and has some specific patterns within the mutation when comparing it to the organism's environment. This point brings to rest the common fallacy that there is a randomized even within the mutations that occur within organisms.