Daedalus

Me too!!! However, I do have a few friends who were not so lucky. I'm just thankful that they are still alive. I was two blocks away from the May 3, 1999 tornado off of 4th street and Santa Fe in Moore, OK. Today, I was at my brother's house in NW OKC.

I'm not sure if this counts as science news, but I live in Norman, OK (it's just 7 miles south of Moore), and my best friend, Dustin, lives right behind the Warren theater where the tornado hit. I went to see the new Star Trek movie at that very same theater last night. *Edit* I just found out that my friend, Amanda, was seeing the movie, Mud, at the Warren theater today. The tornado hit right before the end of the movie. If it hit 10 minutes later, she might not be alive tonight! The following image was taken by her. According to KOMO News, there are at least 51 people confirmed dead. Today's tornado was comparable to the May 3, 1999 tornado that also went through Moore. Both tornadoes were close to each other in size and in the path they took as shown in the following image. The May 3, 1999 tornado is rated as an F5 (261–318 mph winds) and the May 20, 2013 tornado is rated as an EF4 (166 to 200 mph winds). http://www.youtube.com/watch?feature=player_detailpage&v=40fon8AEYII

From my own experiences, I use linear algebra extensively when creating 3D interactive software such as games or motion detection and object tracking algorithms in DVR / surveillance applications.

Although I agree that beauty is in the eye of the beholder, there is evidence that beauty is based on mathematics. I remember watching a show on the science channel that compared people's faces with a beauty mask that is based on the golden ratio. People who are attractive fit the mask better than people who are not. Here are a few links that discuss the relationship between beauty and math: http://www.realscience.us/2012/04/30/beauty-by-the-number/ http://www.goldennumber.net/facial-beauty-new-golden-ratio/ http://www.sciencedaily.com/releases/2009/12/091216144141.htm

http://www.bbc.co.uk/news/world-asia-22148141 Happy birthday Kim II-sung. Now blow out your candle!!!

That would imply that we only know about [math]\pi[/math] because spacetime is locally flat. However, even if spacetime wasn't flat, we'd still know about [math]\pi[/math] due to the nature of circles in Euclidean geometry.

The problem I see here is that you are not using a predefined operation such as the ones listed in my previous post. You have simply defined some function and named your own operation. Anyone can do that. I see this particular game as an exercise for one to extend their knowledge of predefined operations that result in large numbers with some additional rules as outlined throughout the thread. Simply defining your own function as an operator seems to defeat the purpose of this exercise. Please note that while I didn't start the thread, I'm trying to uphold the spirit of the game as stated in the OP. 1.) The rules of the game should be to post an expression that uses three single digit base 10 whole numbers to achieve the highest resulting value possible (excluding infinities). As stated in my first post in the spoiler: Use an infinite base such that we have an infinite number of single digit numbers or symbols to represent a number. However a more practicle base would be something like base [math]2^{64}[/math]. That way a single 64 bit number would represent one symbol / digit. We can always choose a larger base. The point being made is that we can always choose a set that has more symbols / elements and push the resulting value of the operation, whichever one you choose, higher. 2.) We cannot define new operations. Only use predefined operators that can be found in Wikipedia, Wolfram, or a website / paper published by an educational institution such as Cornell University's arXiv. Any such operation must be referenced in the post. 3.) We should rule out using an operation recursively such as nesting a factorial over and over again, and that only one unary operation can be applied to a number to prevent nesting such number in a sea of unary operations. Nesting a unary operation implies [math]n[/math] recursions, which hides yet another variable or single digit number. For instance, Knuth's up-arrow notation is extended by incorporating a variable that defines such recursion: [math]a \uparrow^{n} b[/math] However, using a predefined operation such as the extended Knuth's up-arrow notation is fine. You just can't invent an operation that cannot be found as defined in number 2. 4.) The result must be a finite real number. Of course, integers are also acceptable. Any other rules we should impose?

Well... if we are ruling out infinities, then I would imagine that we should also rule out infinitesimals for the exact same reason, and only use predefined operators that can be found in Wikipedia, Wolfram, or a website / paper published by an educational institution such as Cornell University's arXiv. Although the operator needs to produce a finite result, it does not necessarily have to be a unary operation given the previous restriction to use three single digit base 10 whole numbers.

Exactly... That's why the rules of the game should be to post an expression that uses three single digit base 10 whole numbers to achieve the highest resulting value possible. We should rule out using an operation recursively such as nesting a factorial over and over again, and that only one unary operation can be applied to a number to prevent nesting such number in a sea of unary operations. Nesting a unary operation implies [math]n[/math] recursions, which hides yet another variable or single digit number. For instance, Knuth's up-arrow notation is extended by incorporating a variable that defines such recursion: [math]a \uparrow^{n} b[/math] We can see from the above example that 3 variables are now in play instead of just adding more arrows to the expression. Ajb has introduced super and hyper factorials. So I will introduce exponential factorials and modify my previous result to achieve yet again the largest number to be generated thus far: [math]\text{expofactorial}\left(\text{expofactorial}(9)\uparrow^{\text{expofactorial}(9)}\,\text{expofactorial}(9)\right)[/math] The resulting value is so immense that I do not believe that we could actually calculate the result of the operation without a supercomputer. And even then, your children's children would probably be waiting for the answer

My post messed up when I went to edit it, but yeah...

More like an 8 that got drunk and fell down thinking it was greater than all the other numbers.

Nope that's not a number. It's a limit. If it was a number, I could always add one to it and have a greater resulting value. So far, iterated exponentiation, higher bases, and bignose's factorials gives us the largest number thus far. However, there are operators greater than iterated exponentiation, but I haven't seen any syntax that would represent them. Of course, we could always use infinitely nested factorials... [math]\left(\left(\left(9!\uparrow^{9!}\,9!\right)!\right)!\right)!\,...[/math]

Ok I'll play. I'll use Knuth's up arrow notation to write an expression with three separate single digit numbers. Beat this: [math]9 \uparrow^{9} \, 9[/math] Please note the answer is to large for me to display here due to the use of iterated exponentiation (tetration). Of course, we can always beat this result. Does anyone know how? Edit - In response to Bignose's post... I'll modify mine ; ) [math]9! \uparrow^{9!} \, 9![/math] Now that's an operation with an extremely large value that dwarfs [math]9^{9^{9}}[/math] and [math]9!^{9!^{9!}}[/math].

You're welcome

Neat!!!

You beat me to the punch !!! Oh well, that's what I get for being hardcore and going into exquisite detail (jk). As mathematic suggested, Newton's method can be used to approximate the answer to this problem. Although Newton's method is a root-finding algorithm, it can also be used to approximate the result of many different types of operations (e.g. ath roots [math]\sqrt[a]{b}[/math], logarithms [math]\text{log}_{\,a}b[/math], nested logarithms [math]\text{nLog}_{\, a}b[/math], inverse trig functions [math]\text{sin}^{-1} x[/math] or [math]\text{cos}^{-1} x[/math], etc...), which is actually pretty cool when you think about how powerful it is when used for numerical analysis . In order to use Newton's method for our purpose, we have to shift our function along the [math]y[/math] axis such that the root / zero is connected with our [math]b[/math] variable (I haven't been to bed in a couple of days so I'm not sure if I worded that correctly, but the following example should clarify what I mean): [math]x_{n+1}=x_{n}-\frac{f\left(x_{n}\right) - b}{f'\left(x_{n}\right)}[/math] For instance, to use Newton's method to find the [math]a[/math]th root of [math]b[/math], or [math]\sqrt[a]{b}[/math], we simply use the following algorithm: [math]x_{n+1}=x_{n}-\frac{\left(x_{n}\right)^{a}-b}{a\,\left(x_{n}\right)^{a-1}}[/math] where [math]a[/math] and [math]b[/math] are constants, [math]f(x)=x^{a}-b[/math], and [math]f'(x)=a\left(x\right)^{a-1}[/math]. Because this method should converge to a value, all you have to do is repeat the process until you reach the desired accuracy. It is important to note that this method works for both, unary (trig functions, etc...) and binary (addition, subtraction, etc...) operations. For now, let's rework your equation into a more interesting form (again, I'm probably making this more complicated than it should be due to a lack of sleep): [math]e^{1/x}-x=0[/math] Add [math]x[/math] to both sides: [math]e^{1/x}=x[/math] Take the natural log of both sides: [math]\text{ln}\left(e^{1/x}\right)=\text{ln}\left(x\right)[/math] Simplify the result: [math]\frac{1}{x}=\text{ln}\left(x\right)[/math] Multiply both sides by [math]x[/math]: [math]1=x\,\text{ln}\left(x\right)[/math] Let's get rid of that natural logarithm by raising [math]e[/math] to the power of both sides: [math]e^1=e^{x\,\text{ln}\left(x\right)}[/math] Simplify the result: [math]e=x^x[/math] Now that's an interesting result that we can work with. So, let's define our function as [math]f(x)=x^x-b[/math] where [math]b = e \approx 2.718281828459045...[/math] and with [math]x^x[/math] possibly representing a nested exponential with [math]a=2[/math] such that [math]x^{\left \langle 2 \right \rangle} = (x)^x[/math]. Anyways, without delving further into madness, we find that the derivative of [math]f(x)[/math] is [math]f'(x)=x^x\left(1+\text{ln}\,x\right)[/math] Substituting all of this into Newton's method we finally arrive at our algorithm, and can now determine the value of [math]x[/math] that satifies the equation [math]e^{1/x} - x = 0[/math] : [math]x_{n+1}=x_{n}-\frac{\left(x_{n}\right)^{\left(x_{n}\right)}-e}{\left(x_{n}\right)^{\left(x_{n}\right)}\left(1+\text{ln}\,\left(x_{n}\right)\right)}[/math] Enjoy!!!

I imagine that these turbines would be a lot smaller than those large windmill types, and look similar to a jet engine in order to funnel the air through them and provide an encloser to protect vehicles on the highway. Furthermore, they would be positioned at a height that would have the most airflow. So, they wouldn't be very high off the ground. I figure that they would be between 5 - 10 feet off the ground in order to make use of the wind generated by fast moving vehicles. I have my doubts regarding the amount of power that could be generated using this technique, or even if it would make sense to do such a thing. However, if the idea seems plausible, I could contact the Dept. of Transportation and try to get permission to conduct an experiment using an anemometer to measure the wind speed in various areas in order to do some calculations. Even if this idea is a flop, it would still be fun to conduct the experiment and figure out how much electricity could be generated using this method. The least that could come from conducting such an experiment would be teaching my son, Maxx, about physics and science in general. Now that I think about it, this would be one hell of a science project that could win him a prize if their school ever has a science fair. Maxx loves working math problems. All I would have to do is teach him the physics that would allow him to do the necessary calculations and help him set up the anemometer and gather the data. He could do the rest on his own.

I'm not sure how viable this would be, but how effective would wind turbines be that are located along the side of busy highways and interstates? I came up with the idea after practically being blown off the road due to a semi-truck / 18 wheeler passing me on the interstate. It occured to me that vehicles, especially big rigs, generate a lot of wind as they travel down the highway at speeds of 70 - 80 mph. I am wondering if we could harness the wind using turbines that are located along the side of the highway, and if this could generate a significant amount of electricity? Any thoughts regarding this idea?

Although it makes sense, at least to us, to use radio-type signals to transmit messages, the aliens could use other technologies to communicate messages. For instance, it is possible to use neutrinos to send messages through mediums that would be impossible for electromagnetic radiation. Of course, such technology poses extremely difficult problems to overcome, such as a reliable way of detecting the nuetrinos. However, using nuetrinos is possible and has the advantage of being able to penetrate through most obstacles they encounter, not to mention that they travel near the speed of light. Unfortunately, this doesn't really help the arugment except to further complicate what might be needed to detect alien messages.

That's why I retracted my statement, and now favor functionality instead of form. However, functionality and form are closely related, which is why I wouldn't be surprised if most aliens turn out to be humaniod.

LOL... That's a good one. I admit that my statements regarding aliens as most likely having humanoid form is a slippery slope and easy to pick apart. Perhaps I should've stated that aliens would at least require appendages that allowed them to create and use tools, and keep my opinion regarding their form to myself. However, having a humanoid form, at least in regards to life on Earth, has proven to give us tremendous advantages that other life forms here on Earth do not have (such as being able to create and use complex tools). Well if I had a choice between a slave or a robot that could do the same tasks as a slave. I would choose the robot because it probably could do a better job than the slave and work many more hours. Of course, there could exist the type of alien that finds amusement in enslaving a population. Maybe they would enslave us and use robots to crack the whips lol. I agree. I was just trying to speculate why we don't detect transmissions from them outside the "they are too far away" hypothesis. It could also be that they use a very broad range of frequencies when transmitting a single message. Such technique would make it harder to detect the message, and could possibly hide their existence from other aliens that would be potential threats if they knew where they were.