Saturday, September 24, 2016

Student's t confidence interval

This calculator computes sample mean for the t-score calculator.
If you think that your data is distributed normally (stat 414 uses nomral probability plot to check that), you can enter your series into the left window (spaces, including newlines, and comma- separated values are supported). This will compute the mean and variance and redirect you to the t-score calculator


Rotating the distribution

There are two ways to represent a distribution. Normally, you do it like on the left diagram, with vertical bars (a histogram, pd.f.) which stands on the (X-axis) value and whose height is proportional to the likelihood/probability. It is lends nicely itself for integrating the probabilities to get into a range of values. It is however not suitable for finding the average. To find the average, you need to rotate the plot 90 degrees so that bar height is proportional to the value and bar width is the probability to get into it, like it is on the right.
Specify the distribution in [value, likelihood] format below:

Your browser does not support the HTML5 canvas tag.
I started to think however that if we make the height of the bar proportionally to the density on the interval, that is count of occurrence per interval length, then histogram becomes suitable for average computation. What is the difference with the right diagram them? We compute the average density whereas right diagram still computes the average value?

Thursday, September 22, 2016

Why invention is different from discovery? [duplicate]

This question already has an answer here:
You say that discovery discovers something pre-existing (in the world) whereas inventor comes up with a new idea. But, don't you discover the ideas?
As I understand, there is an abstract world of ideas, where all abstract notions, i.e. ideas, live in. You just discover one or another. They usually tell you how to get from A to B in an optimal way. One way is bad, another is good. And what you do when solve a problem, you find those ways. Mathematicians know very well that solutions are not arbitrary. They exist before you discover them (nobody needs arbitrary solutions as nobody needs garbage). Is desired solution a discovery or an invention? Why do people, particularly academists, insist that there is a distinction between invention and discovery, once you realize that inventors just discover the ideas from the ideal world of ideas/solutions?
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marked as duplicate by Camil StapsDaveJohn AmcommandoEliran H Aug 4 at 14:16

This question was marked as an exact duplicate of an existing question. If this question is different, please edit itto explain how it is different or ask a new question.

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1
 
Welcome to Philosophy.SE. "As I understand, there is an abstract world of ideas..." - from what do you understand this? Plato? Please make your starting point clear. Also, could you articulate what exactly is your philosophical problem? (see also help/on-topic) – Camil Staps Aug 4 at 9:33
  
 
@CamilStaps it's a view also held by more 'recent' philosophers, such as Frege. It is very controversial though, so maybe the question would be better without presupposing it. – Eliran H Aug 4 at 9:41
  
 
@EliranH in any case, the question needs elaboration. – Camil Staps Aug 4 at 9:55
   
I am not considering somebody's doctrine. I consider the common sense. This means that the view is also shared by me, in addition to the whole math community. I gave you example where math (ideal world) assumes that there is a solution before it is found. It also holds for real world problems. There is no need to attribute such obvious thing to anybody, especially if you can find the historical names holding it yourself. You can explain why this view is wrong (and, thus, how invention can be different from the discovery) in your answer. – Little Alien Aug 4 at 10:01   
   
What needs elaboration? Everybody needs to know what is invention, what is discovery and how are they different. I have gave you the obvious reason why the separation is artificial. What needs to be elaborated? Probably, I am wrong that philosophy is about common sense. I have heard that philosophy is a collection of ancient delirium that failed to be true and, thus, failed to be developed by branches of science. – Little Alien Aug 4 at 10:05   
  
 
"The whole math community"? Platonism is a popular but not universal position in math. Moreover, mathematicians are generally ill-equipped to make claims of ontology. Third, common sense is often the prejudice of inexperience, and we prefer proofs and arguments to "it's obviously true" (I, for example, think it's common sense that ideas don't exist in any abstract way - and I've studied math). Fourth, what you have heard about philosophy is wrong. You're speaking with an unusual degree of hostility to what we do here, given you're asking for our thoughts. – commando Aug 4 at 13:42 
  
 
@commando It's funny that that question was highly upvoted while this gets such negative responses. It may be correct to close this as duplicate, but not for other reasons. I think some users here are being too harsh. – Eliran H Aug 4 at 14:13
  
 
@EliranH I agree that this shouldn't be closed for non-duplicate reasons. I think the votes are fair, though, because this question is phrased quite poorly and with the presupposition of being correct, while the other question is more open. – commando Aug 4 at 14:15
   
'As I understand' is the 'presupposition of being correct' Mine question must be closed because it is stronger -- it is not limited to math. I do not understand why it should be confined to math. But, I understand that it would be fine if it only concerned a narrow subbranch of math, like algebra. At the same time, the humen say that stating the problem explicitly limits your freedom and, therefore, is a bad thing. – Little Alien Aug 4 at 14:56   

Giving advises in individualist society [closed]

I see that our society has transformed into individualist society and every individuals around me are quite individualistic. People are quite efficient at the work but their spendings at the private time, when I see them, is crazy. Yet, when I try to fix it with my deepest affections, they prefer to wound me to display that they need the money from me, not the advises. They are ready to listen only from the rich people.
Should I start explaining them anything by my initiative when I feel that I need to? This answer raises also in case when the initiative is theirs, when they ask me anything to explain. I need to decide how deeply should I go in the answer. I can give a short answer, which hardly explains anything or go into the details that I feel critical and important. But, they are not even informed about such nuances ever exist and, therefore, do not ask about them. Should I start telling them something on my own initiative?
Suppose now that one of them goes blindly to fall out of the window. Should I stop them, telling what they are essentially doing? I ask because I see a contradiction here. I should stop them from the ethics point of view, but, I should not from the individualist point of view. From individualist point of view I should silently let them to fall. This is their wish after all for me to keep my mouth shut to let them do quietly what they want to.
Another contraction arises if their action harms me. For instance, you know that you must buy a household and a car(s). It is a must individualist lifestyle. Yet, it destroys the environment. The individualist lifestyle of the dream not only pumps out their budget, it also drains the oil reserves and destroys the planet that I live on. So, on one hand, I must defend my interest and tell them what they are doing. On the other hand, I should shut up and enjoy whatever they do. How to resolve this contradiction?
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closed as unclear what you're asking by virmaior Jul 31 at 23:18

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit your question.

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1
 
First off welcome to philosophy.SE. There may be a question in here, but I'm having a lot of trouble finding it. Could you edit and make this much clearer? – virmaior Jul 31 at 23:18
   
Good trolling, @virmaior, welcome! – Little Alien Jul 31 at 23:29   
4
 
huh? I'm genuinely saying I don't understand the question you're asking about philosophy in there. I see a lot of writing and a lot of claims, but on the simplest level, what is your question about philosophy? – virmaior Jul 31 at 23:38 
   
Saying that I have the claims but not questions when I have questions is trolling. You may say that my questions are not about philosophy but substituting "you have the questions about ethics and, thus, these are claims rather than questions" is trolling. Just tell that you do not bother to read beyond the first paragraph. Otherwise, you troll. When people say that white under their nose is nothing but black, they troll. – Little Alien Aug 1 at 8:38   
   
Probably you should give it as answer. Your trolling suggests that people take individualism because they do not notice the contradictions. When you do not notice the contradictions that I put under your nose you basically demonstrate the way you deal with them. – Little Alien Aug 1 at 8:47   
  
 
I'm really not following why you think I'm trolling. Can you highlight the specific answerable question about philosophy both here in a comment and by editing your question? The Philosophy.SE isn't meant for us to critique essays and write lengthy responses (as if it were a variant on code review SE), it's more like "What does :: mean in php?" type questions that work here... Again, what more specifically is your question? – virmaior Aug 1 at 10:15

Await.result is faster than pure Futures

I tried

def fibAwait(grainSize: Int) = {
def seqF(n: Int): Int = 
if (n < 2) n else seqF(n-1)+seqF(n-2)
def parF(n: Int): Int = if (n < grainSize) seqF(n) else {
val flist = Future.sequence(List(1,2) map 
(i => Future{parF(n-i)})
Await.result(flist, Duration.Inf) sum ;
}
parF(45)

}

vs

def fibFuture(grainSize: Int) = {

def seqF(n: Int): Int = 
if (n < 2) n else seqF(n-1)+seqF(n-2)

def parF(n: Int): Future[Int] = 
if (n < grainSize) future{seqF(n)}
else {
val flist = List(1,2).map(i => parF(n-i))
Future.sequence(flist) map (_.sum)
}
Await.result(parF(45), Duration.Inf)
}


Both compute fib(45) where bottom 42 levels are computed sequentially and upper levels 45 downto 43 start a parallel computation. Benchmarking gives time in centi-seconds (1/100 of a second). Both end up in around 6-7 seconds but first seems to show lower time (needs to be proved with statisitcal test):

(1 to 10) foreach (_ => println(List(fibAwait _ , fibFuture _). map (f => timeit(f(42))._2)))
List(664cs, 696cs)
List(634cs, 707cs)
List(725cs, 738cs)
List(653cs, 702cs)
List(644cs, 680cs)
List(557cs, 684cs)
List(667cs, 683cs)
List(638cs, 765cs)
List(751cs, 700cs)
List(654cs, 688cs)