woelen

I did the same experiment today, and indeed it is quite remarkable. I obtained a yellow smoke and a lot of yellow, orange, and even pink solid, subliming at the glass of the test tube. The yellow smoke is really dense, it fills half of the test tube, with a fairly sharp "almost liquid" "surface", above which the air (mostly CO2) remains clear. The dense smoke is totally opaque when viewed through more than appr. 2 cm. When I opened the test tube while it was still luke-warm, I got really beautiful glowing in the still present dense smoke. I had swirlings of yellow light inside the test tube, especially, when I kept it horizontal for a while and then put vertical again (taking care that the remaining solid powder did not fall out of the test tube, while keeping it horizontal). In order to see the yellow light, you need to go to a darkened room and let your eyes get used to the darkness. The effect is not very strong, but once your eyes are used to the darkness, it is beautiful. So, I really think it is white P, contaminated with red P. I also did an experiment by letting Cl2 gas flow into the test tube with the orange/pink solid. The solid becomes white and seems to liquefy. A thick white fume is produced as well. I did not see any fire though (I first shaked all the remaining red P powder out of the test tube).

You are looking at the sum of the squares of the [math]a_i[/math]. The order of [math]a_i^2[/math] either is 1, or [math]p_i[/math]. In your examples, I, however, only see either squares, which are equal to e, or I see squares, which are equal to an element with order 2. If this always is the case, then your "partial ring" will only have either e-elements or order 2 elements in the set of products, which is not very exciting. Did you find an example, with squares, which have an higher order than 2, i.e. an order [math]p_i[/math], with [math]p_i[/math] being the order of [math]a_i[/math]? I also see squares of elements of order of a prime squared (4), with the square having the order of the prime itself (2). This is the case in your last example, for [math]a^2[/math] being equal to [math]2a[/math]. If this could be true for a 9*2 order group, with [math]a^2[/math] having order 3, while [math]a[/math] has order 9, then that could also be interesting. Summarizing, in order to be really interesting, the set of products must also have higher order elements.

I have heard of this theory before, but newer insights make it highly unlikely. Black holes do evaporate, albeit VERY slowly. Space-time produces pairs of virtual particles, which also quickly annihilate each other. The net effect is nothing, no energy, no matter. But on a micro-scale there is some noise. If this happens near the horizon of a black hole (just in front of the border, where nothing can escape it, not even light), then it could happen that one of the virtual particles falls into the black hole, and the other particle remains outside. They cannot annihilate each other anymore, and the particle, which remains is not virtual anymore. It appears as radiation. The energy, represented by that particle effectively is subtracted as mass from the black hole. As a consequence, the black hole looses a mass E/c², with E being the energy of the newly created particle, and c the speed of light in vacuum. For very large black holes, this only happens infrequently, but the lower the mass of the black hole, the more this happens and black holes hence evaporate faster and faster. A sun's mass black hole would take zillions of zillions of years to evaporate (much more than the currently estimated age of the universe, which is appr. 14 billion years). But finally, all mass will evaporate into radiation and we will have a very cold and empty universe (in the meantime the universe will expand for ever and ever).

Yes, now it is perfectly clear for this example. I am trying to match this with other algebraic structures for which I know applications. In what direction are you thinking for applications of these algebraic structures? Mathematical/theoretical, or practical, such as crypto-systems, data-encoding, etc? Can you tell something about the number of distinct products in general? Did you derive that number? The underlying group should have a fairly high additive order, otherwise the multiplication is rather boring, with the set of products being small. For practical applications the algebraic structure must be sufficiently "rich", both in addition and in multiplication.

I have understood that less sleeping does not really give you more time to do things. Your body is aging more quickly. Having a regular sleep in the night apparently is something we really need, and having a short nap of half an hour or so around 13:00 or 14:00 in addition can make you more alert in the afternoon and evening. But we simply need a certain amount of sleep per day. Some people get away with 6 hours per day, other may need as much as 9 hours per day, but we do need it. Training your body so that you will need less sleep will not be really succesful. You may be able to win a little, but you will feel more tired all over the remaining hours. So, the gain is questionable. It feels really good if you have slept for many hours more than your usual amount of sleep .

YT, I have been thinking about this, and I really think you made white P, contaminated with red P. Here is a picture of a sample of white P, which also looks very orange/red. http://www.periodictable.ru/015P/slides/P1.jpg I think that you made white P, which partly is converted to red P again. The fire you obtain most likely is not due to the water, but due to the air (with oxygen), which gets in the test tube again. Probably the tube still was somewhat warm, when you removed the stopper. At a temperature of 40 C the white P ignited already.

As far as I know there is no real definition of what is simple. Simplyfying usually means making the expression shorter. In this case, I hardly would call it simpler. Usually, manipulating mathematical expressions is done with a certain goal. The concept of simple then is something, which depends on the goal. Which of the two following expressions would you call simpler? ax² + bx + c a(x + b/2a)² + c - b²/4a Probably the first, but their values are the same. But if it comes to solving the equation ax² + bx + c = 0, then the latter is more convenient. Solving the quadratic equation now simply is taking the constant term to the right, dividing it by a, and taking the square root of it. So, simplifying usually is with a goal, and the goal determines what you think is simplest.

Go and look around. Tell more about what you want and what you want to discuss. Not having English as your native language is not a problem to us, as long as your intention is to have a decent contribution to the forums. It helps if you try to pay a little more attention to punctuation and the use of capital letters.

Is this really the multiplicative table for D6? If a is a single rotation, and b is a reflection, then I get different results. e*a is not equal to e, but equal to a. e is an identity element for D6. For any operation z, e*z = z*e = z. Also a*a*a = e and b*b = e. But a*a is not equal to e. It is true that this group is non-abelian. I do not understand the meaning of addition over here. What is e+a, what "physical" meaning should I assign to e+a? Sorry, but I have the impression that I am something missing here . We're not yet "connected" .

Could you give an example of such a ring-like structure, which is not a true ring, but is like a ring, except the commutivity of addition?

What do you mean with "partial ring"? You mean the elements, which are of the form a*r, for a given a? If I read your definition, then you are very close to the definition of a field. If the number of elements in your ring is a prime number, then you create the simple field Zn, with n a prime number. Such fields have applications in cryptography. E.g. the public key cryptosystem RSA is based on properties of fields Zp and of rings Zpq, with p and q distinct prime numbers.

There is a general solution for homogeneous linear differential equations of order N. Such an equation has N characteristic solutions (the eigenvalues of the system of N first order differential equations, which can be derived), which simply are the zeros of the N-th degree characteristic polynomial. Just an example: Suppose we have: 8*d5y/dt5 + 12*d2y/dt2 - 8*dy/dt + 7y = 0. Then we solve the equation 8λ^5 + 12λ^2 - 8λ + 7 = 0 This yields 5 solutions, λ1, λ2, .. λ5. Now the solution of the differential equation can be written as y(t) = c1*exp(λ1*t) + c2*exp(λ2*t) + c3*exp(λ3*t) + c4*exp(λ4*t) + c5*exp(λ5*t) A unique solution is obtained by imposing sufficient initial conditions. For an N-th degree equation, N initial conditions must be specified, i.e. the value of y at time 0, but also the value of the first N-1 derivatives of y at time 0. If all are specified, then one can uniquely determine c1 ... cN, corresponding to those initial conditions. The situation becomes a little more complicated, if some of the solutions λi are equal (multiple zeros of the characteristic polynomial), in that case, terms of the form t*exp(λi*t) also appear, or even higher powers of t, if the multiplicity of the solutions is higher than 2. In the original problem we have to solve the equation d2005y/dt2005 - y = 0. The characteristic equation for this is λ^2005 - 1 = 0. This has 2005 distinct zeros, one of which equals 1, the other 2004 are complex and are on the unit circle in the complex plane. The solution now can be written as c1*exp(λ1*t) + c2*exp(λ2*t) + .... c2005*exp(λ2005*t) Here, λ1 can be regarded equal to 1. In order to find a unique particular solution, you now need 2005 (!!!) initial values before the solution is fixed. For the solution to be equal to exp(t), without other terms we require that at time 0 all initial values of y(0) and also the first 2004 derivatives of y are equal to 1. If one of the derivatives of y(t) is not equal to 1 at time 0, then the solution will be more complicated and will also contain other exponentials with the other λi's in it.

This entire discussion boils down to what is information and what is matter? The analogy between a file and a real-life object (be it a human, an animal or just dome dead matter) is flawed. Files only have meaning, because of the information they represent. How this information is stored physically does not matter, e.g. a file on a harddisk is stored in a totally different way than a file on a CD-ROM or a tape. Still we consider them the same, as long as the information, represented by them is the same. With real-life objects, we also have information, but besides that, we have matter. Just from a physical point of view, there are already painstakingly large differences. Matter is conserved, matter is organized in elements (particles). Disappearance of the source and appearance of the copy at the remote end would violate physical laws. What about the sole? Transferring that also would require violation of physical laws, whatever your religious beliefs. From a materialist/naturalist point of view it violates laws of physics, from a transcendental point of view it in addition violates laws of locality (which in some sense also is a violation of a physical law).

Btw, marapets2 bumped the thread with his "chemicals are fun" message. If one wants to bump an old thread, then that person really should have to add something and to my opinion the message "chemicals are fun" is not of that awesome nature, that it justifies the bumping of the thread .

I can imagine that when we create real superintelligent artilects, and we provide them with the ability to interact with the physical world, that they will try to wipe us out. If their intelligence exceeds our intelligence (and this will happen somewhere between 2030 and 2050) then at a certain point we may be to them what a fly or musquito is to us. If we annoy them, they simply slam us away. Of course, this only can happen if these artilects are given connections with the physical/real world. They need actuators. But of course we given them those actuators. First, we will use simple artilects for relieving us from simple/boring work, or to help us in hostile places. These artilects will become more and more intelligent, due to advances in technology. At the same time, their sensors and actuators also will become more advanced, also due to advancing technology. We still want them, just like we want a vacuum cleaner or a dish washing machine. But at a certain point we will realize that the machines we made are more intelligent than ourselves. We will not be capable anymore to understand what is going on in their "brain", simply because of the immense intelligence, needed to understand that brain. Things become even more threatening when we also provide the artilects ways of communication, either with each other, or with larger centralized entities, we place in data centers, like we nowadays have data centers doing all kinds of things for us. So, the question is, should we build artilects? Or maybe better, how far should we go, and what capabilities should we give them in the physical world? What if we integrate an artilect with our own body? Would humans, with a 100000-times more intelligent artilect, intimitely connected with their brain, still be human? I don't think so. Their body may look human, but they would be alien to us, we would not understand them at all and they could become a serious threat to us. Answers to these questions are very hard to give. I see advances, but I also see threats in the not so very far future.

The L'Hopital rule is not needed when the denominator is 0, while the numerator is non-zero. In that case the result is conclusive. Whether a function is oscillatory or not does not tell anything about differentiability. Also, cusps and the like are not a problem. There are rigorous rules, which describe how many times a function is differentiable in a certain point. So, this reasoning is not valid here. I indeed see no problem to use the L'Hopital rule, also for very wild functions, as long as they are sufficienty often differentiable. A function like |x| is not well-behaved in 0, but for all other values it is well-behaved. Try to read a text on real analysis, in order to obtain precise definitions of concepts like differentiability.

Comparing sulphur with carbon is like comparing apples with oranges. You can't use such analogies. And no, CH4+CO2 do not react, unless when heated to such extreme temperatures, that everything does react. It is even the other way around. Carbon reacts with water at sufficient high temperature to make CO and H2 (this mix in the past was used as fuel gas).

Usually you do need initial guesses to find the roots of an equation, when Newton's method is used. Especially if a problem is new, and it is a one-time situation, then one first tries to obtain an initial guess near the root (and for such purposes, a sketch of the graph can be a good tool) and then Newton's method is used to refine that root. So, although the "guess-and-check" method is too crude, some guessing can be required in real-life problems. Usually, however, the guesses are educated guesses and not random shots in the dark . This method, using initial guesses, of course is not useful for situations, where 1000's or millions of similar equations need to be solved over and over again. In such situations, one usually will have to do more research on the properties of the equations to be solved and one must try to find general rules, which can give acceptable initial guesses and then use Newton's method for refining the roots. This latter approach can be really difficult and requires a good deal of understanding of your problem.

Herme3, I understand that reaction of your aunt. My reaction in that other thread about "why religions are bad", also comes from a similar concern. It is good if young people go out with other young people (and such a thing is not only good for young people, also married people, who have children themselves every now and then should go out and have fun together sometimes , we do on a regular basis, having someone else take care of our kids, and at other times we take care of other's kids). People need contacts, and there are many places where you get contacts. So, going to a good concert (be it rock, or classical music, whatever you like) with some friends indeed is a very good thing to do. Going to a nice bar also can be very good and relaxing. Apparently, in your family and church there is some consensus about not doing such things if you are christian? Of course, getting totally drunk every weekend, or being stoned half of your time, is another matter, but having fun together, having a few good beers occassionally and enjoying good music are parts of a life, which make it worth living. You say that your aunt is not the type, who is worrying all the time. Then my opinion is that she had understood better than all those people around you, who are worrying all the time about their afterlife. I also do not worry about my afterlife, I really believe that it is OK. The bible itself is clear about it. It has passages like "drink wine and have your heart filled with joy", and "enjoy your youth". This does not say that it encourages you to drink until you are totally drunk or to be a party-beast, stiffened up by XTC, but it does say, that occassionally it is good to have a party and then also having a drink is not a problem at all, you even should enjoy it.

Borek, we are talking about different things with the starch. In the case of titrating a vitamin C tablet, I would drip in the solution of iodine into the solution of vitamin C. You are talking about the vitamin C dripped into the iodine? Even better of course would be to use thiosulfate, but in the case of vitamin C and iodine, I'm afraid that will lead to extra errors, because besides the fast reaction between iodine and vitamin C, there will be another much slower reaction between iodine and the clean oxidation product of vitamin C. A reaction, very similar to the reaction, you mention with the starch. So, in this particular case, I would go for crushing the tablet of vitamin C, and dissolving this (any insoluble solid just leaving in the beaker). To this, I would add starch and then I would drip in the iodine. I know, that the iodine solution is somewhat messy in a burette, but when a glass burette is taken (and they usually are), then I see no real problem. As soon as excess iodine is added, the solution in the beaker will turn dark blue. The other option would be to add a well-known amount of iodine to the vitamin C, such that an excess of iodine is added. Then this excess can be titrated with thiosulfate. In that case, I indeed would not add the starch from the beginning. But, this approach has the disadvantage, that the excess iodine may react a little with the oxidized vitamin C (which still is an hydrocarbon, which certainly can be oxidized further). The latter problem does not exist with the former approach, because the iodine only exists for a very short time in solution and quickly is consumed by still unoxidized vitamin C. Iodate, reacts with thiosulfate, forming iodide and tetrathionate, as Borek pointed out. But iodate is quite a strong oxidizer and adding this directly to thiosulfate, without first converting it to iodine with excess iodide, may also lead to oxidation of part of the thiosulfate, all the way up to sulfate. This side reaction makes the titration inaccurate, so it really is important to first make iodine.

A black forum layout sounds like something really disgusting to me. I don't like black at all. I always associate it with the more underground and kewl forums, where real science and real intellectual discussion finds no home.

Herme3, again, I get an unpleasant smell from your post. You seem very frustrated about your past. You think you are free now, but in reality you imprison yourself in your own frustration and negative feelings about the past and besides that, you imprison yourself in your selfmade lonelyness. Whom is to blame for that? YOU! Think twice, you cut away everything of value to you. I remember the thread you started a while ago, where you mentioned you did not need anyone anymore, and you would be happy alone in your own little world. No more contact with college mates, no more contact with your friends. You are cutting off again a possible source of contacts, and I say this, not to annoy you, but only because I see a trend in how you develop. Look at yourself in the past 6 months and how you developed. This may sound very harsh towards you, but it is not meant like that. I just write this as a warning. Whatever direction you choose to go, please do not evangelize your new "freedom" over here, I also already mentioned that in the other thread, you just started. PS: I'm writing this particular message as "woelen" and not as SFN-moderator, so please do not understand this as a threat to take moderator action. Just to make things 100% clear.

Phi, indeed, best would be to redirect this discussion to the theologyforums, but that is not yet possible. Closing it would be too heavy handed, hence the best (of sub-optimal choices) was to move it to GD .

Why wouldn't you always use L'Hopital's rule? As long as the functions are differentiable sufficiently often to obtain a conclusive result, this rule is valid, isn't it? And if so, then a result, obtained with this rule is equally proof as a result, obtained in another (usually more cumbersome) way.

It is very simple. Religion is bad in the eyes of the non-religious and it is the the most important there is in the eyes of religious people. This essentially makes this entire discussion for me a non-discussion. You have your opinions on religion, and I have mine.