Unity+

The only problem is the algorithm he presented, he stated, only solves mathematical problems and doesn't take a current conjecture and say "Yes, this conjecture is true" and it outputs the proof as such. For example, the algorithm I am referring to would be one that can take a conjecture, like the Collatz conjecture, and even if there are infinite numbers to test with the computer would find a proof that would prove that the conjecture is true. Unless his algorithm can do similar things. I might be wrong on this.

Does an algorithm exist that uses the most fundamental theorems of mathematics and creates even more theorems that build up mathematics? If not, I am thinking about pursuing a project as such. Though it might not be completely efficient to make one, I want to see if it is possible to produce one.

The Turing test is only a test to determine whether if you were able to talk to the intelligence that it is no different than talking to a human. Though this is good news, it isn't major news that would involve robots becomes human like. We still have some ways to go.

My first post here: Why did sine divorce cosine? Because there was a Tangent between them.

My inability to interpret such makes me embarrassed to say the least.

It wasn't what I intended to argue, but to end an unnecessary argument I'll just leave it at that. Now it seems like you are trying to be rude.

You are avoiding the whole point of what I said. What I was saying was that though we don't know of any other form or mechanism by which the Universe could be run, there could still be more mechanisms that potentially exist from which the Universe is run(or creates and destroys). I don't know what you are trying to do, but okay then. EDIT: Had to fix some grammatical issues. EDIT2: I don't want to assume anything, but was there any anger in that post? If anger in the topic is causing it to be pushed on me, I don't really want to get in the discussion.

We could end the whole misunderstanding and get back to the topic. I think the topic needs consideration because calculating efficiency of a particular mechanism of the Universe is a very important one.

It was simply my input on personal incredulity. As we know of, this Universe displays one form of an efficient and stable mechanism of creation and destruction. We do not know of any other and therefore we have no relative "view point" to see cleverness for cleverness is a measure relative to another, if you get what I am saying. Yes, that is a conceptual formula for "cleverness." The basic idea is you have a limit based on what is the most efficient and stable mechanism that could be produced using equations that nature has evolved. [math]\lim_{n\to\alpha }O=M[/math] Where O is the "equation" of what nature is using to approach [math]\alpha[/math] to achieve the mechanism M. However, the conceptual equation shows not the "cleverness" value, but simply what the equation approaches. In order to measure such "cleverness", though correct me, would be to find a more or less efficient equation to approach M in a shorter amount of time because it must be relative to another equation to determine "cleverness". [math]\lim_{n\to\alpha }O_{a}=M[/math] [math]\lim_{n\to\alpha }O_{b}=M[/math] This concept is similar to finding faster ways to calculate pi using different summations and such.

I don't think it would be a measure of "cleverness" but rather a measure of how long it takes for nature to obtain a both efficient and stable mechanism. Wouldn't it be better to not use cleverness and instead use some other word to describe it? Cleverness is being able to understand something quickly and be able to apply such an idea. We could mathematically represent this in nature, but it wouldn't be cleverness. For simplicity: [math]C=\frac{T}{I\times M}[/math] Where T is the quantity stable form of a particular mechanism in an internal system and I is the amount of times it took to reach such a stable mechanism and M is the total amount of mecanisms that were gone through to get to the stable mechanism. However, I think another problem with such a measurement is deciding what is clever and what is not. The human mind is not always the best decider in this particular situation.

The Derivative Inverse Theorem produces the following equation: [math]\frac{d_{i}(x_{2}+\frac{2d_{e}}{d_{i}})}{r}=\frac{d_{i}x_{2}+2d_{e}}{r}[/math] More information being added.

Well, potential infinity and actual infinity go along with their descriptors with the fact that something has the potential to be infinite while the other is actually infinity. For example, there is a difference between a set that has the potential to be infinite and a set that is actually infinitely large. One has the capabilities to be infinite because no constraints have been put in place for that set to not be infinite while a set that is actually infinitely large does have infinite sets. A limit would be a mediocre example because though it does seem to imply such comparisons, it doesn't do a very good job of it. For example, Zeno's paradox would not be a good example. This is an example of a limit because it shows that if we were to finitely calculate the distance he travels he would never reach the tortoise. However, if a limit is used then he does reach the tortoise. The potential infinity stage is that Achilles has the potential to reach the tortoise because of the equation behind his differences of distance between him and the tortoise. However, with actual infinity he does reach the tortoise. The difference lies within possibility and actuality. Now, I wanted to address something you wrote in the post: I don't know what he meant by "infinities cannot exist in reality" because they do exist in nature, however not in the ways we would expect them in mathematics. As we know of, black holes either have a really, really, REALLY large density or their density is infinitely large because of how they work. But, I think the person misrepresented Craig's arguments since I have watched some of the debates between him and Lawrence. Craig's argument deals with the idea of an infinite lapse of time at the beginning of the Universe. His argument states that if there is no creator of the Universe and that the Universe has always existed then the beginning of time has, in fact, no "beginning" because the Universe has existed for an infinite amount of time and, therefore, there is no way to determine beginning relative to a certain aspect in time. However, I think Lawrence's rebuttal to the argument was that since space-time at the singularity did not allow time to pass, therefore this would account for such an issue but I do not remember so don't quote me on this. Just to note, this post is not in favor of either Craig's or Lawrence argument. I simply giving a clarification.

I think one theory that would go into this the most is Game Theory, which goes into politics as well. Game Theory goes a lot into the strategy of two groups and how each would react to the actions of the other. Political corruption might be investigated through game theory. I might be wrong though. EDIT: Here is a book about Game Theory and politics. It might not go into political corruption however it goes into politics and its relations with game theory: http://books.google.com/books?hl=en&lr=&id=fihEODPWgHAC&oi=fnd&pg=PP1&dq=Game+Theory+and+politics&ots=Om19M7OqzB&sig=KFvLkyo19NDO9leC6-XkXqsX3oc#v=onepage&q=Game%20Theory%20and%20politics&f=fals http://www.amazon.com/Political-Game-Theory-Introduction-Analytical/dp/0521841070 I'll try to find a free article, but those are some sources.

I am beginning to worry as the OP has not posted in a while.

Alright, sorry for the long time for the next post. I am using the blog less and decided to go back to the topic. The Derivative Inverse Theorem [math]\frac{\mathrm{d}}{\mathrm{d}x}u_{f}v_{f}=\frac{d_{i}rx-d_{e}r}{d_{i}}[/math] [math]v_{f}=\frac{d_{i}r(x+\frac{d_{e}}{d_{i}})-d_{e}r}{d_{i}}=rx[/math] [math]a_{f}=\frac{d_{i}x+d_{e}r}{d_{i}r}-\frac{d_{e}}{d_{i}}=\frac{x}{r}[/math] [math]C(x)_{k\times d}\begin{Bmatrix}\frac{d_{i}x+d_{e}r}{d_{i}r}-\frac{d_{e}}{d_{i}}&\frac{x-d_{e}}{d_{i}}\\d_{i}x+d_{e}&\frac{d_{i}r(x+\frac{d_{e}}{d_{i}})-d_{e}r}{d_{i}}\end{Bmatrix},s(k_{p},d_{p})[/math] Here is another part of the theorem: [math]u_{f}=\frac{d_{i}r(x_{2}+\frac{2d_{e}}{d_{i}})-d_{e}r}{d_{i}r}\times \frac{d_{i}}{r}=\frac{d_{i}x_{2}r+2d_{e}r-d_{e}r}{d_{i}r}\times \frac{d_{i}}{r}=\frac{d_{i}x_{2}r+d_{e}r}{d_{i}}\times \frac{d_{i}}{r}=d_{i}x_{2}+d_{e}[/math] [math]b_{f}=\frac{d_{i}x_{1}r+d_{e}r}{d_{i}r}-\frac{2d_{e}}{d_{i}}=\frac{d_{i}x_{1}r+d_{e}r-2d_{e}r}{d_{i}r}=\frac{d_{i}x_{1}-d_{e}}{d_{i}}[/math] [math]C(x)_{k\times d}\begin{Bmatrix}\frac{d_{i}x+d_{e}r}{d_{i}r}-\frac{d_{e}}{d_{i}}&\frac{d_{i}x_{1}+d_{e}}{d_{i}}-\frac{2d_{e}}{d_{i}}\\\frac{d_{i}r(x_{2}+\frac{2d_{e}}{d_{i}})-d_{e}r}{d_{i}r}\times \frac{d_{i}}{r}&\frac{d_{i}r(x+\frac{d_{e}}{d_{i}})-d_{e}r}{d_{i}}\end{Bmatrix},s(k_{p},d_{p})[/math]

It is possible, but current laws prevent it from occurring. EDIT: Not scientific laws.

The more I look into this, the more interesting it gets. [math]-1>s>1[/math] This function seems to bring about a similar graph as the Zeta function of the Riemann Hypothesis, but having the complex part becoming the real part of the function. In this function, the real solution for an even number s is determined by k as well, where [math]\mathbb{R}_{s}=k\frac{1}{2}[/math].

I admit that I assumed that it was a credibly article due to Moontanman posting it. And I think we are discussing the theoretical. It went from the article to what could be possibilities.

I tried this out with one odd number: (x-1)^(3) - (x^3 - 1) And the solutions are 0 and 1. And the derivative will not always have the same solution as the original equation, but can in particular cases if I remember correctly.

1) You may be correct because we haven't even discovered all species on Earth, let alone in the depths of the ocean where it is almost impossible to go down to the deepest depths because of extreme pressures. 2) I can see your point. However, I think they just made a edumacated guess at this point. 3) You might be right, but until then I think speculations on the credibility of the article will be void until there is more discussion on the topic. If the planet was similar to Earth's, wouldn't it at least have similar structures to us with unique differences related to the different conditions that may exist on that planet? It might be, but most deformations caused by inbreeding were more related to other conditions besides the structure of the skull. It could be the rare case scenario or the common scenario, but I wouldn't think an elongated skull would be the result. http://en.wikipedia.org/wiki/Inbreeding

I did something interesting with the equation that they provided. I took the derivative of the equation and got the following: The interesting thing is if you solve for x when the equation is equal to 0 if the number p is odd then you will always have one solution that is real(which is 1/2) while if it is even then it will only have complex solutions(I detect the Riemann Hypothesis in this equation). This might lead down an interesting path.

It is good to be skeptic, but let me address your other points: I was referring to it being far fetched that these are aliens as many people seem to claim. The ability to breed is mainly based on chromosome counts of each species. Using genetic information, it can be predicted how many chromosomes the species has. I think they made the article for those who aren't very scientifically knowledgeable about the scientific language. I was actually referring to if the species came from Earth. It would be more difficult to explain the use for an elongated skull since many homo sapience have more of an average-sized skull. If the species came from a different planet it would have a simpler solution to the problem because it would mean the planet most likely had a need for an elongated skull structure, while most human species on Earth have the structure related to our own skull.