Stupid and small questions thread

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Stupid and small questions thread Anonymous Tue Jul 15 17:55:46 2014 No.6646480 [Reply] [Original]

Fire away

Anonymous Tue Jul 15 18:07:26 2014 No.6646517

>>6646480
Sorry in advance for the lack of tex notation. If someone has a guide for it please link me, I couldn't find one on the main page.

I have the following function:

f(x,y) = sin(x) * cos(y)

How do I take the partial derivative of f(x,y) with respect to x? Specifically I don't get what happens to the cos(y) term.

>>	Anonymous Tue Jul 15 18:37:53 2014 No.6646572 >>6646517 Change values of x, what happens to cos(y)?

>>	Anonymous Tue Jul 15 18:40:51 2014 No.6646576 >>6646480 why is excess cpu heat not used to power computers?

>>	Anonymous Tue Jul 15 19:19:25 2014 No.6646624 >>6646576 we dont know how to use temperature as energy-source.

>>	Anonymous Tue Jul 15 19:35:50 2014 No.6646644 >>6646624 Nitinol

Anonymous Tue Jul 15 19:44:03 2014 No.6646658

18, college freshman thinking about a future medical school path. How essential is Calculus II for my goals in the medical field? I still want to pursue math skills but I'm worried it'll fuck up my gpa because I seriously can't wrap my head around Taylor and infinite series in general. Study harder faggot, yeah, but should I just let myself off the hook and take an economics class or somethin instead?

>>	Anonymous Tue Jul 15 20:03:24 2014 No.6646679 >>6646517 You treat the term cos(y) as constant, as cos(y) does not vary with x. If you take the partial in respect to y, then you treat sin(x) as a constant.

>>	Anonymous Tue Jul 15 20:06:07 2014 No.6646685 what's the difference between matter and a field?

>>	Anonymous Tue Jul 15 20:21:22 2014 No.6646718 >>6646685 nothing a field is when you think of particles as values in a space where every point has a value

>>	Anonymous Tue Jul 15 22:13:57 2014 No.6646966 >>6646576 Build such a system yourself. Report back to /sci/ or /g/ with your results.

>>	Anonymous Tue Jul 15 22:18:07 2014 No.6646977 >>6646658 Depends how hard Med school is to get intoin your country. Why don't you find a few different resources for the topics you shurggle and see if that helps before you piss away harvard for the university of innuit polytechnic

>>	Anonymous Tue Jul 15 22:19:18 2014 No.6646980 Hypothetically if one had the ability to stop time, that would mean that light would stop around them. So does that mean the person would instantly see blackness if they were to move slightly, then stay in a still position? Is that understandable?

>>	Anonymous Tue Jul 15 22:23:22 2014 No.6646988 >>6646980 I'm no expert, but... You can't move in stopped time. Movement involves at least 1 direction of space plus the dimension of time. Even the process of seeing requires time, cos it involves atoms n stuff moving in your retina.

>>	Anonymous Tue Jul 15 22:24:43 2014 No.6646992 >>6646576 themal base energy generation is probably one of the least efficient in the field of semiconductors. generally its not worth the cost

>>	Anonymous Tue Jul 15 22:25:22 2014 No.6646993 >>6646980 If when you stopped time light stopped moving then it would go black instantly (assuming you are not affected by the time stoppage).

>>	Anonymous Tue Jul 15 22:31:59 2014 No.6647006 >>6646992 citation, etc.

>>	Anonymous Tue Jul 15 22:33:35 2014 No.6647009 >>6646480 Can science save the world?

>>	Anonymous Tue Jul 15 22:34:15 2014 No.6647011 >>6647009 >implying

>>	Anonymous Tue Jul 15 22:47:47 2014 No.6647029 do all the non trivial zeroes of the riemann zeta function have real part 1/2?

>>	Anonymous Tue Jul 15 23:04:15 2014 No.6647046 How can I master entire fields of science overnight like Tony Stark?

>>	Kocoayello !jxaL03vL/Q Tue Jul 15 23:14:21 2014 No.6647056 >>6647046 Be well written.

>>	Anonymous Tue Jul 15 23:22:25 2014 No.6647069 >>6646480 how do grading curves work? ive never had a teacher curve a grade and all the noisy ass kissing students have been whining about a curve in my summer class for the final grade. what are the chances i'll get a curve on a summer class?

>>	Anonymous Tue Jul 15 23:23:21 2014 No.6647070 >>6647046 teleport to earth-616

>>	Anonymous Tue Jul 15 23:23:29 2014 No.6647071 How do I find the gradient of a sphere centered at the origin? Let the sphere be defined as <span class="math"> x^2 + y^2 + z^2 = R^2 [/spoiler] How do I take the gradient of that?

Anonymous Tue Jul 15 23:26:39 2014 No.6647078

>>6647071
The gradient is a vector given by taking the partial derivative in each direction, (i.e. x, y, and z). So your gradient vector would be:

<2x,2y,2z> if I'm not mistaken. Vector calculus kinda sat on the back burner after calc III, hopefully E&M will be a nice refresher.

Anonymous Tue Jul 15 23:34:35 2014 No.6647090

>>6647078
What about the R^2[/spoiler]? As you said, the gradient is defined as the partial derivative of the function in the principle directions (in cartesian space anyway)

But this function has the equality for the radius. I always have trouble thinking about things like this. And yeah, I know the radius doesn't matter here since its just a constant...

Whenever something isn't explicitly defined (say like):

f(x,y,z) = x+y^2+z+3x^2[/spoiler]

I just can't grasp how to deal with it.

>>	Anonymous Tue Jul 15 23:40:11 2014 No.6647098 >>6646718 E&M fields are matter

>>	Anonymous Tue Jul 15 23:41:19 2014 No.6647099 >>6647098 no.

>>	Anonymous Tue Jul 15 23:43:14 2014 No.6647101 >>6647099 meant to greentext to show the flaws in his statement

Anonymous Tue Jul 15 23:47:07 2014 No.6647106

>>6647090
Well, technically, the R^2[/spoiler] becomes zero, as the derivative of a constant is always zero.

Now, on to your next example, which I think is a little easier to deal with. You must forgive me if I fuck up the Latex, I've actually never used it on this site before. Anyways, when taking the gradient of the function:

f(x,y,z)=x+ y^2 + z + 3x^2[/spoiler]

It's helpful to think of what you're finding, which is the following vector:

<\frac{\partial}{\partial x} f(x,y,z), \frac{\partial}{\partial y} f(x,y,z), \frac{\partial}{\partial z} f(x,y,z)[\math]

So, when you apply that, the gradient, denoted \nabla f(x,y,z)[\math] you get:

<1+6x, 2y, 1>[\math]

Once again, I probably fucked up the Latex, but I think you should catch my meaning[/spoiler][/spoiler]

>>	Anonymous Tue Jul 15 23:47:15 2014 No.6647107 >>6647090 *rather that WAS explicitly defined and so its easy to think about the gradient of that but not of a sphere equation

Anonymous Tue Jul 15 23:52:57 2014 No.6647117

>>6647106
Fuck me, hold on.

<\frac{\partial}{\partial x} f(x,y,z), \frac{\partial}{\partial y} f(x,y,z), \frac{\partial}{\partial z} f(x,y,z>)[/spoiler]

So, when you apply this to your function, your gradient, denoted \nabla f(x,y,z)[/spoiler] is:

\nabla f(x,y,z)= <1+6x, 2y, 1>[/spoiler]

If this doesn't work I'm gonna go cry.

>>	Anonymous Tue Jul 15 23:54:31 2014 No.6647121 >>6647117 Oh look at that, it worked, obviously that bracket and parenthesis are in the wrong order, but you get it.

>>	Anonymous Tue Jul 15 23:56:36 2014 No.6647126 >>6647117 What does the bracket on the right side do? Does the equation change when the bracket and parentheses switch position. I'm so god damned confused!

>>	Anonymous Wed Jul 16 00:06:01 2014 No.6647142 >>6647117 guy who originally asked here thanks for solving the second grad too

Anonymous Wed Jul 16 00:18:17 2014 No.6647156

>>6647126
Nope, it's just vector notation, which there are a multitude of forms for, one of which happens to be the notation:

<x,y,z>[/spoiler], of course you can generalize it for more dimensions <x,y,z,d,l,m>[/spoiler], as many as you need, but we're working in three dimensions, so x, y, and z will suffice.

The parenthesis is supposed to go with the function.

>>	Anonymous Wed Jul 16 04:00:49 2014 No.6647361 Given enough time, is there a limit to what we can achieve/learn/do? ie; is sentience/consciousness limitless? Does it expand indefinitely? Or will we hit some sort of 'block' eventually where we just can't comprehend anything further?

MrMcPussyFlaps Wed Jul 16 04:15:38 2014 No.6647384 [DELETED]

Why are nigs black? I mean seriously? Like if you wanted to protect yourself from heat/sunlight why would you evolve to be DARKER and not lighter to reflect light/heat??? Wouldn't being darker cause you to absorb more? People in places with low Sun have paler lighter skin? I mean wtf? Don't you need to absorb sunlight MORE efficiently to get dat vit D? Wtf is going on here?

>>	Orpheus !92wptUrql. Wed Jul 16 04:24:35 2014 No.6647400 >>6647384 the presence of melanin protects your skin from things like skin cancer melanin also produces a brown/black pigmentation so basically they evolved to be black to protect themselve from the sun's natural radiation

>>	Anonymous Wed Jul 16 04:28:19 2014 No.6647410 >>6647384 Melanin acts like a sponge/shield. Yes it attracts light, but it's to absorb it and prevent the radiation from further penetrating the body. The darker the skin, the more it soaks up.

>>	Anonymous Wed Jul 16 04:37:53 2014 No.6647422 File: 48 KB, 344x345, drink.jpg [View same] [iqdb] [saucenao] [google] Is there any simple way to explain how absolute zero isn't colder than a frying pan is hot but heat can in theory kep getting hotter?

>>	Anonymous Wed Jul 16 04:41:20 2014 No.6647424 Why is theta measured from the x-axis on the unit circle rather than the y axis? Angles are usually measured starting from 0 at the top of the circle.

MrMcPussyFlaps Wed Jul 16 04:48:23 2014 No.6647430

>>6647384
>>6647400
>>6647410
Ya actually stopping and thinking about it a bit I think I got it anyway.

It's not about heat or the colour of the skin at all is it?

I mean for example; imagine blinds on a window, dark coloured blinds. From the outside of the house if you looked at the window when the blinds were open you'd see a "lighter" area. The blinds are open, letting more light into the house when you need it. When you have enough light or there's too much, you close the blinds and if someone looked from outside the window would now look "darker"....

I didn't google or anything, did I get the basic premise right?

Also, I was banned for my original post??? Wth? It was a legitimate question...these janitors, I swear

>>	Anonymous Wed Jul 16 04:48:56 2014 No.6647432 Is there an easy way to count the number of weak m-compositions of n whose partial sums are lower bounded by some function?

>>	Anonymous Wed Jul 16 04:53:49 2014 No.6647435 Is the probability that Shakespeare can be found written in binary in pi, 1 meaning certain, or is it "almost surely"

>>	Anonymous Wed Jul 16 04:55:59 2014 No.6647439 >>6647422 Hot has a limit, and absolute zero isn't colder than a frying pan is hot only because you are using an arbitrary scale. If you use kelvin there is no such distinction

MrMcPussyFlaps Wed Jul 16 04:57:00 2014 No.6647440

>>6647430
Well not banned banned but temporarily blocked anyway... y dey do dis?

Also, what caused the sudden explosion of evolution from microbial life to more complex life? I mean it stayed at microbial level for ages and ages and then BAM! Wth happened? And why too? It makes no sense to evolve hard bodies, rather it's more of a disadvantage, what drove all this? Tell me a compelling argument as to why we are not just some goo that photosynthesises to survice/reproduce? There is absolutely no reason to evolve further, why would it happen? Is this why there is no other intelligent life in the universe? I mean there is surely microbial somewhere else out there, but anything more doesn't make sense. Why would it happen? Whatever caused it, could that 'thing' be considered 'God'???

>>	Anonymous Wed Jul 16 04:57:54 2014 No.6647443 >>6647440 Janitors here are shit

>>	Anonymous Wed Jul 16 04:58:55 2014 No.6647447 >>6647440 Also, you are probably going to be banned for 24 hours in a few minutes.

>>	MrMcPussyFlaps Wed Jul 16 05:01:32 2014 No.6647451 >>6647447 B-but for what?! This is so unfair....

>>	Anonymous Wed Jul 16 05:07:45 2014 No.6647454 >>6647451 I've been banned for having a post in a thread being raided by /b/, even though I was just in the thread as a /sci/ poster. I've been banned for off topic posting in a thread that belonged in /x/.

Anonymous Wed Jul 16 05:07:51 2014 No.6647455

>>6647440
It makes sense, single cell to multi cellular life seems like the biggest hurdle toward animals. Once an animal evolved that ability, it basically became a free for all explosion of every possible multicellular combination.

Hard bodies can survive in more varied environments, can allow greater specialization ( sensitive cells on the inside do the chemistry while tougher outer cells make defenses), is a combat benefit, a simple moving hard mass can cut up and eat your goo. Evolution doesn't just go for some optimal win condition, if one of the goos is better able to kill other goos because it become more "animal like" then it has an advantage.

There might be intelligent life, good luck finding it, the universe is fuck huge.

Furthermore, life on earth is pretty damn young in the universe scale. Life has existed here for about 1/4 of the life of the whole universe, we could easily be one of the first truly intelligent races in the universe, we might be the "ancients" we see in movies

>>	Anonymous Wed Jul 16 05:11:11 2014 No.6647460 >>6647435 If pi is a normal number, then it's certain to contain every possible combination of numbers. However we don't know that pi is normal. We are pretty sure though, given that the first 30 million digits are evenly distributed.

MrMcPussyFlaps Wed Jul 16 05:16:40 2014 No.6647467

>>6647454
Ya I've been banned before for 3 days for some serious weak shit. Apparently I was shitposting even though I wasn't and there were many others in the thread clearly shitposting and no one got banned but me. That really rustled my jimmies.

>>6647455
This was a sufficient reply. For now.

Anonymous Wed Jul 16 05:17:41 2014 No.6647468

>>6647451
Because multiple anons (im not even >>6647447) including myself have reported you multiple times for shitposting and dragging racism and sewage-tier politics onto our board.

I would say fuck off back to /pol/, except in all honesty, that board doesn't need you, either.

>>	Anonymous Wed Jul 16 05:20:45 2014 No.6647471 >>6647467 >apparently I was doing something even tho I wasnt full retard, right here. or to put it, ironically, in your language, this is you: >i din do nuthin! >no one got banned but me you dont actually know this, moran

>>	Anonymous Wed Jul 16 08:16:07 2014 No.6647675 \|z+1\|+z+i=0 , find the imaginary part of z. How do I solve this.All I could think is to find the modulus of \|z+1\| but I don't know z.Where do I start with this? thanks.

>>	Anonymous Wed Jul 16 09:56:13 2014 No.6647815 >>6647675 insert z= a +bi you end up with two equations Re(complexnumber)=C1 Im(complexnumber)=C2 solve a and b profit

>>	Anonymous Wed Jul 16 10:08:19 2014 No.6647825 I know nothing of chemistry, is it possible to know the colour of a crystal before you make it? Like if your boss came up to you and told you to make him an orange piece of plastic or ablue crystal would you be able to do it?

>>	Anonymous Wed Jul 16 10:30:06 2014 No.6647854 >>6647675 (real number)+z+i=0 so matching imaginary parts, im(z)+1=0 im(z)=-1

Anonymous Wed Jul 16 10:51:01 2014 No.6647884

>>6647825
>crystal
>plastic

If you have detailed knowledge of the electronic structure of the material, then yes you can predict the color, but not that it is probably more difficult to predict this structure than it is to just make the stuff and have a look.

In the case of plastic, you just add a dye.

Anonymous Wed Jul 16 11:15:28 2014 No.6647913

>>6647468
>>6647468
>including myself have reported you multiple times for shitposting and dragging racism and sewage-tier politics onto our board.

This is absoloute bollox and you know it. What shit-tier politics??? When was I racist? Do you mean me using the word "nig" or "niqqa"? Are you serious? Words that are used almost universally throughout 4chan? Have I ever started shitposting and started to talk shit over one race or another? And what politics exactly have I been shit posting about?

You are full of shit m8. And you sound like a pretty sad person, like one of them old people who get annoyed over some random thing someone says. But really; I am very curious to know what these racist or shit-tier /pol/ shit I was spouting about. Go on, please elaborate, I'm not even gonna ask for exact quotes, I just want a rough idea of what exactly you think I've been saying that's been so offensive to you.

Anonymous Wed Jul 16 11:21:35 2014 No.6647916

>>6647471
>stupid and small question thread - post any stupid or small question!
>post something, that was apparently deemed stupid by some people although it was genuinely a legit question by myslef.
>post gets deleted and I get banned.

Wow. Nice work geniuses.

>>	Anonymous Wed Jul 16 11:27:36 2014 No.6647921 >>6647913 >>6647916 >still can't figure it out >thinks everybody else is stupid let me guess, you are ban-evading right now and think just dropping that terrible trip is enough to sneak by the mods?

Anonymous Wed Jul 16 11:35:59 2014 No.6647932

>>6647921
Well at least two anons seriously replied to my original question so clearly not everyone thinks it was a stupid question.

And no, I didn't drop the trip to work round the ban lol are you stupid? If I'm trying to avoid the ban why would I continue quoting myself and continue on the discussion? Lemme guess, you're gonna report me again? Still, care to explain where I was shitting out racism or shit-tier politics??? Please elaborate.

>>	Anonymous Wed Jul 16 11:40:32 2014 No.6647940 >>6646992 >"not worth the cost" this would revoloutionize everything

>>	Anonymous Wed Jul 16 11:41:26 2014 No.6647941 >>6647854 >>6647815 here... of course... (slaps forehead with trout) ...I feel stupid now

>>	Anonymous Wed Jul 16 11:41:57 2014 No.6647942 >>6647029 best question so far^

>>	Anonymous Wed Jul 16 12:41:44 2014 No.6648019 >>6647675 How to get the real part?

>>	Anonymous Wed Jul 16 13:19:00 2014 No.6648066 >>6646480 a triester and sodium hydroxide react to form?

>>	Anonymous Wed Jul 16 13:22:04 2014 No.6648071 >>6647675 z=a+bi a^2+b^2+a+bi+i=0 a^2+b^2+a=0.... (1) b+1=0..... (2) solve for a and b

>>	Anonymous Wed Jul 16 13:30:23 2014 No.6648080 >>6646644 gross >>6646624 http://en.wikipedia.org/wiki/Seebeck_effect#Seebeck_effect

>>	Anonymous Wed Jul 16 14:12:35 2014 No.6648136 In a superconductor resistance is zero, and as V=IR Voltage is 0, so how do electrons move with no potential difference?

>>	Anonymous Wed Jul 16 14:14:35 2014 No.6648139 >>6648136 <span class="math"> V\neq0 [/spoiler]

>>	Anonymous Wed Jul 16 14:32:26 2014 No.6648162 How do you define real powers? <span class="math"> x,y \in \mathbb{R} : x^y [/spoiler] <span class="math"> = \exp ( y \ln x ) [/spoiler]? Then how do you define the exp function without powers?

>>	Anonymous Wed Jul 16 14:35:21 2014 No.6648167 >>6648071 Wouldn't it be <span class="math">\sqrt{(a + 1)^2 + b^2} + a + (b + 1)i = 0[/spoiler]?

>>	Anonymous Wed Jul 16 14:48:19 2014 No.6648183 >>6648136 http://physics.stackexchange.com/questions/62664/how-can-ohms-law-be-correct-if-superconductors-have-0-resistivity

>>	Anonymous Wed Jul 16 14:48:33 2014 No.6648184 How do I get the real part in the mentioned complex equation?

Anonymous Wed Jul 16 14:51:13 2014 No.6648188

>>6648162
define exp as a power series
power series only require integer powers, which are defined by iterated multiplication

or define integer powers as above, then define rational powers by x^(p/q) = qth root of x^p
then define x^y by choosing a sequence a_n of rationals approaching y, then letting x^y be the limit of the sequence x^(a_n)

>>	Anonymous Wed Jul 16 15:10:58 2014 No.6648232 >>6648162 define exp as inverse to ln, which you define as integral over 1/x

>>	Anonymous Wed Jul 16 15:20:36 2014 No.6648254 Can you calculate the golden ratio like this: Phi=(a+b)/a=a/b such that a and b are integers?

>>	Anonymous Wed Jul 16 15:31:23 2014 No.6648275 File: 62 KB, 423x404, smug essien.png [View same] [iqdb] [saucenao] [google] Is doubling exponential?

>>	Anonymous Wed Jul 16 15:43:57 2014 No.6648294 This may be obvious, but is there any way to simplify 55root3 - 55 without using decimals and keeping the answer exact?

>>	Anonymous Wed Jul 16 15:50:16 2014 No.6648308 >>6648294 55(root(3) -- 1)

>>	Anonymous Wed Jul 16 16:01:04 2014 No.6648334 >>6648275 Yes. Doubling = y*2^x, where y is the number to be doubled and x is the xth double.

>>	Anonymous Wed Jul 16 16:08:54 2014 No.6648346 >>6648254 WTF retard? You think the golden ratio is a rational number?

>>	Anonymous Wed Jul 16 16:22:20 2014 No.6648359 Is there some program/calculator I can download that has a really high upper computational limit. I just want to see larger Mersenne primes. Matlab is way too low.

>>	Anonymous Wed Jul 16 16:39:44 2014 No.6648375 >>6647424 The French. Damn those cheese-eating bastards!

Anonymous Wed Jul 16 17:22:19 2014 No.6648459

>>6646658
>How essential is Calculus II for my goals in the medical field?
I don't know about medical education where you live but clearly calculus of any level is of absolutely no relation to anything with being a doctor. If you really want to, learn it on your own. Medicine education is hard enough

>>	Anonymous Wed Jul 16 17:46:24 2014 No.6648522 >>6648346 I kinda was I guess. I see my mistake now.

Anonymous Wed Jul 16 22:15:06 2014 No.6649150
File: 13 KB, 260x145, Capture.jpg [View same] [iqdb] [saucenao] [google]

If a resistor of R ohms is connected across a battery of 9 volts, with internal resistance of 2 ohms, then the power (in watts) in the external resistor is (pic related)

Find the maximum value of the power.

I began by taking the derivative of P and setting it to zero. I eventually got (see reply to this post) and I do not know what to do from here. I know I am suppose to solve for are and input it into the original problem, but I do not know how to solve after this point.

>>	Anonymous Wed Jul 16 22:16:47 2014 No.6649153 File: 14 KB, 392x88, 1405554037896.jpg [View same] [iqdb] [saucenao] [google] >>6649150

>>	Anonymous Wed Jul 16 22:20:55 2014 No.6649161 Why does the Standard Social Science Model explicitly ignore the role of biology/genetics on human behavior?

>>	Anonymous Wed Jul 16 22:27:49 2014 No.6649181 >>6646480 does P = NP?

>>	Anonymous Wed Jul 16 22:30:53 2014 No.6649189 >>6649181 no

>>	Anonymous Wed Jul 16 22:35:45 2014 No.6649196 >>6649189 prove it

>>	Anonymous Wed Jul 16 22:35:49 2014 No.6649197 Is any even number greater than 2 the sum of two primes?

>>	Anonymous Wed Jul 16 22:37:32 2014 No.6649200 >>6649196 no u

>>	Anonymous Wed Jul 16 22:38:27 2014 No.6649202 >>6649197 every*

Anonymous Wed Jul 16 22:39:11 2014 No.6649207
File: 41 KB, 1122x510, whatduhhell.png [View same] [iqdb] [saucenao] [google]

So I did the 23andme test and my results were
85.4% European, 13.0% Sub-Saharan African and 1.6% Unassigned
So I came across this function on here called "Global Similarity Map " and for reasons I don't know I was put in the Near Eastern group
Why the hell is that?

>>	Anonymous Wed Jul 16 22:44:38 2014 No.6649219 >>6646480 Is there a limit to how intelligent a human can be? Is using one's cognitive abilities while sleep deprived similar to exercising the same muscle multiple days in a row? Have average neuro-typical human beings evolved to work for leaders?

>>	Anonymous Wed Jul 16 22:47:50 2014 No.6649230 >>6648080 >gross Wot.

>>	Anonymous Wed Jul 16 22:50:45 2014 No.6649241 >>6649230 > transform heat into mechanical into electrical

>>	Anonymous Wed Jul 16 22:52:21 2014 No.6649246 >>6649241 >also is cheap and can scale

Anonymous Wed Jul 16 22:53:19 2014 No.6649250

>>6648188
>>6648232
I was worried about that.
I was trying to define powers as generally as possible before proving 1>0.
I ended up with
 \forall x\in \mathbb{R} : x^1 = x [/spoiler]
 \forall x\in\mathbb{R}, y\in \mathbb{N}^ + : x^{y+1} = x^y x[/spoiler]

>>	Anonymous Wed Jul 16 22:56:00 2014 No.6649256 Seems neat a discussion on the best application of science. Else, a thread-debate answering the questions unanswered in the NyeHam exhibition.

>>	Anonymous Wed Jul 16 23:01:32 2014 No.6649268 >>6649250 Elaborate

>>	Anonymous Wed Jul 16 23:09:28 2014 No.6649281 >>6649207 Pls respond ;_;

>>	Anonymous Wed Jul 16 23:11:17 2014 No.6649284 >>6648232 That's beautiful. That doesn't allow for the exp function to take complex numbers though, right? You'd need to be able to get a complex value from the integral of 1/x which doesn't make any sense...

Anonymous Wed Jul 16 23:12:14 2014 No.6649287

>>6649268
?
Properties of an ordered field.
 \forall x \in \mathbb{R}, x\neq0: x^2>0 [/spoiler]
So I needed a definition of x^2 [/spoiler]
I could have just defined it like x^2 = x\cdot x [/spoiler] but that seemed boring.

>>	Anonymous Wed Jul 16 23:18:06 2014 No.6649308 >>6649207 Because former ottoman territories have a lot of african admixture from slaves What do you know about your genealogy?

>>	Anonymous Wed Jul 16 23:19:56 2014 No.6649314 >>6649284 Isn't the same as just defining it as the solution to <span class="math"> y' = y [/spoiler] with <span class="math"> y_0 = 1 [/spoiler] bunch of definitions here: https://proofwiki.org/wiki/Definition:Exponential

>>	Anonymous Wed Jul 16 23:22:23 2014 No.6649317 >>6649314 and by it I mean <span class="math"> y= \exp x [/spoiler]

>>	Anonymous Wed Jul 16 23:23:07 2014 No.6649320 >>6649308 I know I'm Afro Caribbean, Irish-Scottish, French, Polish, Ukrainian, Baltic and Balkan. Weird that I'm clustered near Palestinian, Bedouin and Druze

Anonymous Wed Jul 16 23:53:34 2014 No.6649371

>>6649197
>>6649202

Theorem 1. The integers {1, 2, ..., 2k} can be arranged into k disjoint pairs so that the sums of the elements in each pair is prime.
Proof. We prove this by complete induction. The assertion is true when k=1 since 3 is prime. Now consider the set of integers {1, 2, ..., 2k}, and assume that all the sets {1, 2, ..., 2j} have been successfully paired where j is any integer in the range 0 < j < k. We begin by trying to pair 2k with some other number. The possible pairs are (j, 2k) with 0 < j < 2k. The sums of these pairs are all the integers from 2k+1 to 4k-1. Since 2 (2k+1) -2 > 4k-1 Bertrand's Postulate insures that one of these numbers, say 2k+m, is a prime. But m is odd, so the set {m, m+1, ..., 2k-1, 2k} has an even number of elements. This set can be paired so that the sum of the elements in each pair is the prime 2k+m: just pair m+1 with 2k-1, m+2 with 2k-2, etc. The proof is done because our inductive assumption implies that the initial segment from 1 to m-1 can be paired so that the sum of the elements in each pair is a prime. ¤

Anonymous Thu Jul 17 00:07:20 2014 No.6649400

>>6648136
V=IR is an approximation of an approximation. Ohm's law is actually Current density=Electric field*conductivity (J=E*s). If you take some logical steps from the current density formulation you end up with V=IR for things like circuits, so that is one of the approximations.

Now the J=E*s part is also an approximation. What Ohm's law is trying to describe is how charge carriers are moving around in something when an electric field is applied. A naive first guess would be to say if you apply a voltage across a wire the electrons would start accelerating because the electric field is applying a force and you could use F=ma. The problem is you'd get a current that depends on how long the voltage has been on- that's because current is charge per time and the guess was that the electrons are accelerating. This is also not what is observed experimentally in your run of the mill circuit! So the refined guess is to say the electrons are accelerating because of the electric field, but also decelerating because they bump into crap and have to stop (you've heard of drift velocity right?) which gives on average something that looks like the electrons have a constant velocity when a voltage is applied.

So from the above you can kind of tell that Ohm's law really isn't a law like Newton's laws. It isn't universal and it really isn't even from first principles unless you can establish that there must be a constant drift velocity, which is not going to be the case in superconductivity. In fact, if you're thinking about cooper pairs of electrons flowing down the wire then there is no chance that the electrons are going to bump into stuff and you're left with the first guess above that they keep accelerating

>>	Anonymous Thu Jul 17 00:25:02 2014 No.6649437 >>6649284 after defining the real exponential you do taylor series which gives you exp as a power series. then plugging in complex numbers nets you the complex exponential.

>>	Anonymous Thu Jul 17 02:30:25 2014 No.6649661 If I solved some equation that got me a result like <span class="math"> tan\theta = N_y / N_x+N_z [/spoiler] Can I always assume that <span class="math"> sin\theta = N_y cos\theta = (N_x+N_z) [/spoiler]

>>	Anonymous Thu Jul 17 02:31:52 2014 No.6649663 >>6649661 Sorry, let me write that a bit better if <span class="math"> tan \theta = Ny / (N_x+N_z) [/spoiler] then can i always assume: <span class="math"> sin \theta = N_y [/spoiler] and <span class="math"> cos \theta = (N_x + N_z) [/spoiler]

>>	Anonymous Thu Jul 17 06:06:31 2014 No.6649802 >>6649663 No, you can't. It's possible that Ny = ksin(theta) and Nx+Nz = kcos(theta), for example. Or Ny = sin(2theta) and Nx + Nz = 2cos(theta)^2

>>	Anonymous Thu Jul 17 06:12:44 2014 No.6649813 What is spin?

Anonymous Thu Jul 17 06:28:18 2014 No.6649825

>>6647440
If you want to really understand this question, read Power, Sex, Suicide by Nick Lane. One of the best pop sci books ever written I reckon, the only reason it's not ''proper science'' is because he makes guesses regarding stuff that's tough to falsify. Either way it answers your question perfectly.

Anonymous Thu Jul 17 08:17:32 2014 No.6649929

I've been playing with some intro logic and I've got a question that's been bugging me.

P, Q, R, S are sentences in a logic.
Let G={Q,R,S} be a set of sentences.
If P is Unsatisfiable/Truth Functionally False (always false)
and G is Unsatisfiable/Inconsistent (there is no interpretation/assignment in which all sentences in G are simultaneously true)
Then does G entail P?

Anonymous Thu Jul 17 15:24:04 2014 No.6650583

>>6649813
Spin is intrinsic angular momentum. So when a particle's angular momentum is measured at rest it will have an angular momentum equal to its spin. There is no classical analog to this, so anything trying to compare spin to something classical will fall short in some way (though the analogies are useful for understanding)

>>	Anonymous Thu Jul 17 15:51:03 2014 No.6650625 File: 68 KB, 500x375, tumblr_mo3cpi1DGf1rz1ki7o1_500.jpg [View same] [iqdb] [saucenao] [google] how does a particle get entangled with another particle?

>>	Anonymous Thu Jul 17 16:03:01 2014 No.6650646 G => P is invalid if G is false. b/c essential argument form is, since my premise is true so also must my conclusion be true.

Anonymous Thu Jul 17 16:22:46 2014 No.6650684

>>6649929

I would say yes. I've only dabbled in mathematical logic but if you have a set G in which all statements in G cannot be configured in such a way that all of the statements are simultaneously true, and you have a statement P that is always false, then G does imply P.

or perhaps g is equal to p.

because g can never be true either, assuming g is a statement that looks like

q and r and s

Anonymous Thu Jul 17 16:25:23 2014 No.6650686

>>6646576

Nobody gave you a sufficient answer:

Not all energy is 'usable' energy. You can never have 100% efficient conversion from heat to usable energy, but you can (always) have 100% conversion from usable energy to heat.

The conversion efficiency is proportional to the temperature difference involved in the system. A nuclear power plant at the hottest part of its cycle is roughly 600 F, and roughly 80F at the coolest part. It gets about 35% efficiency.

Your CPU is roughly 180 at its hottest, and roughly 80 at its coolest. Your efficiency would be complete and utter shit, and the effort you put into making the conversion would just be a massive waste of time.

Anonymous Thu Jul 17 16:31:10 2014 No.6650697

>>6646658
You're too dumb to be a doctor. Go find another field.

>>6646980
In special relativity, we have this idea that everything is /always/ moving at exactly the speed of light in space-time. From my reference point, I'm moving at the speed of light in the time direction and not moving at all in any other direction.

Photons don't 'experience' time, because they are moving at the speed of light in a spatial direction.

You'd be a photon.

>>	Anonymous Thu Jul 17 16:33:15 2014 No.6650701 What is the coolest word ending in -phyiscs? Words like metaphysics, astrophysics. Also what about -dynamics? What are some insanely cool scientific words in general

>>	Anonymous Thu Jul 17 16:38:43 2014 No.6650708 >>6650646 oh yeah. that makes sense. I forgot about the rules of implication.

>>	Anonymous Thu Jul 17 16:40:29 2014 No.6650710 I am >>6650708 >>6650684 are you sure? I thought it was only f --> t that was not implication. false can imply false though? right?

>>	Anonymous Thu Jul 17 16:43:01 2014 No.6650715 Is anything actually nothing?

>>	Anonymous Thu Jul 17 16:43:07 2014 No.6650716 >>6650710 fuck this is pathetic I forgot to reply to >>6650646

>>	Anonymous Thu Jul 17 16:50:38 2014 No.6650727 How is the main appropriation of science anything but the one, main problem exhibited by nature, the vigilance necessitated for parasitic-free association.

>>	Anonymous Thu Jul 17 16:50:45 2014 No.6650728 If I wanted to fistfight gravity should I be punching up or down?

Anonymous Thu Jul 17 17:58:14 2014 No.6650839

>>6650625
A simple way to have entanglement is a decay, e.g. a neutral pion decaying to two photons or to a positron and electron. The creation of pairs of particles is pretty much the go to way to create entangled systems.

The crux of the matter though, is that at some time you've lost track of the particles and that there is some conservation that needs to be observed. So imagine that you've got two photons, one in your bedroom and the other one in the kitchen and you're keeping track of them by constantly measuring that they are in their respective room. Then you go have a smoke outside and accidentally left a door between the two rooms open so the photons could travel between them. Entanglement comes in when there is some reason that each of the rooms can only hold one photon, so when you come back and measure that there is a photon in the kitchen you know that the other photon is in the bedroom. It is tied closely to how identical particles interact so make sure you know that as a base.

The best examples to follow are probably what actually happens instead of that blurb I wrote above. So with pion->electron and positron, the two particles are entangled after the decay because they behave identically until some measurement is made, so before that measurement you'd say that particle A and B each have a 50-50 chance of being an electron or positron and that there is one electron and one positron in the whole system. The system disentangles once you measure something unique about them (like their charge), so if you measure a negative charge on A then you know that B has a positive charge and the two are no longer entangled (and if you were to write out the probabilities now, A has a 100% chance of being an electron 0% chance of being a positron and vice versa for B).

Anonymous Thu Jul 17 18:29:33 2014 No.6650863

so do we know why photons change their behaviour when you observe them

what happens if you do the double slit experiment without observing it while it's conducted, but observe it from 5 light minutes away 5 minutes later while it's being "conducted"
yeah I know seeing atoms from 5 light minutes away is practically impossible

>>	Anonymous Thu Jul 17 18:41:28 2014 No.6650871 >>6650701 Not exactly science or what you're looking for but I like a lot of the names for parametric and polar curves. Two I remember were the "Swallowtail Catastrophe Curves" and the "Witch of Maria Agnesi".

>>	Anonymous Thu Jul 17 18:44:04 2014 No.6650874 >>6646658 nobody will blink an eye at a B in calc 2.

>>	Anonymous Thu Jul 17 18:45:54 2014 No.6650877 >>6650686 can i get a link to how you are getting those numbers?

>>	Anonymous Thu Jul 17 21:31:46 2014 No.6651162 File: 47 KB, 647x409, sdf.png [View same] [iqdb] [saucenao] [google] Hi /sci/ I used Wolfram Alpha to try and find the local extrema of a function. However, I don't know how to interpret the output. What are c1 and c2 supposed to be?

>>	Anonymous Thu Jul 17 21:38:17 2014 No.6651174 >>6651162 What did you input?

>>	Anonymous Thu Jul 17 21:39:38 2014 No.6651178 File: 637 KB, 2875x2106, 1373897531237.jpg [View same] [iqdb] [saucenao] [google] Why is normalization of data important?

Anonymous Thu Jul 17 21:44:03 2014 No.6651184

How can I find how fast a human can run if they exert a certain amount of ground force?

For example, I do know that Usain Bolt can push with nearly 453 kg and can run close to 45 km/h.

So how would I go about finding how fast somebody would be if they could for some reason push with twice the amount of force.

Anonymous Thu Jul 17 21:48:20 2014 No.6651191

>>6651174
Basically I want to find the extrema of this function:

A*cos(x)*sin(y) + B*sin(x)*sin(y) + C*cos(x)
[/spoiler]

Where A, B and C are constants. For simplicity I input the following in alpha:

0.577*cos(x)*sin(y) + 0.577*sin(x)*sin(y) + 0.577*cos(x)
[/spoiler]

Anonymous Thu Jul 17 22:00:05 2014 No.6651200

>>6651178
You mean in databases?
If so, normalization allows for minimum redundancy, data independence and simpler SQL queries. Minimum redundancy saves search time and hard disk space. Data independence makes it easier to modify the already existing data. Simpler SQL queries means less bugs, faster query time and more readable code.

Anonymous Thu Jul 17 22:08:36 2014 No.6651209

>>6650728
>If I wanted to fistfight gravity should I be punching up or down?
You should be punching yourself in the head.

>>6650715
>Is anything actually nothing?
If you define it that way, then yes.

>>6650625
>how does a particle get entangled with another particle?
By interacting with it, that's also how it is "destroyed". In a way entanglement and supper position never end. The function is just a minimum when you make a measurement. But after that the particle is entangled with your apparatus.

>>6649813
>What is spin?
A fundamental quantum property. There is no real answer to it. It just describes a property of a particle. Spin has no classical analogue.

>>	Anonymous Thu Jul 17 22:09:48 2014 No.6651213 how do I triforce?

Anonymous Thu Jul 17 22:15:33 2014 No.6651216

>>6649219
>Is there a limit to how intelligent a human can be?
Like any hardware machine the human brain has it's limitations. It's just that no one can give you the right answers yet.

>Is using one's cognitive abilities while sleep deprived similar to exercising the same muscle multiple days in a row?
No, because when you exercise your muscle cells get torn apart, this in turn stimulates the generative process and the muscle buildup. So far there has not been any evidence for such a process in the brain. Prolonged sleep deprivation is correlated with psychiatric illnesses.

>Have average neuro-typical human beings evolved to work for leaders?
Yes and no. Humans have evolved so that they can follow and be followed. If there was just one central figure in a society, it would be a weakness for all of them.

>>	Anonymous Thu Jul 17 22:20:26 2014 No.6651223 >>6651213 >how do I triforce? You use the space character from another character set to crate the indentation.

>>	Anonymous Thu Jul 17 22:29:31 2014 No.6651237 >>6650701 Cryophysics

>>	Anonymous Thu Jul 17 22:32:43 2014 No.6651241 >>6646480 Does there exist any free statistics packages that are functionally similar to Minitab?

>>	Anonymous Thu Jul 17 22:34:31 2014 No.6651242 >>6651241 >Minitab Open Office R Octave

Anonymous Thu Jul 17 22:39:54 2014 No.6651251

>>6651191
To find extrema (maxima and minima) W.A. is essentially taking the derivative and setting it equal to zero then solving for the values that work, which is what you should be doing by hand. You've got a kind of bastardy function because it is in x and y, so you need to take the gradient of the function and set it to zero to get the extrema.

I am also pretty drunk right now.

Anyway, the n1 and n2 in your output are because you're using trig and it is going to repeat over and over again (imagine the curves, they will repeat without a doubt, so the extrema will repeat without a doubt). That is why W.A. gives you that answer.

>>	Anonymous Thu Jul 17 22:52:57 2014 No.6651262 >>6651241 >>6651242 R, choose R. It's a complete language that is growing extremely rapidly

>>	Anonymous Thu Jul 17 22:59:21 2014 No.6651271 >>6651242 Never used Octave, but I use Matlab everyday. Is it worth learning if I have access to Matlab? Is there anything particular it does better than Matlab?

>>	Anonymous Thu Jul 17 23:04:21 2014 No.6651282 >>6651271 Essentially it is better at being free than matlab

>>	Anonymous Thu Jul 17 23:04:37 2014 No.6651283 >>6651271 well for one, it's open source, so by using it (despite having access to R) you'd be supporting the growth of the open source community

>>	dude PhD Thu Jul 17 23:13:44 2014 No.6651293 >>6651282 LOL >>6651283 Right - I use R and Matlab; not sure I'd gain anything but I do like the idea of not paying to use it every year. Can octave run ANY matlab program/wrapper/integration?

Anonymous Thu Jul 17 23:25:33 2014 No.6651304

>>6651293
I am pretty sure the whole premise of octave is that it will run any matlab script, and that the number one priority is staying on top of matlab's updates. One of the problems through is that it doesn't have the exact same syntax as matlab and octave will run more things, so if you translate octave code to matlab it might not work (but then again, who cares, because anyone can run octave). If you are paying out of pocket/your program's expenses to use matlab then switch to octave, since you'll get the full functionality for free- the only problem would be checking to make sure everything runs correctly. I am also >>6651282 if it will give you a second chuckle.

Anonymous Fri Jul 18 01:12:52 2014 No.6651409

>>6646480
I hear all the time that light is a 'wave', also I've seen diagrams of polarization in which photons move 'up' and 'down' in addition to forward. Do photons actually behave like that? If so, how do they know when to turn around (at the bottom/top)?

>>	Anonymous Fri Jul 18 01:14:21 2014 No.6651410 >>6647460 Even distribution doesn't mean it's a normal number, 0.123456789012345678901234567890 etc.,

>>	Anonymous Fri Jul 18 01:17:12 2014 No.6651411 >>6651410 but that number isn't irrational. > Even distribution doesn't mean it's a normal number doesn't it?

Anonymous Fri Jul 18 01:17:59 2014 No.6651414

>>6651409
Not op, but it might help to think of light waves in the same way sound waves occur. Certain frequencies (oscillatory periods) produce certain pitches. The photon doesn't know anything; it behaves in oscillation because it is a photon. If it did not oscillate at the frequency of light, it would not be light.

>>	Anonymous Fri Jul 18 01:23:04 2014 No.6651420 >>6651414 So there is no (easy to understand) reason photons behave like that, it's just a rule that they do?

Anonymous Fri Jul 18 01:33:43 2014 No.6651434

>>6651420
There isn't going to be an easy to understand reason because photons are how you think of light as particles and EM waves are how you think of light as a wave. Classically you can't reconcile the two, which is what makes quantum mechanics quantum mechanics. The diagrams with photons moving up and down to express their polarization are also bogus, the photon just moves in a straight line (think, what would even make it move up and down if it were a particle- there would need to be some kind of oscillating force that the photon exerts on itself, it just doesn't make sense).

>>	Anonymous Fri Jul 18 04:41:34 2014 No.6651597 Is there an intuitive explanation for momentum? let alone moment of inertia?

Anonymous Fri Jul 18 05:59:07 2014 No.6651657

As you move closer to the speed of light why would you age slower? I haven't looked much beyond your run of the mill program, but assuming the twin paradox, both are always existing at the same time no? Only the view of the other person would slow down.

am I just stupid?

>>	Anonymous Fri Jul 18 06:01:12 2014 No.6651661 >>6651597 > momentum how hard it is to stop something > moment of inertia how hard it is to rotate something

Anonymous Fri Jul 18 10:59:15 2014 No.6651949

>>6651216
>No, because when you exercise your muscle cells get torn apart, this in turn stimulates the generative process and the muscle buildup. So far there has not been any evidence for such a process in the brain. Prolonged sleep deprivation is correlated with psychiatric illnesses.

Recent studies have shown that neural waste is created by the brains activity during wakefulness and is 'cleaned out' during sleep.

>>	Anonymous Fri Jul 18 11:01:35 2014 No.6651952 If I just want to study chemistry in order to help produce new chemicals and drugs, should I stay away? Should I focus on physics (my second option) instead?

>>	Anonymous Fri Jul 18 11:02:30 2014 No.6651953 >>6651952 Just practice making chemicals and drugs in your free time. Then use the profit to pay for more degrees.

>>	Anonymous Fri Jul 18 11:11:12 2014 No.6651961 File: 7 KB, 245x300, thXYS3XJRG.jpg [View same] [iqdb] [saucenao] [google] Are there any educational videos including a variety of academic subjects with sexually attractive and sexually suggestive females teaching the subjects?

>>	Anonymous Fri Jul 18 11:16:32 2014 No.6651968 >>6651961 Search "Theoretical minimum" from Susskind.

>>	Anonymous Fri Jul 18 11:34:23 2014 No.6651993 >>6651968 Was information on Leonard Susskind what you intended for me to find?

>>	Anonymous Fri Jul 18 12:57:27 2014 No.6652091 >>6651657 From the perspective of an outsider moving at a lesser speed you would age slower.

>>	Anonymous Fri Jul 18 14:10:55 2014 No.6652162 I want to solve puzzles of minds and human interactions. I want to solve psychological puzzles. where would I find these puzzles online? I'd like the puzzles to be like murder mystery games but without the murder mystery. Would you please help me?

Anonymous Fri Jul 18 14:34:30 2014 No.6652191

House and Holmes: A Guid to Deductive Reasoning:
"Deductive argument: an argument whose premises make its conclusion certain
Inductive argument: an argument whose premises make its conclusion likely"

Is
Deductive reasoning = general information used to form specific conclusions
and
Inductive reasoning = specific information used to form general conclusions
false and "outdated" as stated by House and Holmes?

>>	Anonymous Fri Jul 18 14:45:03 2014 No.6652198 >>6652091 thats what it was

>>	Anonymous Fri Jul 18 14:52:55 2014 No.6652206 >>6646480 How do I solve this? <span class="math"> \int x^{x}dx [/spoiler]

>>	Anonymous Fri Jul 18 15:37:02 2014 No.6652254 How do you prove that <div class="math"> \displaystyle \left(a + b\right)\left(c + d\right) = a\left(c + d\right) + b\left(c + d\right) </div> ?

Anonymous Fri Jul 18 15:52:25 2014 No.6652281

>>6647009
Science is an means to obtain knowledge.
Knowledge can be used to save the world.
Therefore, science can save the world.
If a, then b, if b, then c
Anybody want to check my work?

Maybe we have to force knowledge into the minds of the masses...

>>	Anonymous Fri Jul 18 16:02:11 2014 No.6652297 >>6646480 Is it possible to use Thermite to collapse buildings? How much would you need?

Anonymous Fri Jul 18 16:07:06 2014 No.6652313

>>6652297
To collapse a building one would need to make the structure unable to keep itself from collapsing. One could add weight to the structure or alter the structure.
You can alter the structure with thermite, so, yes.
I don't know how much you would need.
It depends on the size of the building.
You can have some fun building scale models of the building in mind and experiment on that then calculate how much you'd need.

>>	Anonymous Fri Jul 18 16:08:41 2014 No.6652315 >>6652313 Well, I think you can alter the structure of most buildings with thermite.

>>	Anonymous Fri Jul 18 16:11:31 2014 No.6652321 Is there any research on increasing penis size without surgery? >inb4 size doesn't matter >inb4 just be confident >inb4 kill yourself

>>	Anonymous Fri Jul 18 16:15:41 2014 No.6652325 >>6652321 Some BBC documentary suggested that certain creams, that penis extender thing, and certain 'penile exercises' can increase penis size. I' skeptical about it's validity.

>>	Anonymous Fri Jul 18 16:27:02 2014 No.6652349 >>6652321 >inb4 size doesn't matter >inb4 just be confident >inb4 kill yourself Exactly.

>>	Anonymous Fri Jul 18 17:24:06 2014 No.6652449 File: 3 KB, 640x480, .png [View same] [iqdb] [saucenao] [google] >>6652254 whole = top half + bottom half

>>	Anonymous Fri Jul 18 17:27:50 2014 No.6652453 >>6652449 Is it possible to prove without a geometric argument? I tried googling but I'm not sure how to phrase it as "proof of distributive property" only brings up pages related to a(b + c) = ab + ac.

>>	Anonymous Fri Jul 18 17:55:09 2014 No.6652487 >>6652254 (a+b)(c+d) = ac+ad + bc+bd = a(c+d) + b(c+d)

Anonymous Fri Jul 18 19:22:59 2014 No.6652605

>>6652191

Deductive reasoning: You take your premises/facts and bring them to their logical conclusion. This is like regular algebra, e.g. a+b=1 and a-b=-1 then you can solve for a and b using deductive reasoning.

Inductive reasoning works differently. A loose every day example is that every cat you've ever seen has whiskers, so if you find something without whiskers it isn't a cat. Another example is that the sun rose in the east this morning, yesterday morning, and every morning before that so by inductive reasoning it will rise in the east tomorrow morning. These 'everyday' examples using induction are not actually logically sound, unlike a mathematical proof that uses induction.

For mathematical proofs, you need to establish a few things. First there is the "base case" that must be true, and then the inductive step. So if you want to prove that the sum of 0 to n is equal to n(n+1)/2 using induction first you show that it works for n=0 (the base case) and then you show that it works for n=k+1. The algebra ends up working for 0 [0=0*(0+1)/2], and importantly you need to use the base case for the sum up to k, so the sum is: k(k+1)/2+(k+1)=(k+1)(k+2)/2 [see how the first time uses the result we are trying to prove for k?]. Then it is simple to check whether or not that last equation is true or false (it's true, so we've got a full fledged proof). Mathematical proof by induction IS logically sound, but note the importance of establishing a base case- if the base case isn't true then there is no way for the proof to be sound because each successive number depends on the previous number being correct.

>>	Anonymous Fri Jul 18 20:35:52 2014 No.6652706 >>6652605 Okay, thanks.

>>	Anonymous Fri Jul 18 20:52:07 2014 No.6652721 How come the zeta function is zero for negative even integers?

>>	Anonymous Fri Jul 18 21:17:57 2014 No.6652745 >>6652721 https://en.wikipedia.org/wiki/Riemann_zeta_function#Specific_values

>>	Anonymous Fri Jul 18 22:19:29 2014 No.6652824 >>6652453 Look up the Peano axioms and successor function you'd have to start there

>>	Anonymous Fri Jul 18 22:25:59 2014 No.6652834 >>6651184 Can anybody help me with this?

>>	Anonymous Fri Jul 18 22:28:47 2014 No.6652838 >>6652453 proof wiki is nice. https://proofwiki.org/wiki/Natural_Number_Multiplication_Distributes_over_Addition

Anonymous Fri Jul 18 22:43:58 2014 No.6652857

>>6646480
I just read the first introductory chapter of "The Mind & The Brain Neuroplasticity and the Power of Mental Force" by Jeffery M. Schwartz, M.D., and Sharon Begley.
I'm worried that it might be a little outdated.
By reading this book, will I constantly be bombarded with false information or is it relatively sound?

>>	Anonymous Sat Jul 19 03:47:06 2014 No.6653211 File: 5 KB, 220x110, Sine_wavelength.svg.png [View same] [iqdb] [saucenao] [google] Do waves of light with lower wavelengths take longer to get from point A to point B, since it has more rapid 'ups' and 'downs' and the speed of a photon is constant?

>>	Anonymous Sat Jul 19 09:11:08 2014 No.6653447 File: 801 KB, 1116x1100, 1405774785196.png [View same] [iqdb] [saucenao] [google] Why 12 attoseconds? Why not 10? God, I hate number that aren't base 5 or 10.

>>	Anonymous Sat Jul 19 09:40:22 2014 No.6653472 >>6653447 because 5.39106(32) × 10^−44 sesonds

Anonymous Sat Jul 19 09:59:25 2014 No.6653498
File: 71 KB, 463x564, 1371805240698.jpg [View same] [iqdb] [saucenao] [google]

How do I find out the pure imaginary number of a complex number in the trigonometric form?
Like for example, I have to discover the values of an angle which is between [0,pi[, after I'm done and discover the full complex, I was told I had to equal the cis (angle) to " pi/2 + kpi " and discover the value. But why? Is that the way the discover the pure imaginary in the trigonometric form?

>>	Anonymous Sat Jul 19 11:26:06 2014 No.6653567 >>6653498 Nevermind, after some thought I understood.

>>	Anonymous Sat Jul 19 11:30:30 2014 No.6653579 >>6653447 http://en.wikipedia.org/wiki/Planck_time

>>	Anonymous Sat Jul 19 11:46:09 2014 No.6653599 >>6653472 >>6653579 1.2 * 10^-17 = 5.4 * 10^-44?

KenDrun Sat Jul 19 12:07:59 2014 No.6653628

>>6653447
>>6653472
>>6653579
>>6653599
The 12 attosecond thing just comes from the best measurements ever made. Article is here http://phys.org/news192909576.html .

If that blurb were written in like 1930 and the best measurements possible were from quartz crystals vibrating at 2^15 HZ, then the 30 microseconds would be the shortest measured period of time. The blurb is shitty because they used measurable instead of measured.

As far as we know time is continuous so an experiment can measure any length of time, it is just a question of equipment. Planck time would be the smallest possible time to measure, but as far as I know it would be the smallest time measurable because of other factors, not the nature of time. So for example if you used a simple t=d/v using a photon going at c, the precision of your time measurement is dictated by the precision of your distance measurement, and the most precise distance you could ever measure would be 1 Planck length. So the max precision of time measurements has nothing to do with how time behaves, and has everything to do with how other things are quantized.

Anonymous Sat Jul 19 12:45:38 2014 No.6653669
File: 26 KB, 459x271, black hole.jpg [View same] [iqdb] [saucenao] [google]

Can gravity slingshot an object in the completely opposite direction?
And if it's possible, can black holes slingshot photons in the completely opposite direction, thus making it a "mirror"?

Anonymous Sat Jul 19 13:27:18 2014 No.6653715

>>6646480
Is it possible to run an optimization algorithm in MATLAB (for example) where I state as a restriction that one of the variables is contained in a region [a,b] U [c,d] ? Some people that are helping me with this problem say it's only possible in a single region [a,b]. Mind you, I know very little about optimization. If it's possible, can you point me to something useful for me to read about it?

>>	KenDrun Sat Jul 19 13:50:41 2014 No.6653744 >>6653715 If you can optimize for a region [a,b] then why not just do it twice e.g. optimize over [a,b] and optimize over [c,d] then compare? Wouldn't that be exactly what you are trying to do in one command?

Anonymous Sat Jul 19 13:57:55 2014 No.6653753

>>6653744
The objective function describes the functioning of a pump/turbine system, and the variable I want restricted in a joined interval is the water level variation, so when the said variable is positive the pump is working and when it's negative the turbine is working. As so I need both of them included in the "system" at the same time. I'm sorry if this is not clear enough, I'm trying to say as much possible without making this too long

Anonymous Sat Jul 19 15:18:15 2014 No.6653851

>>6646480
why are the outer sections of Earth's atmosphere charged electrically, and why is it always charged with one polarity with respect to ground?

if the solar wind is neutral overall (excluding small pockets of a particular species of ion) and there is no current flowing between the sun and the rest of the galaxy, how is the Earth's ionosphere charged?

>>	Anonymous Sat Jul 19 15:20:04 2014 No.6653856 File: 59 KB, 865x489, princess bubble gum - scissors 7.jpg [View same] [iqdb] [saucenao] [google] >>6646480 What is the interacting mechanisms thing in this video called? http://www.youtube.com/watch?v=57UknNloFWo

>>	Anonymous Sat Jul 19 15:27:36 2014 No.6653872 >>6653856 https://en.wikipedia.org/wiki/Rube_Goldberg_Machine

>>	Anonymous Sat Jul 19 18:17:07 2014 No.6654120 >>6653872 Thanks.

>>	Anonymous Sat Jul 19 20:33:59 2014 No.6654387 >>6650874 Sure they will, because 100 other students got that A and had tons of volunteer experience and yada yada.

>>	Anonymous Sat Jul 19 20:35:57 2014 No.6654391 >>6650701 I think a lot of medical terminology is cool, but that's just me. Pyrexia = fever.

>>	Anonymous Sat Jul 19 20:39:03 2014 No.6654395 I'm having trouble proving set relations and equalities using logic operators. I guess i just need to work more.

>>	Anonymous Sat Jul 19 20:46:44 2014 No.6654413 >>6648359 Mathematica?

Anonymous Sat Jul 19 20:50:34 2014 No.6654421
File: 6 KB, 200x200, 1401865256741.jpg [View same] [iqdb] [saucenao] [google]

This isn't homework but rather personal planning...

I got a major university scholarship that is contingent upon me getting at least a 3.25 GPA. I tried setting up and solving a system that allows me to figure out how many hours I would need to make an A in and how many hours I would need to make a B in order to maintain that GPA, under the assumption that I would make As and Bs. I have to take 30 hours per year as a requirement.

I know that: \displaystyle GPA = \frac{Quality \, Points}{credit \, hours \, attempted}[/spoiler]

Assuming that an A is worth 4 points and a B is worth 3 points, I could say that quality points will be equal to 4x +3y[/spoiler]. So,

<div class="math">3.25 = \frac{4x + 3y}{30} \;\; \Rightarrow \;\; 4x + 3y = 30(3.25) \:\: \Rightarrow \;\; 4x + 3y = 97.5</div>

Thus, I set up the following system where x[/spoiler] denotes the number of hours in As I must make and y[/spoiler] denotes the number of hours in Bs I must make.

x + y = 30[/spoiler]
4x + 3y = 97.5[/spoiler]

Solving this system yields a value of x = 7.5[/spoiler] and y = 22.5[/spoiler].

My main question is did I even make this type of calculation correctly? From an analytical standpoint, what do my results imply? To be safe, I suppose I should round down the value for a B and round up the value of an A. Does this mean that regardless of how many classes I take, I only need 8 of my hours to be As and 22 of my hours to be Bs? That seems like a lot of Bs but I guess my results make sense since Bs are what will mainly drag my GPA down to a 3 and those As are gonna try to push my GPA up just a marginal amount.

>>	Anonymous Sat Jul 19 20:58:53 2014 No.6654429 I'm a highschool student going into my senior year. I wish to pursue a career in forensic science. WHat should I do once I graduate?

>>	Anonymous Sat Jul 19 21:02:06 2014 No.6654434 I'm an anon on /sci/. I want for there to be interesting and informative threads here. WHat should I do to encourage this?

>>	Anonymous Sat Jul 19 21:13:18 2014 No.6654448 >>6654429 What do you like about forensic science? Want to be in the FBI?

Anonymous Sat Jul 19 21:22:00 2014 No.6654463

>>6654448
I find bio chemistry and crime scene analysis to be pretty fascinating. Something about applied science and detective work seems to just capture my imagination.

My best case scenario would be to join the FBI for a period of time and then eventually earn enough money to be able to go to college for eight years to study neuroscience and neuro-chemistry.

I can't really say that I've wholly researched far into either of these fields.

Is this a smart pursuit on my behalf? Is there any decent job opportunities in forensics work?

KenDrun Sat Jul 19 22:41:52 2014 No.6654568

>>6654421
First thing, the equation you wrote out has you taking exactly 30 credits. So what it is saying is if you take 30 credits, to meet your credits you need 8 credits of As and 22 credits of Bs to get just above a 3.25 (not even thinking about A- and B+ because I don't know how they work for you).

Instead it would be better to just think about it as a ratio, you need 1/3 of your classes to be As and 2/3s to be Bs for you to get a 3.25. This is easy to reason out in your head, but you could also use your results by doing 7.5/22.5 (or solving for credit hours =1 instead of 30).

Anonymous Sat Jul 19 22:46:45 2014 No.6654572

>>6654463
Sure.
But only if you have any real impressions into the job other than TV.

Depending on the exact job you will be cleaning up shit, spreading dust on shit, scanning pictures, sending stuff to a different lab, blabla and the most exciting thing is telling a jury that this is science and then having a lawyer rip you a new asshole because there is always a margin for error or because of something you had nothing to do with. If you get lucky.

But it's a paycheck.

>>	Anonymous Sat Jul 19 22:53:31 2014 No.6654582 >>6654572 Is it a very time consuming job? WIll I be able to still go to school to study neuroscience, or should I just start that pursuit once I get out of high school?

Anonymous Sat Jul 19 23:05:59 2014 No.6654589

>>6654582
No fucking clue.
But getting a proper degree in the field that includes your impulse interest is always a based idea.
If you need money, try getting a job at the university. Or part time at a company that deals with your field. Doesn't even matter if you were a fucking secretary.

You might also want to consider moving abroad. I honestly don't understand why Americans aren't flooding into Europe.
Good universities, they cost little to nothing, looks amazing on your CV, immigration is easy as fuck, it's a fun experience, easier to get a job here, etc.

Some people seem to think that it is di

>>	Anonymous Sat Jul 19 23:06:15 2014 No.6654590 >>6654568 I've checked. Apparently there's no such thing as <span class="math">\pm[/spoiler] at my university, so I won't have to worry about that. I just have to worry about getting either a flat A or a flat B

>>	Anonymous Sat Jul 19 23:11:38 2014 No.6654599 >>6654589 Thanks anon, I'll consider it.

>>	Anonymous Sat Jul 19 23:13:43 2014 No.6654600 >>6654599 Oh, apparently your High School diplomas don't cut it for our universities. But you seem to have that IB thing, that qualifies you if you pick the right classes. Go see a counselor about that.

Anonymous Sat Jul 19 23:24:49 2014 No.6654610

I'm starting an electronic engineering technology course at a local CC and in about 2 years I plan to transfer to a uni for a full BS in EE. I figured I probably wouldn't be able to get internships for an electrical technician job until around year 1.5 however a friend who has a degree in Aerospace engineering and who interned at Sikorsky for awhile assures me that I should start applying now in spite of the fact that I have 0 experience with EE since companies love to hire people fresh. I don't know if this is for financial reasons, or if it's a way to better mold you to become a long-term employee for the company. Either way should I take his advice and apply for internships in spite of the fact that I have no experience? If so what's the best way to go about it?

A bit about me:
I've been doing fast food for the last 3 years and I hate it, I want out. My HS GPA was 3.4 but I did bad in college. It's up to a 2.0 now and I've been doing better the last couple of semesters, if all goes well I expect to be back above 3.0 within a year. I make about 10k/yr and spend about 2k/yr on school. I have no financial aid. I've completed math through diff eq. but no engineering courses. My full scale IQ is ~108.

Anonymous Sat Jul 19 23:58:42 2014 No.6654640

>>6647101
It's not that certain things have matter and other things don't, there is really no such thing as "matter". Particles are described as having some arbitrary value of "matter", but in the end particles, waves, and fields are all just the same things with different mathematical representations.

>>	Anonymous Sun Jul 20 01:17:19 2014 No.6654682 What is the probability of losing 2 family members on MH370 and 2 more on MH17? http://www.independent.co.uk/news/world/europe/malaysia-airlines-family-who-lost-two-members-on-flight-mh370-have-lost-two-more-on-mh17-9614230.html

>>	Anonymous Sun Jul 20 03:12:12 2014 No.6654769 >>6646480 Why is a raven like a writing desk?

>>	Anonymous Sun Jul 20 03:25:00 2014 No.6654776 >>6654769 Because there's a b in both and an n in neither.

Anonymous Sun Jul 20 03:36:59 2014 No.6654785
File: 49 KB, 790x433, bull.png [View same] [iqdb] [saucenao] [google]

When graphing the spectral distribution for a blackbody you get something like pic related, they are using arbitrary units for intensity, how are you supposed to interpret and measure arbitrary units?

Anonymous Sun Jul 20 04:25:35 2014 No.6654816

>>6654785
if you were actually measuring something it wouldnt be arbitrary. They say arbitrary because all they can show you in a generalised way is the shape. Like if you have two different sources with different intensities they would follow the same graph shape, but the size etc would vary

>>	Anonymous Sun Jul 20 04:57:37 2014 No.6654839 >>6653669 I'm not 100% sure that a perfect slingshot of a photon would be possible, but if it is, then the trajectory required by the photons would be so marginal that any use as a mirror would be unachievable.

Anonymous Sun Jul 20 05:06:57 2014 No.6654851

>>6650686
It's basic thermodynamics
<div class="math"> \eta = 1 - \frac{T_{cold}}{T_{hot}} <div class="math">

>>6646572
On a side note, I always wondered why we wouldn't use the heat generated by every electronic devices in one's home to heat water through a house-wide water-cooling system.</div></div>

Anonymous Sun Jul 20 05:19:39 2014 No.6654858

>>6651410
Yes it does, it's the definition
However, a number being normal doesn't mean you'll find Shakespeare work in it, that's the definition of an universe number.
0.1234567891011121314... is a universe number (for obvious reasons) but is not normal IIRC

I wonder how much we'd have to look into Pi to find a valid ASCII text.

>>	Anonymous Sun Jul 20 05:26:31 2014 No.6654861 >>6648359 If matlab is too low for what you're doing, you'd better write your own C program. Be careful though, if you want very large numbers, you might have to use mallocs and memsets.

>>	Anonymous Sun Jul 20 05:28:03 2014 No.6654862 >>6648346 >treating someone of retarded on a stupid questions thread

Anonymous Sun Jul 20 05:33:12 2014 No.6654863

>>6649181
>does P = NP?
I guess not, if P=NP I'd wager that nature would have given our brains such algorithms to solve problems, but instead of this it chose complex data structures (neuron networks) and analog processing (neuron integration).

This idea just popped out in my mind, feel free to shit on it.

>>	Anonymous Sun Jul 20 05:39:15 2014 No.6654866 >>6648359 fortran preferably. or C or something like that if you cant program then use it as a learning exercise

>>	Anonymous Sun Jul 20 06:13:05 2014 No.6654883 >>6654851 On a side note I always wondered why we wouldn't use the heat generated by every electronic devices in one's home to heat water through a house−wide water−cooling system

>>	Anonymous Sun Jul 20 06:39:30 2014 No.6654899 What are the axioms one has to accept before one knows anything ? Do these specific axioms have a special name ?

>>	Anonymous Sun Jul 20 06:47:01 2014 No.6654902 >>6654899 There's the ZFC axioms for mathematics. But I think you're talking about logic axioms, I know there are a few, but I can't tell what they are. A quick search on wikipedia will do the job.

>>	Anonymous Sun Jul 20 06:49:52 2014 No.6654907 >>6654902 these threads wouldn't exist if people were efficient at googling information.

>>	Anonymous Sun Jul 20 07:04:36 2014 No.6654912 File: 824 KB, 180x135, a10able.gif [View same] [iqdb] [saucenao] [google] Should I get a cheap 2DS or a 3DS XL? I just want to be able to play a few nintendo games, nothing fancy.

>>	Anonymous Sun Jul 20 07:06:13 2014 No.6654915 >>6654907 To be fair, when you google question like this, you often find forums where someone asked the same question than you.

>>	Anonymous Sun Jul 20 07:44:08 2014 No.6654930 If hydrogen is highly flammable and oxygen is an essential part of fire then why isn't water flammable?

>>	Anonymous Sun Jul 20 07:57:23 2014 No.6654939 >>6654930 Because water is the result of dihydrogen combustion. <span class="math"> 2 H_2 + O_2 \rightarrow 2 H_2 O[/spoiler]

>>	Anonymous Sun Jul 20 07:58:54 2014 No.6654940 >>6654930 The Oxygen and Hydrogen atoms share their electrons, filling up each other's outer shells, making the molecule stable.

>>	Anonymous Sun Jul 20 08:11:24 2014 No.6654946 >>6654912 Get the XL. It's definitely worth it - more comfortable and the screens are so much better.

>>	Anonymous Sun Jul 20 09:31:34 2014 No.6655041 >>6647825 photonic crystals allow for exactly this. Its not trivial though, very difficult

>>	Anonymous Sun Jul 20 09:37:43 2014 No.6655054 >>6651952 wha? no! do chemistry, focus on organic and medicinal chem, and be prepared to feel pain. If you're good at it you'll be set, working for research and pharmacologists. If you're shit, well, there's always bikers and cartels.

Anonymous Sun Jul 20 09:42:41 2014 No.6655068

>>6646480

I am pleasantly surprised that /sci/ is allowing stupid threads now. When did this happen?

>>6653669

Theoretically yes but you just as likely to curve a different photon coming in from a different angle so it would be hard to tell which was which.

>>6654434

Research a topic a few hours instead of just blogging right away. Create a unique way to entertain other anons with knowledge. Example: Design a Jeapordy game for /sci/ topics.

>>6654915

It would help if a larger % of people were able to discuss these questions. When I went through college all my first year classes were answered on Google somewhere, most of my second, a few of my third year, and almost none of my final year.

Anonymous Sun Jul 20 09:57:11 2014 No.6655090

>>6646480
IQ is based on age, correct?
Presuming that the IQ tests are an accurate measurement of intelligence, if an 8 year old with an IQ of 100 were to be tested as if he were 25, would that 8 year old score lower than 100?
If so, how would I calculate this?
If the 8 year old scored 300 on the IQ test as if he were 25, what would his IQ as an 8 year old be?

>>	Anonymous Sun Jul 20 10:38:54 2014 No.6655122 How can I calculate the minimum turning radius of a car in relation to the maximum steering angle and it's length? Assuming front steering and not 4wd

>>	Anonymous Sun Jul 20 10:43:25 2014 No.6655128 >>6655090 There are many different IQ tests, all scored differently.

>>	Anonymous Sun Jul 20 10:58:13 2014 No.6655146 >>6655090 There are different IQ tests with different scoring systems. But generally they are built on age-specific bell curves.

>>	Anonymous Sun Jul 20 12:02:12 2014 No.6655206 >>6655128 >>6655146 Assuming that the 8 year old took the same IQ test and that practice does not affect one's score.

Anonymous Sun Jul 20 13:08:01 2014 No.6655299

>>6655206
Again, it depends on the test.
The formula normally used is:
>IQ = 100 + 15*(x-M/s)
>x = indiv. Score
>M = emp. mean of age group
>s = emp. standard deviation of age group

It's difficult to directly transform IQ to a different age, since the development is not linear.
But what you could do is simply use the same test and then calculate two IQs, using the variables of both age groups. (Assuming that you know them for the 8yo age group.)
Isn't exactly practical though. You would have to devise a test that can score an 8yo accurately, have enough items to score a 25yo satisfactorily and still have some way of testing that doesn't bend the score by exhausting the child.

And as some might notice: IQ isn't exactly the best indicator for intelligence.
I prefer models based on factor analysis, including as many different items as possible.
That way you can get some neat hierarchies explaining contributing factors and sub-factors or cubical grids with up to almost 200 factors of intelligence.

>>	Anonymous Sun Jul 20 14:27:51 2014 No.6655443 why do i luv memes so mcuh

>>	Anonymous Sun Jul 20 14:45:06 2014 No.6655462 >>6655443 >why do i luv memes so mcuh Because they give you a feeling of belonging to an in-group, that you are most likely lacking in "real life."

>>	Anonymous Sun Jul 20 14:53:17 2014 No.6655469 >>6655462 I agree with this.

>>	Anonymous Sun Jul 20 15:01:36 2014 No.6655480 >>6655299 This helps. Do you have information on some models based on factor analysis or some guidelines on how to create some?

>>	Anonymous Sun Jul 20 15:13:06 2014 No.6655487 >>6655480 Read up on Spearman, Thurstone, Vernon, Cattell (and Horn's version of it), Guilford, BI model of Jäger. Especially Spearman (who was also a mathematician) and Guilford and the BI model are interesting.

>>	Anonymous Sun Jul 20 15:17:12 2014 No.6655490 >>6651961 Haze her is what you're looking for, friend.

>>	Anonymous Sun Jul 20 15:17:59 2014 No.6655493 >>6655480 >>6655487 The latter is called Berlin Intelligence Structure Test.

>>	Anonymous Sun Jul 20 15:24:14 2014 No.6655501 >>6655487 >>6655493 Thanks.

>>	Anonymous Sun Jul 20 15:29:57 2014 No.6655512 >>6646480 >Solve P=nP

>>	Anonymous Sun Jul 20 16:00:05 2014 No.6655558 >>6655122 pls respond

>>	Anonymous Sun Jul 20 16:12:51 2014 No.6655577 I'm going to change my career to industrial design engineering and I'll make a masters in motors, I think. What does /sci/ think?

>>	Anonymous Sun Jul 20 16:35:26 2014 No.6655614 >>6646480 What gasses does Mars surface contain?

>>	Anonymous Sun Jul 20 16:45:29 2014 No.6655631 >>6655614 Carbon Dioxide, a bit of Methane and a lot of dust.

>>	Anonymous Sun Jul 20 16:46:32 2014 No.6655632 File: 114 KB, 1047x1176, Mars_atmosphere.jpg [View same] [iqdb] [saucenao] [google] >>6655631 pic related

>>	Anonymous Sun Jul 20 16:46:58 2014 No.6655633 >>6655631 >all dem organic chemicals make me wet

Anonymous Sun Jul 20 16:49:14 2014 No.6655636

When presented with second order PDE's, one of the go to methods is separation of variables, which assumes that solutions are the product of functions of the individual variables, so that if we had a PDE with partial derivatives in X and Y, we'd assume that the solution f(x,y)=g(x)*h(y).

My question is, are there any such separable PDEs that have solutions that AREN'T separate like that?

>>	Anonymous Sun Jul 20 17:08:51 2014 No.6655671 >>6655633 Methane is the simplest organic compound. Not that exciting.

>>	Anonymous Sun Jul 20 17:12:34 2014 No.6655677 >>6654858 Can you give an example of a normal number that wouldn't be a universe number? Intuitively it feels like normal should imply universe...

>>	Anonymous Sun Jul 20 17:56:35 2014 No.6655739 >>6655122 pls respond

>>	Anonymous Sun Jul 20 18:02:33 2014 No.6655748 >>6655677 Well you are right, normal implies universe. The reciprocal is wrong though.

>>	Anonymous Sun Jul 20 18:08:34 2014 No.6655757 dx / [ (1+x)* sqrt (x^2 - 1) ] How to integrate this thing without using sinh(x) and cosh(x) substitutions?

KenDrun Sun Jul 20 18:29:20 2014 No.6655785

>>6655636
>Are there any separable PDEs that aren't separable?

Uh, I'd have to go with no as an answer to that...

The whole notion of having a solution that is separable is the f(x,y)=g(x)*h(y) step, and that allows all of the machinery that was developed to solve separable PDEs to work. You can keep extending it too, like f(x,y,z)=g(x)*h(y)*u(z) and you'd go on to solve it as before. If you've done the Schrodinger equation for the hydrogen atom you've done a separable PDE with three variables.

I don't know if you're asking this, but you wouldn't assume something like f(x,y)=g(x)+h(y) because that would mean your problem is actually simpler (this type would be called additively separable, and is included in multiplicatively separable functions, mixed derivatives are also 0 which make it simple). Also realize that when you do separations even the correct way you're just starting with an assumption and hoping it is going to work. AFAIK there is no real reason to actually assume a PDE should be separable, it just happens that many useful ones are. So it is essential to go back and check using the formulation of your problem whether or not your answer actually works, because it is hinging on that assumption.

One more thing! When you write f(x,y)=g(x)*h(y), g and h are arbitrary functions, so making the assumption really doesn't place a harsh condition on what f could be. Non separable functions would be something like f(x,y)=x^y. You can't turn that into two functions of one variable multiplied together, so when you make the multiplicatively separable assumption you're discarding inseparable solutions like that, but ANY separable solution is fair game because g and h are arbitrary functions, e.g. if f(x,y)=x+xy you could have g=x and h=y+1 or any other possible way to separate it.

>>	KenDrun Sun Jul 20 18:34:31 2014 No.6655791 >>6655757 Substitute using secant. It is tough.

Anonymous Sun Jul 20 18:51:16 2014 No.6655815

In quantum mecanics, something regarding the whole uncertainty things (such as Heisenberg's principle of uncertainty) seems logical to me but I'd like confirmation. Am I correct when I say that every particle have a precise and definite position and velocity but that we simply cannot mesure them without changing them?

On a related topic, is there actually true randomness or is everything just a logical sequence of reactions so complex that they seem random to us?

Anonymous Sun Jul 20 19:05:38 2014 No.6655835 [DELETED]

>>6655757

\displaystyle \int \frac{dx}{(x + 1)\sqrt{x^2 - 1}}[/spoiler]

Let \displaystyle x = \sec\theta \;\;\; \Rightarrow \;\;\; dx = \sec\theta \tan\theta \, d\theta[/spoiler]

 = \displaystyle \int \frac{\sec\theta \tan\theta \, d\theta}{( \sec\theta + 1) \sqrt{\sec^2 \theta - 1}}[/spoiler]
 = \displaystyle \int \frac{\sec\theta \tan\theta \, d\theta}{( \sec\theta + 1) \sqrt{\tan^2 \theta}}[/spoiler]
 = \displaystyle \int \frac{\sec\theta \tan\theta \, d\theta}{( \sec\theta + 1) \tan\theta}[/spoiler]
 = \displaystyle \int \frac{\sec\theta\, d\theta}{( \sec\theta + 1)}[/spoiler]
 = \displaystyle \int \frac{\sec\theta\, d\theta}{( \sec\theta + 1)} \cdot \frac{\sec\theta - 1}{\sec\theta - 1}[/spoiler]
 = \displaystyle \int \frac{ (\sec^2\theta + \sec\theta)\, d\theta}{( \sec^2\theta - 1)}[/spoiler]
 = \displaystyle \int \frac{ (\sec^2\theta + \sec\theta)\, d\theta}{ \tan^2\theta}[/spoiler]
 = \displaystyle \int \frac{ \sec^2\theta\, d\theta}{ \tan^2\theta} + \int \frac{\sec\theta \, d\theta}{\tan^2\theta}[/spoiler]
 = \displaystyle \int \frac{ (\tan^2\theta + 1)\, d\theta}{ \tan^2\theta} + \int \frac{\sec\theta \, d\theta}{\tan^2\theta}[/spoiler]
 = \displaystyle \int \frac{ \tan^2\theta\, d\theta}{ \tan^2\theta} + \int \frac{ d\theta}{ \tan^2\theta} + \int \frac{\sec\theta \, d\theta}{\tan^2\theta}[/spoiler]
 = \displaystyle \int d\theta + \int \cot^2\theta \, d\theta + \int \frac{\cot^2\theta}{\cos\theta} \, d\theta[/spoiler]
 = \displaystyle \theta -\theta - \cot\theta + \int \frac{ \cos\theta}{ \sin\theta}\frac{1}{\cos\theta} \, d\theta[/spoiler]
 = \displaystyle -\cot\theta + \int \csc\theta \, d\theta[/spoiler]
 = \displaystyle -\cot\theta + \ln |\csc\theta - \cot\theta| + C[/spoiler]
 = \displaystyle \frac{-1}{\sqrt{x^2 - 1}} + \ln \left| \frac{x}{ \sqrt{x^2 - 1}} - \frac{1}{\sqrt{x^2 - 1}}\right| + C[/spoiler]
Too lazy to check my math. It's probably wrong somewhere.

KenDrun Sun Jul 20 21:17:49 2014 No.6656004
File: 147 KB, 945x445, read a book.png [View same] [iqdb] [saucenao] [google]

>>6655815
See image and its captions. The best way to think about HUP is probably to look at a wave. Position is still position and wavelength can give you momentum. Note in the first figure, how would you describe where the position of the wave is? If it were a nice sine curve all the way across the rope then you'd be forced to say the position of the wave is equally probable at any point on the rope.

Measurement and HUP is more about forcing a particle to have some well defined characteristic. So thinking about waves, you could have a wave that is somewhere in between the two in the picture, but when you measure the position it is forced to look like the second one (think, since you have made a measurement of where it is, then it better be there). HUP says that it also can not be known exactly, and that there will be a trade off between how well you know where the wave is and its velocity (so if you made a more accurate measurement of the position, the little peak that is the wave would decrease in width).

As a side note, HUP works for any two incompatible observables, position and momentum happen to be very fundamental.

>>	Anonymous Sun Jul 20 21:18:53 2014 No.6656006 >>6655791 that doesn't look tough at all

>>	KenDrun Sun Jul 20 21:34:32 2014 No.6656019 >>6656006 It depends on how you do it. Plowing right along with a bunch substitutions is tough, but it can be easily simplified to an integral that is probably memorized. If you're not looking for it though you're kind of stuck doing those substitutions.

>>	Anonymous Mon Jul 21 09:21:20 2014 No.6656829 >>6655122 pls rspond

>>	Anonymous Mon Jul 21 14:11:26 2014 No.6657103 What does the term "closed-form" mean?

Anonymous Mon Jul 21 14:39:58 2014 No.6657133
File: 30 KB, 1000x1000, 1000px-Time_dilation.svg.png [View same] [iqdb] [saucenao] [google]

In the equation
 K.E = M_{0}c^{2}(\gamma -1) [/spoiler]
I assume you are finding the kinetic energy of the object,but is that the same as the energy required to bring an object up to that velocity

>>	Anonymous Mon Jul 21 15:07:26 2014 No.6657165 >>6655490 That just seems like porn, friend.

>>	Anonymous Mon Jul 21 15:10:22 2014 No.6657169 is bioengineering worthwhile have i made a terrible mistake

>>	T !ZnBI2EKkq. Mon Jul 21 15:28:05 2014 No.6657189 >>6646480 What is a simple explanation of Eulers Identity?

>>	Anonymous Mon Jul 21 15:29:34 2014 No.6657191 >>6657103 When something is written using known functions and not an infinite sum, or something like that.

>>	Anonymous Mon Jul 21 15:31:36 2014 No.6657193 >>6650646 Not necessarily. G=>P is only invalid if a truth implies a false.

>>	Anonymous Mon Jul 21 15:33:19 2014 No.6657195 I have a question, /sci/. Is it possible to make an atomic bomb using reactor-grade plutonium? If so, has any party ever claimed to achieve this?

>>	Anonymous Mon Jul 21 15:50:31 2014 No.6657220 Wouldn't traveling back in time violate the conservation laws?

>>	Anonymous Mon Jul 21 16:03:10 2014 No.6657234 File: 303 KB, 634x592, 498435464354.jpg [View same] [iqdb] [saucenao] [google] What should i do now? It's my turn.

>>	topkekm8 !!EVgk4lINiWM Mon Jul 21 16:04:28 2014 No.6657237 >>6647046 Enter an alternate universe where fiction is fact

>>	Anonymous Mon Jul 21 16:10:22 2014 No.6657239 >>6657191 Why is it called that?

>>	Anonymous Mon Jul 21 17:10:44 2014 No.6657353 >>6652162 Anyone?

>>	Anonymous Mon Jul 21 17:15:36 2014 No.6657366 >>6657353 http://www.brainbashers.com/logic.asp

Anonymous Mon Jul 21 19:59:47 2014 No.6657594
File: 14 KB, 489x329, Screenshot from 2014-07-21 19:58:18.png [View same] [iqdb] [saucenao] [google]

hi

given the triangles in the picture and sides a, b, d[/spoiler] I need to solve for x, y[/spoiler].

Usually I'd use sin and cos and all that but I want to compute the solution frequently on a computer.

Does anyone know how the solution

x=0.5*(d+(b^2-a^2)/d)
[/spoiler]

was obtained?

Anonymous Mon Jul 21 20:00:49 2014 No.6657596

>>6657594
>Usually I'd use sin and cos and all that but I want to compute the solution frequently on a computer.
Just to clarify, using sin and cos is somewhat 'expensive' in software when calling it over and over again rapidly. The solution given is faster cheaper in comparison and I want to know how it was solved.

>>	Anonymous Mon Jul 21 20:22:19 2014 No.6657615 >>6657596 >>6657594 found the solution on this page using circle cirlc intersection: http://paulbourke.net/geometry/circlesphere/

>>	Anonymous Mon Jul 21 21:45:11 2014 No.6657706 Posted this in /g/, but I realize it's more relevant here: What's the most cost effective algorithm to calculate pi very accurately?

Anonymous Mon Jul 21 22:02:41 2014 No.6657725 [DELETED]

good evening /sci

I'm studying Simpson's rule, specifically how the sum is constructed. I've looked at the lagrange interpolation proof but that is beyond my capacity for now.

Does anyone know of a more elementary proof of Simpson's rule? Could I get there from a proof of the exact value of simpson approximation on polynomials of degree three or less?

>>	Anonymous Tue Jul 22 03:24:13 2014 No.6658032 >>6646658 If you can't comprehend that <span class="math">f(x)=\sum_{k=0}^\infty \frac{f^{(k)}(c)}{k!}(x-c)^k[/spoiler] then you really shouldn't be cutting people open. Try harder.

KenDrun Tue Jul 22 14:43:24 2014 No.6658685
File: 17 KB, 1041x1041, Euler's_Formula_c.png [View same] [iqdb] [saucenao] [google]

>>6657189
Euler's identity/formula is tricky because it seems like there is going to be some nice geometrical explanation, especially since sin and cos are being used, but there really isn't any afaik.

The red curve in the attached pic is the curve that is drawn out when you have e^(iz). It looks the same as circularly polarized light if you're familiar with that. The curve "propagates" on the z axis, but if you look dead on to the XY plane you'd see it making a circle that keeps repeating. When you have a circle you can use polar coordinates easily and write it in terms of sine and cosine. If you want to convert polar to cartesian it is just x=r*cos(theta), y=r*sin(theta). If you use the complex plane with imaginary numbers on the y axis you can write 2D coordinates as a single complex number with the real part as the x coordinate and imaginary as the y coordinate. So I think that explains how to use it but not why it exists.

Before I mentioned how there really isn't a geometrical reason behind it, and that is because the existence of the identity doesn't come from sine and cosine being ratios of sides or anything like that, but instead it comes from e^l being the solution to linear ODEs. The most straight forward way to show it is going to work is by writing sin and cosine out in exponential form in the equation, and unsurprisingly you'll get 2e^iz=e^iz+e^-iz+e^iz-e^-iz. And so now the question is, why can sine and cosine be rewritten in terms of exponentials? Well from various arguments you can set up a differential equation f(x)=-f''(x) which should give you sine or cosine, but if you solve it using the normal methods your solution is e^ix+e^-ix, so sine and cosine must be a linear combination of e^ix and e^-ix.

There are actually a ton of ways to prove Euler's formula, and I didn't give airtight reasoning above because my point is more to show that it uses that e^l is the solution of ODEs is the reason why it happens.

>>	Anonymous Tue Jul 22 18:21:13 2014 No.6659148 >>6657366 That's not exactly what I'm looking for.

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