Daedalus

There are lots or reasons why aliens would be interested in us. For one, they might be interested in how life evolved on Earth and how we have evolved to deal with diseases. We find lots of medical / industrial uses from chemical interactions in lower life forms, and I imagine that aliens would also see the benefit in studying us for the same reasons, especially if our chemistry is different from what they have encountered. I'm not convinced that they would use us as slave because they would most likely not need slaves due to advanced robotic technologies. As for why we haven't detected any transmissions from them, it is possible that they have advanced communication capabilities that might use wormholes to transmit data as that would be the most optimal way of communicating over large distances. The humaniod part isn't as difficult to explain as you suggest, at least when it comes to being able to develop technology. Without appendages that allow them to create and use tools, it would be practically impossible for them to create advanced technologies such as computers and integrated circuitry. While this does not truly imply that they need to be humanoid in shape, we can speculate that they would most likely have similar organs as we do because they would still need vision, hearing, etc... to be able to gain similar advantages that we also have when it comes to understanding and manipulating environments. I wouldn't be surprised if most aliens are humanoid given the advantages that it gives us.

I would imagine that we are still dealing with the same type of difficulty as locating a new asteroid or planetary body, except that we would be able to determine that such an object is out of place and unique given its location. For instance, a body radiating a lot of thermal energy in the kuiper belt would indicate that the body is either large enough to generate enough internal heat as to stand out from other kuiper belt objects, or is so out of place that it merits further investigation. As we can see from the above bolded and underlined quotes from Wikipedia, such a body radiating a lot of thermal energy would most definitely stand out. However, unless the body's heat output / radiation was so extreme that we couldn't help but notice, it would still be difficult to find such an object due to the distances and sizes involved. However, new technologies / surveys are making it easier to detect such objects as outlined by this paper written by Chadwick A. Trujillo from Caltech.

I would guess that it depends on the extraterrestial's intent by being in our solar system. If they are here to invade Earth, then they might employ some type of subterfuge to prevent us from detecting them until they are right on top of us. Perhaps they would invade Earth by disguising their craft as a comet like the Necromongers do from the Chronicles of Riddick : ) If they are peaceful and just want to meet us, then I would assume they would send us a message letting us know of their existence. However, if they are just cruising through our neighborhood, then I would presume that it would be as difficult as finding an asteroid or planetary body using current techniques, or by locating a signal that they may be producing.

I realize that, and I am also aware that the expansion of space cannot be modeled as such (at least not without being highly speculative and needing evidence to support such notion, which is contrary to observations). However, the topic is dealing with the bug on a band concept as it relates to a simpler form of a mathematical space that is expanding. I'm sorry I didn't clarify that, but this thread was split off from a thread in the brain teasers forum due to discussing the bug on a band concept, which is an analogy to help explain expanding space, and the effects this particular model has on motion. I naturally assumed that everyone understood that we are discussing expanding space and not the literal concept of a bug on an actual rubber band that is being stretched.

Think of it this way michel123456. If the expansion of space exerted a force upon the bug, then such force would be pushing the bug in all directions effectively cancelling out the effect. For instance, space is expanding behind the bug pushing it forward at the same time it is expanding in front of the bug pushing it backwards. If the the force is equal in all direction, then the effect would yield a zero net force upon the bug when dealing with its motion. Now, I'm not saying that the expansion of space exerts such forces upon the bug. Only that if it did, the effect would cancel out regarding the bug's motion. Furthermore, if a force was exerted upon the bug in all directions, then the bug should observe some sort of pressure as a result. Now imagine that you are in a spaceship that is crossing a void that seperates superclusters of galaxies. You have already accelerated to your desired velocity and are coasting through the void. Although you are actually coasting along with a constant velocity in your local space, we here on Earth would observe you to be accelerating away from us and vice-versa from your FoR due to the expansion of space. Although we observe you to be accelerating, you would not experience a force because you are moving with a constant velocity through your local space.

Mooeypoo split the "Bug on a Band" thread so that we can discuss the mathematics / physics from the ant on a rubber rope problem here in this thread. Michel123456 and I are discussing the observed acceleration of the bug due to the expansion of space according to the mathematics of the "Bug on a Band / Ant on a Rubber Rope" problem. The function for the position of the bug / ant according to the problem is [math]x(t) \ = \ \left(v_r \, t + x_1\right) \frac{v_a}{v_r} \, \text{ln} \left(\frac{v_r \, t \, + \, x_1}{x_1}\right)[/math] such that the acceleration observed is the second derivative of the position function [math]\frac{d^2x}{dt^2}\ x(t) \ = \ \frac{v_a \ v_r}{v_r \, t+x_1}[/math] We can see that the acceleration approaches zero as time approaches infinity. However, the acceleration would be very different if a nonzero net force were to act upon the bug. In that case, the bug would be accelerating relative to the rope instead of just having a constant velocity. The posts above this one resulted from discussing such acceleration, and why the bug or observer does not feel a force acting upon them even though each would observe the other to be accelerating. I will work the problem with the bug / ant having a constant acceleration relative to the expanding space / rubber rope and post the results.

It is the kind of motion one finds when dealing with a space that is expanding. Such motion is non-newtonian and does not obey Newton's laws of motion. Therefore, force does not equal mass times acceleration when dealing with the acceleration observed from expanding space. However, Newton's laws are close approximations when dealing with interactions in the bug's local space. If you would like to continue this discussion, we should start a thread regarding the mathematics of an expanding space, or perhaps a moderator can accommodate us and split this thread into a new thread to allow this discussion to procede further without hijacking this one.

This is getting a little off-topic, but you have to consider that the bug is travelling with a constant velocity in the space local to the bug, and therefore would not feel a force acting upon it due to the expansion of space / the rubber rope. We only observe an acceleration because space / the rubber rope is expanding everywhere.

I already showed the math. Check the spoiler tag in my previous post.

This is from a previous post of mine that not only solves the problem, but also provides an explanation. You are correct michel123456, the bug on the rubber rope is observed to be accelerating by an observer at rest relative to the rope. Given the position function [math]x(t) \ = \ \left(v_r \, t + x_1\right) \frac{v_a}{v_r} \, \text{ln} \left(\frac{v_r \, t \, + \, x_1}{x_1}\right)[/math] the acceleration can be found by taking the second derivative [math]\frac{d^2x}{dt^2}\ x(t) \ = \ \frac{v_a \ v_r}{v_r \, t+x_1}[/math] We can see that the acceleration approaches zero as time approaches infinity. However, the acceleration would be very different if a nonzero net force were to act upon the bug. In that case, the bug would be accelerating relative to the rope instead of just having a constant velocity.

The comet PanSTARRS can be seen from now until around the end of the month, but you will most likely need a telescope to see it. Here is a nice pic of the comet.

Your proposal reminds me of a theory developed by Alexander Burinskii. He modeled the electron as a naked ring singularity. Don J. Stevens discusses this model at http://www.absoluteastronomy.com/discussionpost/Electron_as_a_ring_singularity_56595 Check out the above link. It may help you understand the model you are proposing.

The Goldbach conjecture isn't part of the mellinnium prizes. For a list containing a few more unsolved problems, check out Wolfram's website.

Hi mryoussef2012. To answer your question, there are equations, algorithms, and proofs yet to be found that will have an impact on mathematics and science. Check out the Clay Mathematics Institute's website to see some of the most highly prized problems that are still unsolved to this day. Dr. Grigoriy Perelman has been the only person so far that solved one of these problems. He was awarded one million dollars and bragging rights for proving The Poincaré Conjecture. As for what these undiscovered solutions will be like, well, it really depends on the problem and the area of mathematics in which it resides. It could result in new functions or be a proof that provides deeper insight into a particular problem set. The more complicated areas of mathematics will generally have more unsolved problems. However, a major break through might be found rooted in easier areas, but it is highly unlikey because they are well understood. For instance, I developed equations for nested exponentials, which are understood in mathematics, that lead to discovering the nested root and nested logarithm, which might be new. The chance that I am the first person to write a paper regarding these operations is extremely low, and the chance that nested roots and nested logarithms will lead to some profound understanding in mathematics is astronomically lower. However, you never know what advantages and discoveries your work might lead to down the road. I experience that feeling every time I discover something new for myself. Whether the problem is new or known, there's nothing like cracking a pattern and putting all the pieces of the puzzle together for a solution. The very first problem I solved for myself was the binomial theorem. It was the tenth grade in high school and I was taking Pre-Algebra. The teacher showed us how to expand binomials the hard way, which can take up a lot of paper if the exponent is particularly large. That night while doing my homework I was able to see the pattern for the coefficents in the expanded result and formulated an easy method to work the problem on a single line of paper. I showed the teacher the next day and he let me teach it to the class. My senior year I discovered Newton's interpolation formula for myself because I wanted to find an equation the predicted the summations of [math]x^a[/math]. It took me a year and three months to work the problem, and I was very surprised to discover that the binomial theorem is rooted in the solution. My work on Newton's interpolation formula, although already known, allowed me to get a $2000 scholarship from the University of Oklahoma. That sparked my love of math, and I have been expanding my knowledge and solving problems ever since.

Hi Amaton. Thanks for your interest in my work. I'm not sure if hyper operators are a relatively dark corner of mathematics as you suggest, but they do not get much attention due to a lack of practical application. It would be nice to discover a physical application that involves such operations. Most people think of very large numbers or operations that grow very quickly when dealing with hyper operators. However, the inverse operations, nested logarithms for instance, grow slower than traditional operators such as logarithms. Perhaps one day, we will come to learn how such operations plays their part in the scheme of things.

How do we know that this isn't one of those self-fulfilling prophecies. It could be that the College of Cardinals is influenced by such things when electing a new pope. I guess we will know once "Peter the Roman" is elected and this prediction comes to its conclusion. I'm going to go out on a limb and predict that it will be just as disappointing as Dooms Day (Dec. 21, 2012).

I've heard the same thing and I am also going out tonight, which is exactly why I created this thread.

To all of you celebrating Dooms Day tonight, be safe out there. Don't drink and drive because It could be you that ends somebody else's world.

I would say so considering my experience of driving on the interstate lol : )

You have to remember Moontanman, back then, guns were part of every day living. As with most things as time progresses, they get phased out or used very little as newer technologies simplifies our daily lives. So knowledge of how to use and defend against such things also dwindles. As for the increase in violence, I wrap that up to people having to live in tighter spaces as the population grows. Of course this can't account for every situation, but I do know that we as a society have to deal with more idiots than what was in the past.

I guess my concern is that a student could gain access to the weapon(s) either by a teacher being careless or through other means to obtain access to the weapon(s). So instead of having to find a way to obtain a gun outside the school grounds, a student or students working together could obtain them at the school and use them on the faculty and student body. A worse case scenario would be a group of students that take down a few teachers that carried weapons in order to enact their diabolical plan. For most of you that do not know, I am a parent of two boys ages 5 and 9. So, this is something that concerns me directly.

In the wake of the shootings in Connecticut, the lawmakers in the state of Oklahoma (my home state) are working towards legislature that would allow CLEET-certified teachers and principals to carry firearms at school and school events. http://kfor.com/2012/12/17/rep-wants-teachers-to-carry-guns-at-school/ I am aware of our other thread concerning gun control, but I would like to hear what other members and parents here at SFN feel about this type of action being taken by our lawmakers. Sure, you may not live in Oklahoma, but if our lawmakers here can pass this type of legislation, then governments can pass the same sort of measures regardless where you live. Personally, I believe that this is a bad idea. Who's to say a teacher won't flip out and pull their gun on a student, or worse a student takes the weapon from the teacher and uses it?

The following integral is set up correctly: [math]\int_{0}^{4} \int_{0}^{3x} y \sqrt{36+x^3} \ dy \, dx[/math] I checked both integrals and the one listed above is the easiest one to work. You should get a positive answer : ) To answer your question, at my college, double integrals are covered in Calculus 3. Of course, we also covered cylindrical, spherical, and rectangular coordinates as well as transformations between coordinate systems.