psi20

When I was a kid, between ages 5 and 10 or so, I used to be able to control my dreams, or at least recognize that a dream was a dream. When monsters started attacking me, I would just blow them up with my "spirit gun." Then I would say ,"Wake up," and wake up a second later. I could be walking along a path and say to myself, "This is just a dream and I can do anything I want here. Let's go flying." Then I would lift myself off the ground and fly somewhere. When I got bored with a dream, I could say "Wake up," and then wake up. But now I can't do that. I can't tell the difference between dream and reality. I'm still not sure whether or not I skipped classes in middle school to get some food or if it was just a dream. I can't tell that I'm dreaming when I do dream. I haven't flown in like 2 years. When I have dreams about someone trying to kill me, I run for my life instead of blowing them to smitherines. When I get bored with a dream, it goes on and on, sometimes for days until it stops. Any reasons why?

Oh, I didn't know that not all rational functions were symmetric. What I meant was how do you, if you can, use derivatives for rational functions to find out when the slope is 0? How do you find the vertex of the parabola-like shape?

I remember reading a science fiction book called Space Odyssey or something and there were giant gas clouds on Jupiter that were the size of cities but were living. They could throw lightning bolts at each other. I don't remember if this is true or if I just made this up off the top of my head right now, but I remember reading about some jellyfishes being made up of 99% water.

My pseudoscience goes like this. Life was here since the beginning of the universe. That's part of the reason why there's clumping in the early universe. You might argue that there's no way bacteria could survive in a period where no atoms even existed, absolutely no way that anything could exist in such conditions. But this kind of thinking made people think there was no life in the arctics, deep in the sea, in volcanoes, etc. Just because we can't survive in these conditions, it doesn't mean no life could exist. Anyways, as planets form and bacteria land on them through meteors or what have you, the planets surge with life. You might argue that if this were true, we should be finding life on Mars or more in space. However, life can't expand as fast as the universe, so it's ridiculous to say that you can find life everywhere. Then evolution occurs on these planets. Meanwhile, as planets and moons start being bombarded with comets and oceans develop, random chemical reactions also form the basics of life. Depending on how much water is present, life could form anywhere from a couple thousands of years to billions of years. Then evolution occurs on these places as well. As intelligent life form, they figure out how to manipulate their structure and start enhancing themselves. We see this in ourselves, too. We cut our nails, bleach our hair, spray perfume, etc. Later, these life forms might consider genetically changing themselves or perhaps adding other compounds to enhance their structure, meaning becoming robotic or the like. These life forms might also decide to create life on other planets. So we came here perhaps because of basic life from space, chemical reactions in our primordial soup, and/or other life forms planting the seeds of life.

I don't think so, just use triangle similarity properties. Using the top of the tower, the point where the tower meets the ground, and the end of the tower's shadow, we have triangle ABC. I walk a distance until the tower's shadow hits the top of my head. Using the top of my head, the point where my foot meets the ground, and the end of the tower's shadow, we have triangle DEC. These triangle are similar from because two angles are the same, one right angle and angle C. AB/BC = DE/EC Then you just find AB since you can measure the rest.

Another way might be, assuming that the ground that the tower's shadow goes onto is flat, to walk along the shadow until the shadow hits the top of your head. Then use your height, the total length of the shadow, and the total length of the shadow - distance you walked to find the height of the shadow.

Ah, speaking of trig, sin c * cos c = -.5 Is it possible to find out c?

Hey, in our physics class, we're using lasers for an application of trigonometry. Anyways, today we were supposed to find out the height of a tower at our school. I thought we would be using lasers to figure it out, but we won't. To do it, I believe you need a side and an angle. My friend says to use a straw and look through it as a telescope to aim it at the top of the tower while you're close to the ground, then measure the angle. Then measure the distance you are from the tower and that should be enough to figure out the height. This method would give a relatively accurate measurement since the tower is pretty tall. But is there some other way to do it that would be less error-prone? Using the straw to look through it would be hard to do close to the ground and it would be easily blown away by the wind now.

Whoops, I think I mis-stated my question about discontinuity at 0. I meant to ask whether or not (-1,0) was a part of the graph or not. The question then is whether the graph is discontinuous as -1 or not. We learned that for rational functions f(x) = N(x)/D(x), if the degree of the numerator is less the denominator, y=0 is the horizontal asymptote, which means that that function has a horizontal asymptote of y=0. "As for the other thing, I believe the definition of the asymptote has something to do with the bounding of the function over a particular domain, so it's impossible for graphs to cross them." I can see how this is true for vertical functions, since vertical functions are figured out by finding the zeroes of the denominator. If the denominator is 0, the functions is undefined. Horizontal asymptotes are figured out by comparing the degree of the numerator and denominator, but it doesn't mean that the graph would become undefined at this this point or anything.

f(x) = (x+3)(x-3)/(x+2)(x-2) This yields 6 quadrants with a parabola-like curve in the middle. The curve isn't a parabola, correct? How do you locate the center of this curve? f(x) = x/(x+2)(x-2) The inner graph looks like x^3. Is its center the origin?

"B is certainely not a solutions as you can get f(x)=1 for x=4" I was doing some rational functions today, and in class, the problem was g(x) = 4(x+1)/x(x-4) It has vertical asymptotes at x=0 and x=4 and horizontal asymptote at y=0. The confusing part was that the asymptote was y=0 and x=-1 gives y=0. I said that it's alright for the graph to pass the asymptote because the asymptote only tells the value a variable approaches as the other variable approaches infinity, but everyone unanimously said no, even my teacher. My teacher then opened his book and said, something about it being a slant or oblique asymptote. However, upon reading my book, I saw oblique asymptotes occur when the numerator is a degree greater than the denominator. And I was still certain y=0 is the horizontal asymptote. So is the graph discontinuous at 0? Or can graphs pass asymptotes?

I once saw this Discovery Channel documentary about guillotines. There was a story about 2 scientists who wanted to know how long one can live without a head. One scientist had his head sliced off by a guillotine and the other watched his head. The head-less scientist was supposed to keep on blinking to let the other time how long he was still alive. Supposedly, he was alive for 15 or so seconds. So how do people and animals live without their head for a certain amount of time. I heard that cockroaches can live without their heads for a week.

I don't remember correctly from history, but I think I remember my teacher talking about the Olmecs inventing the wheel independently from the other side of the world. But my teacher said the Olmecs never used the wheels for carts or carrying stuff. Then I read something about how some Native Americans came to America from the Pacific islands. If this is true, perhaps they could've used the wheel for steering the boats.

I close my eyes when guessing, so I don't think I could pick them up visually. But I think you're right about the body signals. I noticed when I guessed something and the next card was the card I just called out, he gave off body signals, such as shifting his body or giving off a subtle sound.

I asked my friend if he believed that psychic abilities exist. His reply was, "It'd be cool if it did. I wish it exists. But I don't know. I can't say for sure." Then I suggested to him that we practice on our psychic abilities. I pulled out a deck of 40 cards (I took out the kings, queens, and jacks), shuffled it, and layed it on the ground. We took turns guessing exactly what it was, like 7 of hearts. For me, what I did was ask myself what color it was, then what suit, then what number. I don't remember the results of the first time we tried, but it wasn't too shocking. Sure, we had a couple exact hits, but that could be luck. Then my friend suggested that the person trying to guess the card holds it up for the other person to see the card. He and I both noticed that our success rate increased by quite a bit-- I noticed that we got several more suits and a couple more numbers than the last time. Then at lunch, it just became freaky. I don't remember the exact numbers. I got 4 exactly correct, and a lot more numbers than last time. He got 2 exactly correct, some more numbers, and some more suits. But we observed something strange. Sometimes I would guess the next card exactly. Like if I said 7 of hearts, it might've been 4 of spades, then the next card would be a 7 of hearts. This happened like 6 times altogether. I'll try to record the data tomorrow. That way, I can see whether or not these were just lucky guesses. My friend said he could feel sometimes that he was definitely correct for the suits, and just guesses on the numbers. I had that kind of feeling for like 3 of my exact hits.

I was trying to prove that P can be put into the form xm + yn where x and y are the number of stamps, m and n are the prices, and P is the lowest price. So x and y are non-negative integers whose sum is at least one. (mn - a(m+n) + a^2)/a = P mn/a - (m+n) + a = P Let m = ab and n = ac, so a = m/b mn/1/m/b - (m+n) + m/b nb - m - n + m/b n (b-1) + m(-1 + 1/b) ... Now I'm just confused. Does that mean x = (-1 + 1/b) and y = (b-1)? That means that b <=1 for x to be non-negative. I'm sure my logic is flawed though.

Yeah, that's what I just thought up.

I'm not sure if this is a proof or some kind of flawed logic I made up, but here goes. With this problem, we can see some generalizations. One is that the possible prices continue at an interval after a certain point. The second generalization is that if a price is a factor of another price, the smaller price will be the starting point. The third generalization is the interval of possible prices after the starting point will be the greatest common factor of the two stamp prices. Let m=price of one stamp, n =price of another stamp, a= greatest common factor of the stamp prices, and P = starting point. A formula was found to determine the starting point of two stamps with prices m and n. This formula was : (mn - a(m+n) + a^2)/a = P, where m <> n. (m does not equal n) First, we show that it works for the first case. Let m = 2 and n = 3 (2*3 - 1(2+3) + 1^2)/1 = P and P = 2, therefore it works for the first case. Next, we show that there isn't a price lower than P that is actually the starting point and works. Using our third generalization, which is that the interval after the starting point is the greatest common factor of the two stamp prices, we say that P - a <> xm + yn , where x and y are non-negative integers. x and y represent the number of each stamp and therefore can't be negative. We're going to prove that P - a = xm + yn is wrong, therefore proving P - a <> xm + yn Assume P - a = xm + yn (mn - a(m+n) + a^2)/a - a = xm + yn Because (mn - a(m+n) + a^2)/a = P (mn - a(m+n) + a^2 - a^2)/a = xm + yn Because a^2/a = a (mn - a(m+n))/a = xm + yn Because a^2 - a^2 = 0 Let m = ab and n = ac (ab*ac - a(ab+ac))/a = x(ab) + y(ac) Substitution (bca^2 - a(a(b+c)))/a = xab + yac Because a*a = a^2 and Distributive Prop. (bca^2 - a^2(b+c))/a = xab + yac Because a*a = a^2 bca - a(b+c) = xab + yac By dividing by a on the left side a(bc - (b+c)) = a(xb + yc) Because Distributive Prop. bc - (b+c) = xb + yc Divide by a bc - b - c = xb + yc Distrib. Prop. b(c-1) - c = c(b-1) - b = xb + yc Distrib Prop. However, this is impossible because x and y are non-negative integers. Therefore , P - a <> xm + yn . Hey, I think I solved it.

If you're wondering "How do you derive the formula based on other formulas and theorems?" I have no idea. But it'd be a good challenge to derive it. If the formula does work, which I think it does because nobody can find a counter-example to it, then it means that there is exactly 1 "lowest price" and that the interval is the GCF of the two prices. I'm just guessing here but it might be figured out from sequences and series. After the lowest price, there's an arithmetic sequence. There's another weird sequence before it.

I'm still at a lost at what you're saying . Could you define your variables maybe? Each person uses a different variable for the same thing-- i used m and n, but others used x, y, a, b, etc. The price of the stamps are going to be non-negative integers just by nature. If the stamps' prices were negative, that means that the person SELLING the stamps PAYS the buyer. As much as I would like that, it just doesn't happen, normally, in this world. The number of stamps are going to be non-negative integers by nature, too. You can't buy negative stamps, unless you consider selling stamps buying negative ones. If you buy negative seven stamps, and the next day you buy ten stamps, how many stamps would you have? You don't hear questions like that everyday. Because the price of "x" number of stamps = the price of 1 stamp * x and both the price and x are positive, the price of "x" number of stamps will be positive too.

I'm not sure I understand what you're asking Primarygun. But are you saying that each different set of two stamp prices, x and y, generates a different "lowest price," n? This is not true because 3 7 12 4 5 12

Oh, does GCD stand for greatest common factor? I've heard of GCF, greatest common factor, and LCD, least common denominator, but not GCD before. But then again, it's been a long time since I was taught those.

I should go ask my teacher about it. I never approached him about whether or not he or anyone proved it.

But the problems in my classes is there isn't enough seats for everyone. Actually now, the district is going to take kids out of certain classes, in my case honors chemistry, and putting them into regular chemistry or physics or something if they don't voluntarily change their class schedules. Secondly, if there isn't enough students in the honors physics, then the class will be gone. So that's tough right there. I'm going to voluntarily change to the honors physics one, but I don't even know if that class is going to still be there in a week.

Well like I said, my math teacher gave us this problem. He said it took the teachers at the school 45 minutes to figure it out. He's really smart and all the math teachers combined took pretty long to figure it out. The math teachers tried to figure out a formula after they had the problem. They were unsuccessful. Then they did e(ho0n3 's method of "plugging, chugging, and looking." They came up with the formula after that. Well, my math teacher gave us the problem without any hints. In 45 minutes, the class came up with some generalizations. One was that the numbers continue at an interval after a certain point. The second generalization, a pretty obvious one, is that if a number is a factor of another number, the smaller number will be the starting point. The third generalization is that if both numbers are even, then they will have an interval of 2, which turned out to be wrong. After the class was over, I "plugged and chugged" until I had a list of about 15 sets of numbers. I came up with another generalization. The interval was the greatest common factor of the two numbers. I don't have the list anymore because I threw away the paper. Actually, I'm not 100% sure this is the formula I came up with several months ago, but it works. The first two numbers will be the stamps' prices and the third number is the lowest price. 2 3 2 2 5 4 2 7 6 2 9 8 3 4 6 3 5 8 3 7 12 3 8 14 4 5 12 4 6 4 4 7 18 4 9 24 ... 6 8 12 6 9 6 6 10 16 ... 8 10 24 ... 100 263 25937 No, I didn't actually write out the 100 and 263 one. But this is what the formula predicts. The formula is (if you don't want to stare at those numbers and see for yourself) (M*N/Greatest Common Factor of M and N) - (M + N) + Greatest Common Factor of M and N Oh, but I do warn you, my teacher never told me whether or not I got the answer. So I don't know if that's it. And even if he did, I wouldn't have remembered.