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#1201 Re: This is Cool » The Golden Ratio by Mario Livio. Anybody read it? » 2006-06-23 16:10:59
After a tiring investigation I find Classical is not as solid as many people think. Probablity is a hard subject, and neither classical nor Bayesian can make progress without sacrificing something.
95% in confidence interval is the probablity generated by samples. Actually it's the X-bar probablity. If you want expectation(parameter) probability, (if you want more), you have to make assumptions that expectation u couid be everywhere and initially its probablity in everywhere is equal. By adding new knowledge of samples you can get conditional (treamed) probility of u. And this time whole distribution, better than just interval. Though the distribution is fake due to assumption.
Luckily, they get a same answer with classical until now. But Bayesians'competitive advantage is to change the equal assumption for expert prejudice. By doing that they can make the predicted interval narrower.
The difference is like if you allow a forecaster to add his personal intuition according to his experience beyond given theory and compution or not. If you allow him to do so, he may get a narrower forecast but more subjective one.
And it's a philophical debate whether a person's experience is more subjective than staticians' theory. Is their theory qualified enough to be truth?
And there's some time that a narrower but more risky forecast overweighs the less risky but broader one. 
#1202 Re: Help Me ! » balls inside the pyramid » 2006-06-23 15:23:05
Okay RauLiTo , why don't you get some hard-paper and some ping-pang balls to get it yourself? That's the most correct way...
#1203 Re: Help Me ! » calculating normal vector from equation for a shape » 2006-06-23 15:11:30
You'd better get a vector calculus book or a calculus book with sufficient vector calculus.
#1204 Re: This is Cool » The Golden Ratio by Mario Livio. Anybody read it? » 2006-06-23 15:08:30
Bayesians are good at helping court. In that case, only Bayesians could help.
I discover that many people believe in Classical and are against Bayesian just because they think they understand Classical. So may I ask you a question: what does 95% in confidence interval mean? (what does it stand for)
#1205 Re: This is Cool » The Golden Ratio by Mario Livio. Anybody read it? » 2006-06-22 20:34:11
Actually there are competitions in math theories!
for example, staticians are debating whether classical or Bayesian for decades! Econometritians are debating whether (Ax)'=A or (Ax)'=A' for a long time!
So I would rather put existing theories as the competitive theories that win their opponents or at least due than being the truth.
But my view looks tricky, lol~
#1206 Re: Help Me ! » balls inside the pyramid » 2006-06-22 20:24:40
so you mean you can virturely fit 5 balls on the base.
But I insist a square arrangement.
when you kick a ball into the very corner under two side surfaces, you can imagine make it two and roll them away under the two surfaces. The paths would be orthogonal to each other and the new two balls now have no difference than two balls kissing their own one side and the base.
#1207 Re: Euler Avenue » An abstract introduction to Groups and Fields. » 2006-06-22 20:09:40
Like Euclid reduced geometry theorems into 4 or 5 assumptions as an origin, Hilbert reduced operation rules into several conditions as an origin. Great work, Ricky! Hope you have a lot of time to complete this topic!
#1208 Re: Help Me ! » balls inside the pyramid » 2006-06-22 20:03:13
suppose θ is the angle between waist surface and base surface.
tanθ=3/4, sinθ=3/5 and cosθ=4/5
radius/nearest ball center position=tan(θ/2)=sinθ/(1+cosθ)=1/3
nearest ball center position=3
let's see how many balls can we mostly have in one row or in one column on the base
two side balls take up distance 3+1+1+3=8
so at most 2 balls in one column and 2 balls in one row.
the best way to put balls on base seems to be 2 by 2 arrangement.
then can we put other balls on the 4 balls?
you can only put 1 ball on them, I'm afraid. More balls will not be contained under the narrower space between side surfaces.
so together 5 balls at most.
#1209 Re: This is Cool » The Golden Ratio by Mario Livio. Anybody read it? » 2006-06-22 14:30:19
I think it's mainly Gaussian-Elimination that simplifies linear equation solving.
And it's vector combination that underpins theory for multi-solution linear equations.
Becaus if you throw away matrices multiplication and make small adjustments in the form of the two theories (or a method and a theory) above, you will probably find little difficulty in linear equations dealing.
Then why complicated matrices combining multiplication and addition together?(Actually it took me a long time to accept that concept)
Matices multiplication and determinants are some kind of winners , as there are actually many other competing definations that are not as poplular as them.(A lot of mathematicians are inventing new definations to arrange numbers) The reason why they win over might be that their usefulness are not limited to linear equations solving - matrices multiplication is good at handling data, especially in statistics, and determinant is popular among physicians.
And I guess determinant's application in physics is quite lucky- the inventor wouldn't have ever dreamed about it!
#1210 Re: This is Cool » The Golden Ratio by Mario Livio. Anybody read it? » 2006-06-20 20:04:24
I guess if x and y are not independent and have some certain kind of relation that can be described by complex numbers, they will be very useful.
for example, negative numbers, dot product, and matrices initially seem a waste of time. But when they just fit the certain problems, they become very useful indeed!
#1211 Re: This is Cool » 1600 to the power of 1600 (and later 16000^16000) » 2006-06-15 13:23:54
Mathematica...
#1212 Re: Help Me ! » Probability » 2006-06-15 13:22:49
Cheat
#1213 Re: This is Cool » 1600 to the power of 1600 (and later 16000^16000) » 2006-06-14 14:50:05
16^16000=
831232460999333652239585333103635610886900466185671504606004315200220906068523\
469713722100299463513721982461601573667588699938507317028143778331910759502182\
695990576206254004390990981773923736351921518598129245427682295805264626773846\
198525221723061189844462315898785804231642365367858585399149956132155655007346\
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#1214 Re: Help Me ! » Parametric Differentiation » 2006-06-13 14:01:44
#1215 Re: Help Me ! » Please Help! » 2006-06-13 13:55:07
If Mathematica wasn't that clever in plotting!
In handling theoritical problems, Mathematica is better.
#1216 Re: Help Me ! » Simplifying an Expression » 2006-06-12 14:18:20
Unless you know another way to solve a cubic equation.
#1217 Re: Help Me ! » Some More Math Problems » 2006-06-12 14:17:07
Great job! Franklin!
#1218 Re: Help Me ! » My exam is tomorrow and i am in need of some DESPERATE HELP! » 2006-06-12 03:42:55
check this website and you will find lots of demonstrations well editted by Mathsisfun.
#1219 Re: Help Me ! » Simplifying an Expression » 2006-06-12 03:41:19
2/3*19^(1/2)*m-1/3
#1220 Re: Help Me ! » Simplifying an Expression » 2006-06-11 18:00:26
Thanks, MIF. From your graph, I get positive solution about 1. And treat√19 = 4.5
Use these approximations, I get an answer 2+2/3.
m is the cosine.
#1221 Re: Help Me ! » Simplifying an Expression » 2006-06-11 15:21:13
If any one could solve
manually,
I will get you a satisfactory answer.
#1222 Re: Help Me ! » Please Help! » 2006-06-11 01:45:27
You solved it using Maple (or any other math software out there), didn't you?
I already solved the equation myself, but my teacher complains about my answear being long and ugly. (Containing cosines and arc-cosines and stuff.)
Yours looks better.
What does 'i' stand for?
Maple and Mathematica, which is better? How do you feel about it guys??
In Plotting, I really support Maple.
#1223 Re: Help Me ! » Master Sum » 2006-06-11 01:41:41
I used to think it hard. But as I put entries on paper, it's easier than I thought. for i=4
traditionally, multiply above by 2 and see
this expression should be substracted but 2^2-1^2 and 3^2-2^2 are the special pattern in lefted.
use a formula:
what should be substracted next are expressions below:
next problem is to find:
I know how to solve it, but I would like to leave it to next volunteer
#1224 Re: This is Cool » Geometric probability » 2006-06-10 14:38:38
the sum of their facing angles to be 180°?
Any circle?
How do you define "random"?
#1225 Re: This is Cool » projectile motion » 2006-06-08 15:19:34
It's a pleasure to share with you one of the greatest inventions in math- the vector concept, mikau! 