md65536

Oh. Well, in that case what you'd be measuring wouldn't be euclidean space. As mentioned previously in this thread, if you draw a big enough circle in curved space, it won't have the same ratio of circumference to radius of 2pi. So then the question might be, "Has local space always been euclidean?" Again I don't think it's possible that it can vary by small amounts, and yet we just happen to be in a situation where it is, by chance. http://news.discovery.com/space/once-upon-a-time-the-universe-was-really-weird-110321.html This article suggests that the 3 spatial dimensions of euclidean geometry were not always "there" in the early universe. Pure speculation based on very weak understanding of all this: Perhaps curved space can somehow have fractional dimension to it, but it can always be observed consistently with an integer number of dimensions, so that "local space" is always flat no matter the number of dimensions. Perhaps if space can curve so much that it would fold over on itself, we would instead experience 4 spatial dimensions??? So, it may have been the case that local space was non-euclidean in the early universe (since euclidean space is defined as having 3 spatial dimensions), and may not be in the distant future? I don't know if pi or an analog would be defined for such spaces, and if so what its value would be. But I would still assume that if it changed, it would not do so gradually.

I'm still confused, with questions like "Is flatness subjective?; what defines euclidean space and could any of those properties be modified?" But I think that a big part of the confusion is that since pi is irrational it can appear to be just an arbitrary sequence of apparently random digits. It can be calculated by fairly simple infinite series that corresponds to some geometric interpretation... Such as: [http://en.wikipedia.org/wiki/Pi] This is a series of very simple rational numbers. From this, I would think that pi would not change by small amounts over time. If you imagined that pi changed somewhere in say the billionth decimal place, over the past few million years, then what formula could be used to calculate that different value? What small change in geometry could yield a different pi, but still allow it to be calculated with a simple series?

Coincidence?! Or... ? ...not! Consider this: Every two or three years the estimate of the age of the universe increases by two or three years. AND, every few years they find that there are even a few more digits to pie than they previously thought! Mostly due to faster computers with bigger hard drives, is my guess. Just a couple years ago, they thought that pie had only about a million digits, but then they found a whole bunch more. Maybe, just like the universe, pie ages, and it grows. What is this mysterious stuff that grows on pie as it gets really old?

A hexagon inscribed in a circle (so that the hexagon's side length = the circle's radius) will have a perimeter of 6. I've tried to reason that if you can get the hexagon's perimeter to equal the circle's, then tau (=2pi) would be 6, so pi would be 3. What does that mean though, I dunno! Could you curve space so that a hexagon and circle are the same? Could you pinch one side of an equilateral triangle so that the hexagon's perimeter becomes smaller, and the circle's becomes 6r? There's a link on that page to: http://en.wikipedia.org/wiki/Astroid Surprising to me, "An astroid created ... inside a circle of radius a will have ... a perimeter of 6a." Does this mean that if pi were 3, then a unit circle would be an astroid? So in Tres Juicy's ideal universe, an astroid (not a hexagon) and a circle would be identical? Edit: Oh wait, there must be some value of p > 1 (unlike an astroid where p=2/3) but p < 2 where the perimeter of the unit circle is 6r. Maybe p=3/2??? That would be an "ideal universe" that is closer to our own than the space where p=2/3. Edit2: I was curious and tried to look it up... the best I found was http://www.procato.com/superellipse/ If you use a value for n of 1.582 (not 1.5 = 3/2 as I'd guessed), and a=b=2 you will get a plot of a superellipse with a perimeter of approximately 6.00. This would be a unit circle if pi were 3. Unfortunately I can't find anything that is more precise. With a=b=1, a value of 1.57 is good enough, so I thought at first that maybe an Lp space with p=pi/2 would give a unit circle of perimeter 6. Does anyone know if there's any significance to this value (about 1.582)?

Now now, there's no reason to accept reality to the point that it is depressing. A little bit of delusion is probably essential for all of us to bother going on living! What is hope in spite of an acceptance of statistical chance but a belief that it even matters if something goes one way or another. We will ALL go to the grave ignorant and foolish, moreso if we think we understand the universe so well that we can be certain that others are wrong. I disagree that anyone should ever have to grow up just because someone else thinks it's time. What's best is balance, as determined by whatever works best for each of us. knowerastronomy: If your understanding of the universe gives you happiness then accept it. I wouldn't recommend pushing it to the point that it diminishes that (arguing on the internet etc). Perhaps one day your ideas will inspire others to create a theory out of it, and they will become famous (and likely, you won't, but such people who have inspired others have made it into history books and are still studied). The thing is that ideas are usually so vague and ambiguous that you can't always say whether they're right or wrong. It takes mathematical precision to do that, so the question is whether an idea is good or bad -- whether it can lead one to figure out some math that can be shown to be right. However, despite the ideas, any claims made that contradict the evidence are wrong. I'm certain.

http://www.gizmag.com/genetically-modified-mosquitoes-aegypti-mosquito/20668/ Quote: "a scientific consensus forming that the complete eradication of mosquitoes would have limited, if any, adverse environmental effects" But it also says: "The humble mosquito, and the deadly diseases it carries, is estimated to have been responsible for as many as 46 billion deaths over the history of our species. That staggering number is even more frightening in context - it means that mosquitoes are alleged to have killed more than half the humans that ever lived." To me that says that mosquitoes have a pretty big direct influence on humans!, and wiping them out will have major consequences, including the intended consequences of saving lives but also unintended consequences that we'd better be prepared to deal with, which I doubt we will be!

Okay. So now this thread has fallen into the disappointingly typical mode of many threads involving a "new theory that explains everything". You haven't convinced anyone yet and you're not going to convince anyone this way. What is the next step forward for you and the theory? - Are you done the work on it, and want to market it to others? - Are you willing to do whatever additional work is needed to move it forward, even if it involves math and even if it is more difficult than you can handle? - Are you willing to give up? - Other? If you choose the first option, you should accept that someone's going to have to do the math and figure out a testable hypothesis etc. before this will convince anyone, so you will need to figure out how to inspire someone that the idea is good enough for them to work on it. To be realistic, you must realize that the real work on this hasn't even been started yet. Others have spent entire lives trying to figure it all out and no one has done it yet, so chances for success are not great if your goal is too high. Perhaps this thread may help with an answer to "what now?"

It sounds similar to "seeing stars". http://en.wikipedia.org/wiki/Phosphene lists some possible causes. Any time I've seen stars they were noticeably bright, and I think probably white. I'm not sure if that's what you're describing.

Yeah! I think that basically when you're multiplying probabilities, including with all the factorial factors, you're essentially saying "What is the probability that this first thing happens, and assuming that it does, what is the probability that this second thing also happens, and assuming that it does, what is the probability that this third thing also happens, etc..." If you ever get a probability factor of 0 for any of the individual factors, then the whole thing comes out to 0. BUT ALSO, if the probability that "the second thing" is 0, then you can't assume that it happens when looking at the probability of the third thing. That is why the formula can fail in impossible cases, because it assumes impossible things. So you would state the domain of the function, and either state that you assume the problem is within the domain (ie assume that T is big enough) or you would handle the other cases separately. I think the reasoning is good; I hope the math works out! I haven't tried putting it all together myself, but I usually end up making mistakes that need correcting.

I keep making the mistake of mixing up the phrases "logic" and "intuitive reasoning or common sense" and I think you are too. Logic "is the formal systematic study of the principles of valid inference and correct reasoning." [http://en.wikipedia.org/wiki/Logic] Intuitive reasoning is fine but you're not going to overthrow Einstein without the "formal" or "systematic" or "valid" or "correct reasoning" parts. I started watching the videos and they look well-made. Early in the first of the ten videos is the statement, "Nothing [in the new theory] is said about the speed of light being relative to anything. The speed of light is just that, the speed of light. Hence, the hypothesis that nothing can travel faster is illogical." That's not logic! If you really feel you have the answers to how the universe works, you're going to have to tackle the math. Doing the math changes an idea, the way that using a paintbrush changes a painting you've only imagined.

I remember being told that tastebuds don't work when dry. Does this mean that any time we taste salt, it is in a soluble form? So that if dry salt and dissolved salt tasted different, it is always the dissolved form that we taste (and dry salt, with dried tastebuds, would have a different taste, possibly harsh or metalic? I suppose I could experiment...). I tried dry salt on a dry tongue and didn't taste anything, so I can't answer my own question. I don't know if the way that tastebuds react to salt makes use of some unique properties when dissolved, or if they would react the same whether the chemicals are in crystal form or dissolved.

Very similar to: Very similar to: Very similar to: You ask this question over and over but you don't accept any of the answers that people give. Both philosophy and science are concerned with the answers to questions. You do not seem concerned with answers. Are you sure what you're doing is philosophy? You've mentioned that philosophy of science is interested in knowing how we know what we know. But you don't seem concerned with even knowing what questions can be answered. You'll ask questions over and over again regardless. I might consider it some form of meditation to repeat unanswerable questions over and over, but your posts seem to me more about the statements than about contemplating questions. I still don't know what your goal is. Are you "enlightening us" with questions but no answers? Or are you waiting for someone to come along and say "You were right all along and Einstein and everyone after him were wrong!", and then for that elusive genius to give definitive answers to all the meaningless questions you incessantly ask ("What is IT that curves?")? These are questions for which you've never provided a lead in to a discussion of any answers. Science does fine without your questions. It has its own questions and it actually works toward answering them. What is the goal of the questions you ask? Have you even begun to figure out how one would go about answering them, let alone actually tried to answer them? You ignore answers, and then ask again. Is there any progress being made? Not always! But plenty of evidence in this thread for how it can be.

What's been discussed here so far involves iterating over a grid of pixels and using a function to evaluate a color for each pixel. To draw fractals on paper you'd probably want to do it a different way. If you take a shape or a line segment, and modify it in some way to create additional (smaller) shapes or line segments, and then modify each of those segments in a similar way, and keep going until the details are small enough, you should end up with a fractal. Some easy fractals to start with: Mountain: Start with two horizontal points at either end of the page. For each set of two adjacent points, find the midpoint and then raise it or lower it randomly by some factor that is proportional to the horizontal distance between the points (so that the random offset gets smaller as the points get closer together), and add a point there. When the points are close enough to not be worth subdividing further, connect them with a line. Tree: Start with one vertical branch from top to bottom of the page. For each branch, add some specific formulation of child branches. Eg. split each branch into thirds, and add a "twig" 1/3rd along the branch, pointing 60deg to the left, with length 2/3rd of the branch, and add another twig 2/3rd along the branch pointing to the right with length 1/3rd of the branch. This particular formula will give you a lopsided looking tree. Repeat for all new twigs/branches that are big enough. If you do this and look at what you've drawn, you'll see that each branch on its own looks exactly like the full tree, only smaller. Lame-looking snowflake: Draw an equilateral triangle. For each line segment, divide it into 3 sections and draw an equilateral triangle jutting out of the middle section. Repeat. These are just 3 simple examples off the top of my head. There are probably much cooler, interesting ones out there, with instructions. It's not hard to come up with your own variations. If you look at simpler computer-generated fractals, you may be able to detect a pattern that can be used to draw each smaller iteration, based on a bigger iteration.

Well, it's an interesting puzzle and I think I must have OCD. In the case that X=Y=T, the probability that N elements in X match exclusively with N elements in Y is 1 iff N = X, otherwise the probability is 0. I think it's okay for the formulae to fail in impossible cases, and usually you exclude impossible cases in the description of the problem (because we'll already know that it's impossible if N is too low relative to T, etc). The reasoning is that "This formula only works when there is enough of the T elements to be split up among A and B so that after the N elements are matched, there are still enough unique elements to fill out A and B." Otherwise if it's impossible to do so the probability is 0. So we can say "For X-N+Y-N > T-N, the probability is 0, otherwise it's... (some formula)". But I must have been on crack in trying to figure out the "P2" part in my last post. So I'll give it another go! Basically, in the P1 part we match the first (in an arbitrarily chosen order) N elements in A with elements in B. We can remove this subset C of matching elements from A, B, and the full set with T elements. We're left with 3 smaller sets and we want to find the probability that none of the elements of the first are in the second, where both sets are subsets of the 3rd. So let's look only at the P2 part with some new names. Let's call the sets E, F, and G, with size e,f,g respectively, where E = A \ C, F = B \ C, and G = {the full set with T elements} \ C. We want the probability that no members of E are in F. I tried to do it one way above and the math didn't come out nice. But I realized that the problem is equivalent to finding the probability that all the members of E are in the remainder of G after removing F. That is, if all members in E are in G \ F, then no members of E can be in F. So like with figuring out P1, the chance that the first element in E is in G \ F is: (g-f)/g And for the next element is (g-f-1)/(g-1) etc for all e members... with a product of P2 = (g-f)!/(g-f-e)! / (g!/(g-e)!) I just checked an example in a spreadsheet and I get the same value as the convoluted math of my last post! Note that e=X-N, f=Y-N, g=T-N So I think the P1*P2*(XCN) formula is now something manageable, when it's all put together!

So, out of curiosity I tried working through the first part and I get the same answer you did. I should warn you that I'm not a mathemagician! ALSO NOTE: At the end of writing this I ran into a problem that puts the math for "P2" below in doubt. If you can follow my reasoning below you might be able to figure out if it's okay or if not, maybe you can see the right way to do it. I'll probably look at this again later and see if I can figure out the problem, but it might be beyond me!!! First part: Consider the first N elements of set A. The chance that the first element is in Y is: Y / T. The second (Y-1)/(T-1), etc. The product of all N is: P1 = Y!/(Y-N)! / [T!/(T-N)!] This is the same answer that you came up with. So while we were doing this we removed matching elements from B and the set that had T elements so that they didn't affect the probability of matching subsequent elements. We're left with (X-N) elements that we want to make sure are not in a set of (Y-N) elements, which can be chosen randomly from a set of (T-N) elements. Sorry for the mess of notation but let's call C the matching subset with N members. The chance that the first element in (A \ C) IS in (B \ C) would be: (Y-N)/(T-N) So the chance that it's not is 1 - (Y-N)/(T-N) Now, we don't have to remove any elements from (B \ C), because we didn't match any! I'm not so sure if we should remove it from the "main set" that has (T-N) elements left in it. But I think that we should! So the chance that the second element in (A \ C) is NOT in (B \ C) is 1 - (Y-N)/(T-N-1) We do this for all (X-N) elements... ... exceeding my math abilities... We get the product P2 = [1 - (Y-N)/(T-N)][1 - (Y-N)/(T-N-1)] ... [1 - (Y-N)/(T-N-(X-N-1)] I don't know how to simplify that. There's gotta be a simpler expression! Finally X C N = X! / (N! (X-N)!) Then the final answer would be P1*P2*(X C N) Note: If (X-N)+(Y-N) > (T-N) then P2 must be 0, because there is no way to divide the "leftover" elements of the full set between sets A and B, with no overlap between them. If we allow such a case, then one of the products in P2 should be 0, but you could also end up dividing by 0. Hrm.....................

Atheism in general isn't specific enough to exclude either a belief in the non-existence of deities, or a lack of belief. I think both sides in this thread have used the word atheism in an over-specific way to exclude one or the other. See: http://en.wikipedia.org/wiki/Atheism#Implicit_vs._explicit, and more-so http://en.wikipedia.org/wiki/Atheism#Positive_vs._negative If you want to exclude one side or the other, use more specific terminology.

I think that using the number of combinations and simply multiplying by that, assumes that only one possible combination can work. Otherwise, the probability of one combination working can overlap with the probability of another combination working, so you can't just add their probabilities together. As an example, say that X = Y = T = 10, and we choose N = 5. Obviously, all 10 members in your chosen set (A) match all 10 members in the other's chosen set (B). Probability is 1. Any subset of 5 that we choose will also match (but not exclusively; the remaining 5 will also match). 10 C 5 is 252, so if we just add up the probabilities that each possible set of 5 matches, then we get a probability of 252, which is wrong. My formula is wrong for doing it this way. If your formula is right, mine won't work with it. However, with the original question of matching only exactly 5, if say X = Y = 10 but T = 100, and say that the intersection of X and Y has 5 members... then there is only 1 possible combination of 5 members from X that matches exclusively with 5 members of Y. The chance that one combination matches excludes the chance that some other combination also matches. I haven't wrapped my head around the first part of the puzzle enough to know whether either of our methods seems right or not. That is... my strategy is to find the probability that some specific (but generic) set of size N will match exclusively, and then multiply by all the possible ways you can choose that set. If you can find the probability that any set of size N will match exclusively, then you don't have to worry about the number of ways you can choose such a set.

Folks, owl has been kind enough to provide some discussion material to keep us going while he is away and there is no one to tend his thread, and we haven't even managed a half-decent answer to this thrice-asked question yet. I myself don't feel qualified to answer, having already given unaccepted answers to same question when it was asked in the form of "Do you honestly think that..." and "No seriously, do you really really really think that... (really?!)" He'll be back soon and it would be quite embarrassing if we didn't have an answer this time that's at least better than the pitiful sets of replies we gave last two times around.

SN1987a is 168000 LY away. A burst of neutrinos was detected at 3 separate observatories about 3 hours before visible light was detected. http://en.wikipedia.org/wiki/SN_1987A These two observations can fairly confidently be correlated. With OPERA's 60 ns "faster than light" speed, neutrinos (of another flavor I guess) might be expected 4.1 years in advance. With an estimated error of 10 ns, that translates to +/- 0.69 years. So that's over a year's worth of possible observations of a neutrino burst that could be connected with SN1987a. I can only answer your question with more questions: - Are there any other observations of super novae that have occurred recently? - Does the detection of a neutrino burst give you enough information to connect it with a super nova event (such as the direction the neutrinos came from, etc)? If not then it's possible that neutrinos from SN1987a could have been detected over a long period in 1982/83 without any way of determining whether they came from SN1987a or some other source. - Were there any neutrino bursts detected in 1982/83? As swansont mentioned, possibly no one was looking for neutrino bursts in 1983/84. I would hope that if there are any known detections of bursts from back then, that someone has checked to see if they might correlate! Otherwise, with no news about it either way I'd assume that it's because there have been no measurements (either of a burst or of a lack of bursts) that could support or oppose the idea of neutrinos arriving years before a supernova is visible.

I haven't worked through the math or logic of the first part, but I'll go on to this part. The first part deals with the probability P of an arbitrary selection of N elements matching in sets A and B (and importantly if you haven't done it*, it must also include the probability that the remain elements don't match). http://en.wikipedia.org/wiki/Combination X C N ("X choose N") tells you the number of different ways of choosing N elements from a set of X members. Each of these possible subsets are similar and each has a probability of P of matching exclusively to sets A and B. Each of these possible subsets is equally likely to be chosen as an "arbitrary selection of N elements". Each of these possible subsets are unique, so the possibility of choosing one vs another is mutually exclusive. That means that you can just add up the probabilities of any one of them matching (which is P), for each of the possibilities of actually choosing that group. So the final answer should be: P * (X C N) If it's confusing, consider it to be rephrasing the question to be: "What is the probability that this group of N elements from A matches exclusively with B, or that this other group of N elements does, or that this other group does (and so on for each possible group of N)?" * Glancing at your solution to the first part, I'm guessing that it doesn't take this into account? If you calculate the probability that all N elements match, but leave open the possibility that additional elements will match, then the probabilities of one combination matching vs another are not mutually exclusive or whatever, and the second part won't work.

1. Eloss = 0 (Assuming closed system) 2. f = random() 6. v = [0, 1, 0, 0] (With a coordinate system aligned in standard configuration???) 8. f = sin(x) Is this a cryptologic word puzzle? Are my guesses at all close?

I would try this: Suppose you have your set A, and the other has their set B. For an arbitrary subset of A, with N members, what is the chance that each of the subset's members is in B? Also what is the chance, assuming that each of the subset's members is in B, that each of the remaining members in A is not in B? Then use combination to find the number of ways to choose a subset of A with N members. Without filling in the details, I don't know if this work properly and simply enough. Is it enough to inspire a solution???

I think you're hiding flawed logic in a fog of vagueness. Relativity is not so flimsy, and it's easier understood when you state everything clearly. First of all, I don't think "a ruler is a clock" is meaningful. How is it a clock? The answer to that question is what makes it a clock (or not a clock, depending on how you answer). Eg. it's not just a ruler that makes a clock, but a ruler and a light source and a light detector, or some other combination. In this case, the ruler moving against an incline makes your clock. Even if you're not moving relative to the ruler, it is still moving relative to the incline, so it can still be used as a clock in the ruler's frame. Second, clocks measure proper time. (I suppose you could build an apparatus that doesn't, and still behaves like a clock... then maybe you could call it something like "a clock with a limited domain" or something like that???) The universe is consistent, so if one observer observes that a device accurately measures proper time (and is thus a clock), then all observers will observe observations that are consistent with that (everyone will agree that the device measures proper time).

No, you would measure the sphere to be accelerating. The reason you can measure time this way is that the ball is moving in a precise, consistent, known way. It is known that it is accelerating, and the rate of acceleration is known (as a function of g and the angle of the ramp; they would need to be precisely fixed and/or known in order to use this to tell time precisely). So you can create a formula to describe the movement of the sphere, and find t from that, and if everything's accurate you'll find t to behave just as expected. Changing the spacing of your tick marks doesn't affect time, nor does the angle of the ramp, though they'll affect the formula and measurements. Perhaps you can create some useful time-like property measured by equal spacing of lines on the ruler, but that isn't time (as measured in consistent intervals by other clocks).

Do they even need to have a purpose? Could it be just part of the brain continuing to function when it is not really needed? In that case it might be like asking "What is the purpose of a sink with a leaky faucet when no one is using it?" Then the question might become "What (if any) are the advantages offered by dreams?" If there are evolutionarily significant advantages, I suppose you could say they have a purpose or developed a purpose. I don't have any clue whether dreams came "for free" along with brains, or if they evolved later as separate brain functions. It's not hard to guess at some possible advantages offered by dreams. They offer practice for cognitive skills. They offer time to contemplate situations when there aren't more immediate things for the brain to deal with; one can simulate decisions or emotional responses to different situations, so when faced with real situations the brain already has experience dealing with similar things.