SamBridge

Well thanks for the formula, it actually worked (btw colic wasn't a sockpuppet I just forgot my old username and email associated with (making it my main account) it since I haven't been here for a long time and I received absolutely no help from the staff member for looking them up and so spent a lot of time looking through my 12 emails for any info after the other acc was banned, so sorry for the delay too). I had one other question too: Apparently with the sequences I was dealing with, they ended up turning into something that resembles a power series for a function, but I can't quite nail down one of the properties for manipulating summation it seems. The series I have converges, but I'm trying to divide out a whole other power series so I can just have some irrational number as a remainder, and my basic attempts seem to yield a remainder that doesn't converge somehow. Just as an example, if I have [math]1=sum[((x+1)^n)(2^n)/((2n+1)!)][/math] and I divide the whole summation by a power series where say, [math]f(x)=sum[((x+1)^n)(n!)][/math], would I or would I not get [math]1/f(x)=sum[((2^n)/(((2n+1)!)(n!))][/math]? And why or why not? Because I searched all over the internet and for whatever reason there doesn't seem to be anything describing sum(a)/sum(b) or factoring out a function from a power series.

Then I'll just stick with what I was saying before. Because there's been billions of opportunities (literally) and nothing else has showed up, whereas the first microbial life we are related to got one shot and now there's us. We have more reason to doubt that life anything like life we have on Earth has a high chance of developing, and even less support that life unlike what we know can develop on Earth. But as I keep saying, there's many many many many different places on Earth where there's a diverse array of chemicals with no bacteria we know of. The different nascent genes as you mentioned are still part of the same time period and most likely event of whatever started life. There's no reason to expect that creating a hyperdrive or warp drive will spontaneously make the galaxy like star wars. And if it's so easy to create life forms from a bunch of random organic chemicals how come scientists still haven't created life forms from scratch? It's because it's a lot harder than your giving it credit for and it's not something to take for granted, it's very improbable.

it's called a compromise, I thought you liked those things. Because there's been thousands of opportunities with diverse arrays of chemicals in various locations every single day for over 4 BILLION years and there's no new life. Maybe you are just not understanding how long a billion years is, just a single billion is a really really really long time for something to not happen. Well, we found some very old bacteria called Algae and we can trace its lineage back from various rocks we found to around 3.8 billion years ago, and all life on this planet has the same base pairs as it does. Also, see above response.

As you implied before, there's a wide variety of conditions on Earth. If life could so easily form, then it definitely would have taken the opportunity to do so somewhere. There could easily be locations without much bacteria in places like concentrations of sulfuric acid, extreme cold temperatures, or lava which only a small amount of life can survive, or just random geographically isolated sections of land and caves. There's been millions of years for other types of life to develop in a constantly changing landscape with new opportunities arising, but it really doesn't seem to happen that often. I don't understand where anyone said life as we know it is the only life that can possibly develop. I said life as we knew it could have formed again.

No we don't have one data point, we technically have 4 billion data points, 4 billion x365 if you wanna be more specific, though I'm sure the number of days in a year has changed a little bit. Every year or really even every second of every day on Earth, a bunch of random chemicals has the chance to spontaneously create life as it did before. But after 4 billion chances it's only done that once, at least successfully. So even if the chances of life forming is less slim, the chances of it developing and progressing are definitely slimmer. I'm not really sure what you're trying to say. Obviously one organism cannot be adapted to every environment, but the general properties of carbon based life that we know of, like having cells with a nucleus and cytoplasm, and even common structures like having a mouth and skin and digestive chemicals, cells communicating with each other and DNA structures taking part in evolution, are pretty common here.

Wow I can't believe this topic is still going on. Ok here's how it is: People who believe in god aren't broken and anyone has the capacity to believe something that's not true. But as mentioned before, choosing a life of pure belief leaves you open to be wrong about many things, some things which you may not want to be wrong about, some things which you may not want to even question, or somethings you have spent your life living by for so long that you've become accustomed to them. No one is inferior one way or the other, it just depends on what lifestyle you are most connected to, what events in your life you need to explain the most, how you cope with various losses and how you are able to provide yourself with emotional stability or if you need something else to do that for you. Objectively I still can't rule it out either way. Just when I thought I had decided god couldn't exist again, I find myself thinking that there could be a being of pure consciousness who doesn't have to be super-natural in any way, it's just that the universe could essentially be their "playground", that perhaps the boundaries of it's consciousness have extended beyond any localized form and for whatever reason it decided to mess with Earth. It reminds me of those "Q" beings from Star Trek.

I'm not really sure what you mean, but it sounds like some kind of mis-interpretation of the limits placed by the Lorentz Transformation. Classically we can not observe anything traveling faster then or observe mass traveling at, the speed of light. And this is because as you speed up, not only does time slow time, but the relative perception of space moving away from an object contracts while the space in front in a way expands, making it so that two objects going away from each other observe the distance being reduced and time slowing down just enough that neither fully reach the speed of light. With the warp drive however, it is a completely different concept that requires very dense matter or advanced manipulation of the fabric of space. If you can imagine a gravitational well, that 4 dimensional space is being distorted, and as being composed of matter you will have to naturally follow the path of that distortion. But, what if you could ignore that gravitational well and proceed to the next point in Euclidean space? Well then there's no problem because it is the same exact principal as reducing the distance to the next point from the relative view of the space craft. A warp drive basically reduces the distance between two points in Euclidean 3 dimensional space by warping the 4 dimensional Einstein space and ignoring those deformations in some way. At least that's my interpretation of how it could physically occur in reality. Otherwise there is a notion that it is space which is moving from the relative perspective of the space craft, and because there is no limit on how fast the fabric of space itself may travel, there may be a way to move space itself past the space ship to reach the next point. But since that's basically what you're already doing when you walk, which is to say that you observe the world moving past you and not vice-versa, it seems that is still limited by the speed of light. Otherwise there's also a hyper-drive in which you effectively slide into a topological sub-set of normal space where hopefully the rules of dimension and distance time will be different enough that a space ship can travel a small distance in hyperspace, then exit hyperspace to find they have traveled a greater amount of normal space distance. As far as I know there isn't very much research on the Jump Drive, but my guess is that it could involve a wormhole to effectively bring two different points in space together. Or, you can change the probability of the ship's location to correspond to some other location in physical space like the imagined transporter that has been inspired by properties of quantum physics. Though for now it seems we would be limited to star-gate like technology where at most we would only be able to teleport between any two transportation devices and most likely in the form of photons unless we can find a direct way to control the probability of matter. Unless of course there is some way to manipulate the manifolds of space to create a correlation of position in space itself similar to a wormhole.

So as I understand it many people are hopeful (except for Stephen Hawking) that there's much life on many different planets. But has anyone stopped to think that the Earth is perfectly suitable for life as we know it, yet in it's 4 billion years of history the base pairs for DNA only spontaneously formed once? I mean if it only happens once in 4 billion years (and still counting) and not even scientists have done it, that's got to make it a pretty improbable event. But I guess we'll have to see what's under Europa to make sure.

Ok well this is mainly what I was originally asking about and I've looked at QFT for some time in my free-time. What is the more physical reason for the decay to happen? Maybe nature likes to have things at the lowest possible energy state, but it's still possible to have higher energy states. I suppose you can relate it to that when you jump in the air, you naturally fall back down to a lower energy state, that is unless you have enough energy. Though an electron in an atom doesn't exactly "fall" to the nucleus because that would imply it has a continuous spectrum of energy. I suppose if time itself was quantized then there would be a limit because I'm sure after a certain point the hypothetical decay time would have to be less than a Planck second and the decay time would imply certain factors about the oscillation like it's mass, but that's all I can think of. What else would place a "limit"? "That's just the way it works out"? Although I thought kinetic energy was continuous, but I thought I read something about the quanitnizaton of free-particle wave packets that implied it wasn't. Is there truly a continuous form of any type of energy or is the distance between nodal surfaces of varying oscillation modes of things like free-particle wave packets in kinetic motion just too small for us to measure and so it only appears continuous? Are there only quantized amounts of every type of energy? Because I know that's true for some, but then I read an article about beta decay which said it had a continuous spectrum of kinetic energy http://en.wikipedia.org/wiki/Beta_decay

So that is why the higher generation neutrinos don't decay? But wouldn't that imply they would decay "at some point"? Yet somehow neutrino oscillations make it from the Sun to the Earth without the different flavors decaying, but seeing as how they don't really decay, there must be a more direct factor that can inhibit the decay of other generations of leptons. Yeah but that's just due to the fact that there isn't a lower state to decay into which is directly based off of the number theory that describes that matter, there cannot mathematically be a sustainable Lepton oscillation below the mass of an electron because that's just how the mathematics of oscillation work out, which then relates to number theory, so it's really just a fancier version of saying 1+1=2 or really just 1=1. But at least I have some better idea of it with the natural tendency to be in a lower energy state which I forgot about, but I still don't understand the physical mechanism by which it happens. Is it like trying to use a hand blender without a lid and the other oscillation modes just happen to somehow escape because there's nothing holding them together? But then why wouldn't they just form a single oscillation pattern like with neutrinos or two electrons in the same orbital? There is one other thing though too. isn't it theoretically possible that there are higher generations of particles like higher than Tau but they just decay too quickly for us to see them with our current technology?

Wow that really answers nothing, I can't believe I expected more from you when you do this with every single damn topic I start, 1+1=2, woop-de-doo. And then all you do is make things even more complicated because the implied questions of your rather empty statements are "why is there nothing for an electron to break down into?" and "why is matter quantized that way?" which you didn't even touch, which of course asks why muons aren't the first generation leptons themselves. Furthermore, you in no way describe anything of the actual mechanism by which a tauon decays which is more of what the topic is actually about. If you don't want to give a good answer just don't bother answering, or PM someone and say "hey <other staff member>, can you handle this one for me?", and that's it. Someone get's a good answer and you don't have to waste time on something you can't bother to answer. You've been doing it for years now and I'm seriously tired of you making all of my question topics more complicated or filling them with empty and unhelpful posts, please stop posting on my topics. My suggesting is take a break, I'd much rather have quality over quantity.

I can't seem to find much on the specifics of tauonic atom formation and decay, which I guess makes sense because the tau particles we observe don't live long. As I understand it tauons on their own decay very quickly, but their orbital is more limited by their higher mass rather than the decay. But, why exactly does a tau particle decay so quickly? We have an oscillation mode of an electron, it just sits there and there's nothing happening, no decay, why does the higher energy cause decay? Perhaps it is a more physical property than I am giving it credit for and there is simply enough energy for a separate oscillation of a matter field to "spit off" or something to do with the uncertainty of the energy exceeding the boundary of the smaller localization of the tau particle, but I'm sure that can't completely describe it. Why exactly do muons and tauons decay so quickly, or really at all? I mean we could theoretically have like 13! periodic tables here if we can create sustainable atoms harnessing varying generation leptons, and just when I thought chemistry was pretty boring too.

I suppose you could treat it like that, but quotient rule or product rule should be applicable, I get an answer after all. I think one mistake I made though was putting the ln(2) in the denominator rather than the numerator. However, I still can obtain (2^*nl(2)*e^x - e^x2^x)/e^2x using the quotient rule, which actually reduces to what you said, since it equals 2^x(ln2-1)/e^x.

That's almost what I was looking for, but if you can imagine triangular prisms, they won't form perfect cones.

This would imply there is an instance where without any outside force, the inertia of an object would shift angles due to eccentricity and thus become hyperbolic, but what doesn't make sense to me is it takes force to accelerate past the velocity which is required for it to be hyperbolic, which doesn't happen with inertia alone. The only time I can think this happens is when a comet happens to pass so close to the sun that it accelerates enough to break free of orbit. Otherwise, I don't know what you're saying. It would be interesting to see the math changing as well though, to see exactly when the plus sign switches to a minus sign.

That post was from a while ago, and no he's actually not very patient because he already ran out patience with religious fanatics on this site.

I sincerely hope that is a joke, I'm talking about the distance of the moon from the only planet we know of inhabited in this solar system with a single object in orbit around it that we call "the moon", there is no reason why you should assume otherwise, we have been talking about comets hitting Earth this entire time, the fact that you misinterpreted such a basic, easily understandable part of my post must suggest you aren't reading what I am saying very seriously, which would explain previous misconceptions you had that I pointed out. As I said before, I didn't guarantee anything, all I know is it is certainly possible to launch many explosives to intercept the comet, I pointed out they would not act as much more than small gamma-ray bursts, but as I also said before, we are not incapable of attempting. Any energy we put into reducing the mass or velocity will reduce the damage it does, but if we can't use explosives far away enough they may damage Earth in some way.

Problems a,b and c are pretty straight forward. [math]2^x/e^x[/math] is the same as 2^x times e to the power of negative x. With this, not only do you have the product rule, but the chain rule in each product as well. Product rule is a'b+b'a, you mark one multiplier as "a", and the other as "b". and do (derivative of "a" times normal "b"), then add (derivative of "b" times normal "a"), which would be [math]2^x/(ln2 *e^x) + -e^(-x) * 2^x[/math]. It's a similar circumstance for b and c, but if you'll recall, the derivative of lnx is 1/x, so you'd do 1/polynomial times the derivative of that polynomial. Uses the quotient rule, but you still do a similar thing and us chain rule, you do [math]((a' * b) - (b' * a))/(b^2)[/math], where "b" is the denominator and a is the numerator. To find the slope at a certain point, just find the derivative of the function, then plug in the x value that you are suppose to find the slope at. I think you can complete the first page. The second page is related rates and optimization. For the first related rates problem a good thing to do is to mark down the "permanent", "instantaneous" and "what you want". What you want is [math]d(water level height)/(dt)[/math], or the rate that the water level is changing. What you need to do is come up with an equation that uses the variables given in the problem, simplify it, and differentiate it so that you get dw/dt (w=water level height). The "permanent" is the equation that describes the shape and how the volume of water fills it, which is what appears to be an equilateral triangular prism, so you need an equation for that prism involving the height of the water that fills it. For the second one on the second page, just make an equation to model the profits and find the maximum by taking the derivative of the profit equation and seeing where the y value equals 0. The third problem is related rates, you can solve it easily by labeling what I suggested before with marking what you want and the permanent and instantaneous and use the relationship of similar triangles. Try the fourth one on your own if we can do these other ones.

So in other words it would never change on it's own, you'd just have to add some energy, which makes sense because hyperbolic trajectories break the orbit.

Sorry???

I don't think you correctly interpreted what I was saying. I implied that when we sent the missiles, they would explode within a few moon orbits because they meet the comet there which was already traveling for 2 months. If we would have detected the comet as just becoming outbound and had a couple months, we would have time to send explosives to meet the comet at the distance of at least few moon-orbits from Earth. Otherwise, it wouldn't be a bad precaution to use some kind of giant underground facility and evacuate.

So there's no chance it would change on it's own...?

Yes, that's why I said to a bubble. Gradually the energy would be dissipated into heat energy through friction and kinetic energy from sound waves or in other words the entropy would increase, according to thermodynamics, so if you could make a bubble that trapped all energy inside from ever escaping, with mechanisms to support life that were powered by chemicals which released a lot of energy in one reaction and were fueled by the surrounding air temperature in a endothermic reaction, since the heat wouldn't ever escape the system, you could hypothetically have a small enough radius such that the thermal and kinetic energy builds up to power those chemical reactions that release that energy in the first place to support interior life in the first place. Though I would imagine you would have some initial energy because someone wouldn't want to start out at 1K and wait for a chemical reaction to heat everything up. I don't know of anything that can do that, but that's really the only time I can think of where resources wouldn't be limited considering the population stayed the same.

When elements lighter than iron fuse, they release enough energy to make the star expand and overcome the gravitational force preventing it from collapsing. When only iron is left, the star cannot produce enough outward heat to stop the star from collapsing, so depending on its mass it will collapse and shed its out layers and form a different nebula with a different core, sometimes a white dwarf, sometimes a neutron star, sometimes a black hole. Nothing to do with neutrinos or space repelling. Then you can't say it's wrong, you can only say its unproven. Incoherent are sentences these. Dimensions are not reducible objects, there are ways to define the location and physical existence of something. This has little to do with the mind, dimensions exist whether we acknowledge them or not.

Isn't it an unproven belief that people who believe in god are broken?