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Pi In The 4th Dimension
Anonymous Coward writes "Hoy! There is some crazy guy who is all set to prove that the value of the mathematical constant Pi is same for all dimensions. He has calculated Pi for the 4th dimension - and it..it's almost equal - 3.1447817532635 wheras the calculated value of Pi in 2 dimensions (circle) is 3.1416999189943. Math nerds can calculate the percentage error. The project is on SourceForge.net and they even have an online version "
the saying that you can't step into the same river twice? :-)
Great one!
Reposting again. Managed to get up to 50 Karma, posted ONE pro-Troll message, and got mod-bombed. This diatribe was truer than I thought. CLiT, I shall be honored if you accept me as a member!
Visitors to the website slashdot.org [slashdot.org] will by now have surely heard of the act of Moderation. This is where a contributor's post can be 'Moderated' either positively or negatively, depending on how the Moderator perceives the value of the post. There is a sliding scale of total moderation points, from -1 to 5, along with snappy summaries of the reason for moderation, such as "Funny", "Insightful", or the ever popular "Troll". An additional benefit offered to Moderators is the ability to ban a poster from contributing, by negatively moderating enough of his postings in a 24 hour period.
In order to retain some level of fairness for the Slashdot population, the Slashdot Editors (adopting the role of 'Benevolent Dictators') have implemented a scheme whereby regular users of Slashdot, chosen essentially at random, are given the ability to act as Moderators.
This underlines an inherent flaw in the system. Psychological studies have shown that in any community, no matter how small, should a random sampling of people be given the slightest grasp of power, they will immediately abuse it. There is a primal, evolutionary desire in Man to place himself higher than his peers by whatever measurement they can muster. Slashdot Moderation provides the ideal means for which a man can prove himself more equal than others.
At the risk of invoking Godwin's Law at such an early point in my thesis, I have no choice but to compare Slashdot Moderation to the systematic genocide of the Jewish community in 1930's Germany.
A bold statement, I admit, and deliberately designed to shock, but I feel the statement is necessary. I shall now offer a more rational explanation, as well as a comparison of the parallels between Slashdot Culture, and the National Socialist regime.
First, some history. National Socialism did not spring up overnight. It grew from a feeling of national bitterness and resentment at the war reparations Germany was forced to make after World War One. Germany was a broken country, populated by desperate starving people. And to the desperate, an extreme ideology begins to seem like a rational choice.
The advent of new technology forces a paradigm shift in the way the beholders of that technology think. The Christianity Meme was made wide spread by the invention of the Gutenberg press. And the rise of National Socialism was made popular because of the invention of Cinema. Here we had a new means to control the flow of information to the populace, that they are willing to unquestioningly listen to due to the 'novelty factor' of moving pictures. It is no coincidence that some of the best Cinematography of the early 20th Century came out of the National Socialist propaganda machine.
Why is this the case? It is yet another fault of man that a new means of distributing memes is perceived, due to the 'newness' of the medium, to have a greater 'validity' than older media. Those harnessing new inventions have the power to win control of the hearts and minds of others.
With the tools in place, who should the National Socialists target? Clearly, as a counterpoint to Man's desire to hold power over others, there is also a desire to resent the success of others. If someone is successful, they reduce the self-worth of their beholders. Although times were harsh in Germany in the prelude to World War II, there were still successful inhabitants of that country. Possessing shrewd business acumen as well as the contacts in other countries needed to maintain support in such a poverty stricken and broken land, who else should deserve the wrath of the populace more than the Jews?
Fast-forward to the latter quarter of the 20th Century. Computing technology is focused in niche markets, and limited to big successful companies like IBM and Microsoft. As the markets were limited, there were also limited opportunities for employment. This gave rise to a rising number of college dropouts, seething with resentment and unable to relate to society beyond the staccato clatter of keyboards and the pallid green glow of an 80x24 text display, and lacking the basic business skills (and a smart suit) needed to secure employment at one of these companies.
At this time, a new invention was beginning to take hold in College campuses throughout the world. The Internet. As with the Gutenberg press and Cinema beforehand, this new technology would grow to spread one of the most virulent memes of the modern age - Open Source Software, created as the antithesis of successful business practise.
So, the parallels between the birth of Anti-Semetic National Socialism and the birth of Open Source Software have been made. Of course, it is easy to claim that A=B without providing further logical evidence in support. So, the next task of my thesis is to provide further parallels, and bring this discourse back to the initial focus on Slashdot Moderation.
Slashdot was conceived, in it's original 'Chips 'n' Dips' incarnation, as a vehemently anti-corporate Open Source website. Roughly 10-15 years down the line from the birth of Open Source, it has become saturated with propaganda, and now forms the centrepiece of the Open Source Development Network. An authority in it's field, Slashdot's success is in no small part due to the ability of the editors to 'pick and choose' valid news articles submitted by users, and present the same old tired "Open Source Good / Closed Source Bad" rhetoric time and time again, dabbling with anti-copyright and the right of the 'common man' to remove an artist's ability to gain compensation for the work. In essence, this is similar to the 'paring down' of artistic worth in 1930's Germany. If no-one is willing to contribute valid and vibrant art to the community, then all art shall become harsh and functional, possessing a certain intimidating aesthetic.
Which leads onto Open Source's shining achievement - Linux. This diatribe is not aimed towards Linux in particular, as it is a well-oiled, well-tuned machine. A technically adept Operating System, it is worthy of admiration by any rational man. The point of this thesis is not to attack the art produced by Open Source coders, which in itself is worthy, but to enlighten all as to the political processes behind the OSS movement.
By the same scale, it is hard to fault Mercedes for the technical excellence of the vehicles which were used by the National Socialist party. But the politics behind the party are what taint the image of Mercedes' vehicles of the era. The Swastika itself is a benign symbol, found this day in such diverse locations as Pokemon cards, but is permanently tainted with the history of the acts made under its auspice. In the same way, companies switching to Open Source solutions will begin to regard the Penguin with the same trepidation as their profits fall.
It should be worth noting at this point that IBM, previously one of the world's greatest companies, has begun reporting servere financial losses, no doubt due to its adoption of Open Source practises. This epoch-making event was NOT reported on Slashdot, even though articles were submitted.
And what of the other great company mentioned above? Microsoft, aka Micro$oft, Mickeysoft, Microshaft, Kro$oft, and many other derogatory and undeserved names. Throughout the previous 25 years, Microsoft has grown from strength to strength, again possessing shrewd business acumen as well as providing products that people want. This makes them the number one target for the OSS movement. Incapable of standing by their own merits, the OSS zealot would rather attack Microsoft as a priority than produce anything of worth for their community.
Slashdot Moderators, crazed with their limited new-found power, exhibit this behavior. It is a sad state of affairs that the majority of article moderations are negative. Where is the positive feedback and sense of social contribution? Nowhere to be found. Moderators are too focused on putting their peers down to make themselves appear superior, rather than doing the hard work and becoming better on their own terms.
As the National Socialists required a scapegoat, Slashdot Moderators require a constant stream of Postings to label '-1, Inferior'. Once a posting is reduced to the score of -1, it becomes invisible to the casual user. Again, this is a parallel to the Ghettoization of Germany upon the election of Hitler.
In essence this would not be so bad, were postings to be evaluated on their own terms. However, alongside the moderation of their postings, each user has a 'Karma' value, namely the sum of their worth to the Slashdot community. As a user's posts are moderated up or down, so their Karma fluctuates. As Karma becomes negative, a user's default posting score is reduced, until they are posting at a default of -1. Again, ghettoizing PEOPLE, not just their opinions.
This ghettoization is reinforced with the often fake belief that a negatively moderated post, and therefore the poster, is a "Troll". (Is it any wonder that such a name has been chosen to describe these people, invoking mental imagery of facial disfigurement and hooked noses?) As the Jews were accused of fraud, dishonesty and being subhuman animals, so too are Trolls accused of FUD, Crapflooding, and obfuscated goatse.cx links. Quite often, these 'undesirables' are capable of providing a valid insightful comment on a topic, but because it is in opposition to the Political dogma of Slashdot they are moderated back into their ghetto. The person becomes moderated, not their opinion.
This is just the thin end of the wedge. Although, as memes are transient, it is difficult to silence an opinion, it is trivial to silence a person. Upon the rise of National Socialism in Germany, the populace were motivated by propaganda into entering the Jewish Ghettos en masse with the sole purpose of causing as much damage as possible to Jewish businesses and residences. The infamous Krystalnacht. This parallels far too accurately with the Slashdot Editor's non-discouragement of the act of IP-banning. As mentioned above, this occurs when an individual user's postings are repeatedly moderated down in a short period. They then become incapable of posting any contributions themselves. In essence, they have been silenced, regardless of the worth of their postings.
Of course, the editors claim that Meta-Moderation is the panacea to solve this clear abuse of moderating privledge. But if a Meta Moderator is presented with a list of moderations that they disagree with, such as this targetted 'silencing' mentioned above, they cannot note them as such without in turn becoming an 'Undesirable' themselves, as too many Disagreements with the Moderation groupthink also result in loss of Karma.
Throughout all of this, the Editors have claimed a false level of detachment from the acts of moderation. In a same way, as the National Socialists gathered their power and began working on their Elite Political wing, The SS, they too remained detached from the civilians working in their name. Why? Because after inspiring the populace to such acts of violence through their propaganda, they could then claim that they were only giving the people what they want.
And then began the next stage of the atrocities. The Gestapo, Germany's secret police, were recruited from the best and the brightest of Germany's elite. As is the case now, the best and the brightest of society were often shunned and ostracized in society. In essence, the Gestapo were a tightly controlled 'Geek Army' of intelligent young men with a burning, seething resentment of normal society. The perfect psychological profile for the cause.
After all, give a normal man (with an active sex life) a gun and he will use it responsibly in self defence. Give a geek a gun and he will behave according to his sociopathic logic and hatred of the world he arrogantly presumes to be distant from. Ask yourself why Slashdot flat-out justified the murder of innocents at Columbine. And then ask yourself why, even for a brief moment, you almost began to sympathize with the killers after Jon Katz' manipulative and pseudo-emotive Hellmouth articles.
How this relates to Slashdot is clear. The majority of Slashdot posters are Sociopathic OSS zealots, unable through lack of social finesse or personal hygiene to mate regularly. Sexually and emotionally frustrated and with grudges to bear, incapable in their blinkered sense of self-righteousness of accepting any dissenting opinion than the OSS cause. Now give these people the opportunity to Moderate these dissenting opinions. Of course they are going to want to silence them, by any means necessary.
Now, the Slashdot Editors have admitted taking this silence of opinion into the next stage, by moderating whole swathes of 'undesirable' posts negatively. And then permanently banning anyone who moderates said posts back up from moderating EVER again! The result of this new policy? The few Moderators with any sense of fairness and decency are removed from the moderation pool, leaving the power ENTIRELY in the hands of the zealots. Clearly, positive moderation is discouraged under this regime, which is a direct parallel with the way the National Socialists moved their own sympathisers into positions of power throughout Europe.
So how does this compare to the genocide performed in Auschwitz and their ilk? I would like at this point to explain that in NO way do I wish to belittle the horrors that were performed in the name of National Socialism. The six million innocents killed were a cry of anguish from which humanity may never recover. And a vast distance in time and scope from a few banned posters on some shitty "My Favourite Links - now with comments" website. But these stories need to be retold before the horror is lost forever.
For the only thing that we learn from history is that we never learn anything from history. Time and time again, the St. Vitus dance is played out, we make the same mistakes, and we perpetually fail to see the warning signs.
So, moderators, the next time you moderate a rational, insightful post down, maybe because you disagree with it or because it's posted by a 'Known Troll', just ask yourself this...
--
hemos_: Alterslash [alterslash.org] is illegal. And is violating copyright.
"Why did they cancel my favorite Sci-Fi show? I downloaded ALL the episodes!"
Pi isn't different for different geometries, its just the series converge slower for the higher dimentions.
The only way pi could be different was if space itself was not "flat" but curved.
So he's all set to prove they're the same. A simple web page shows they're different.
Doesn't sound like a very exciting story to me.
I minored in math and I'm not sure just what is meant by Pi in the fourth dimension. By definition a circle is a two dimensional object. By definition Pi = C/r where C is the circumference of the circle, and r is the radius of the same circle. Therefore Pi by definition is the ratio of two properties of a two dimensional object.
Which leaves me (or us) with the question of what does the fourth dimension have to do with the value of Pi?
Just showing my ignorance...
"Oh drat these computers, they're so naughty and so complex, I could pinch them." --Marvin the Martian
If you did more cycles you would see that all the pi's are about equal and closer to the real pi. It just uses a brute force method so you need more cycles to see that they are more equal.
Pi is 3.1415926...., not either of the values claimed in the article. Approximations of pi could perhaps have the values claimed in the article. I could approximate pi as 3, but that wouldn't make pi = 3.
"Those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded."
i had to go through the source to figure out what they meant by pi in higher dimensions. at first i assumed it had to be something interesting, since they bothered to post it, but it's not. they're just useing simple calculations to find the volume of spheres and hyperspheres, and plugging that into the known, proven formulas to find pi.
for a circle, A=pi*r^2
for a sphere, V=4/3*pi*r^3
for a hypersphere, V=pi^2*r^4/2
by "proving" that pi is the same in multiple dimensions, they merely demonstrate these well-established identities. of course, since they're using a clumsy "brute force" method to initially calculate the volume, they're not actually proving anything, since they only get an approximate answer.
#define F(x) int main(){printf(#x,10,#x);}
F(#define F(x) int main(){printf(#x,10,#x);}%cF(%s))
I WILL KICK YOU'RE FUCKEN ASS!!!!
You are obviously a paki. I suggest reporting yourself to the authorities immediately.
"Why did they cancel my favorite Sci-Fi show? I downloaded ALL the episodes!"
It seems that the Slashdot editors agree with my anti-islamic stance. They are keeping my posts marked high.
Who's going to a barbecue tonight? I am! Hopefully we'll be able to roast a small muslim child alive.
"Why did they cancel my favorite Sci-Fi show? I downloaded ALL the episodes!"
Math nerds can calculate the percentage error.
Why the percentage error is exactly 3.14157429...%
Pi is defined to be the ratio of the circumference of a circle to its diameter. pi = c/d. Okay, we all know that.
Using calculus, you can determine the area of a circle in terms of pi.
Using calculus, you can determine the volume and surface area of a sphere in terms of pi.
And so on, and so on. Therefore, why would anyone think pi would be any different for higher dimensions? Are they also speculating that calculus is a load of poppycock?
OOOOOAAAAHHHHH (drool) N-Dimensional Pi......
"I would rather have your time than your money" --Henry Rollins Jan 14 2003 on the topic on internet file trading
You fuckhole, that's not Pi, Pi is 3.141592654. What the fuck are you slashdot losers smoking? It doesn't matter a rat fuck "how many dimensions" it is... Pi == Pi.
pi == 3
God told me so
I have been pwned because my
Thats because they didn't run the calculation for any real length of time. Behold:
./2d3d4d_1
--[~]--
INPUT
Calculate the Pi for circle, sphere and hypersphere.
Let us start the verification for 2d, 3d and 4d, Give Cycles
Cycles = 100000000000
CIRCLE
Area of circle by brute force method = 78539815867
Radius = 158113.883008
Calculated value of Pi = 3.141593
SPHERE
Volume of sphere by brute force method = 52359877534
Radius = 2320.794417
Calculated value of Pi = 3.141593
HYPERSPHERE
Enclosure of Hypersphere by brute force method = 30842511725
Radius = 281.170663
Calculated value of Pi = 3.141593
The longer it runs for, the closer it gets. Whether or not this actually proves anything is, of course, up to debate.
Paranoid
Bwaahahahahaa.
I'm impressed!
Thats the real aim of the program. The C code wcich you ran is the actual verion. The Php one is for idiots without compilers who cancot download and compile the simple bit of code. I advice all the sceptics here to please download the original code and give it a try with BIG numbers.
Yeah, I figured. I was surprised a PHP version existed at all, because you wouldn't want to run such hefty calculations on the server side anyway - make the clients do it. In any case, there is a .exe version available for download, suitable for most compiler-deprived idiots.
The Pi it calculates doesn't seem to have many significant digits... is there any way the algorithm can be reworked to use a BigFloat library or something, for better precision? And perhaps fork off some children to do the actual work, so the load will spread across my MOSIX cluster and SMP boxes? Even if it just used one process per dimensional calculation (one each for 2d, 3d, 4d), the run would have finished in 20min rather than an hour... =)
Paranoid
Bwaahahahahaa.
pi in 2d is defined in terms of a ratio of the circumference of a circle to it's diameter.
pi in 3d is conventionally defined in terms of the ratio of the 2d circumference of a circle to it's 2d diameter. It's pi, damn it, it is a constant.
But you can also use 4piR^2 for the surface area of a sphere, and 4/3piR^3 for the volume, which has been mathematically proven for quite some time. The authors of this program appear to be defining 3D pi wrt these ratios... physics geeks will note that the units balance out nicely.
As for 4D pi... I can only assume the ratios are something like npiR^3 surface and mpiR^4 for volume, seeing as how the units must balance and hypergeometry wasn't an emphasis at my college.
Still, though. Writing programs to calculate pi is a fun little project that everyone seems to do at some point in their high school or college career. I did pi in HS. In college I did 4D Tic Tac Toe. These people appear to be doing both. More power to them.
This Sig is a mnemonic device designed to allow you to recognize this author in the future.
As far as I know pi is just a number: it exists and it has his own value, like 666, sqrt(2), e, i, etc.
I suppose that the main reason why it has a name is that lots of geometrical constant happen to belong to Q(pi) (i.e. the minimal subfield of the complex field that contains all rational numbers and pi); since Q(pi) is also an (infinite dimensional) vector space on Q, and most of the useful constant belongs to the subspace generated by 1 and pi, we can just write them as a*1+b*pi and we're able to work with them in an easier way.
The "definition of pi" is just like the definition of any other real number, as a Dedekin section (not sure it's the name you use in english), and it happens not to say much about its value. Then when you have real numbers you can say whether two of them are the same or not, so you can demostrate that, e.g. the ratio between circonference and diameter of a circle is the same number as the limit of a few series, but calculating an aproximation of the first or some term of the second won't help much in this demonstration.
The main point of the project seem to dabble with different algorithms to calculate the decimal development of pi. While this is interesting, they are in fact very low level since the current record is in the millions (billions ?) of number. There are whole books dedicated to this sole topic.
Xavier
Do I make sense? Please report if not.
So, someone got fed up running endlessly in circles, and decided that he wanted another slice of pi. Got four dimensions, and did a new number.
I just what type of pi. Personally, I go for chocolate cream.
Have you read my journal today?
from http://www.joyofpi.com/pifacts.htm
Pi.
1.The Greek letter P or p, corresponding to the roman p.
2.A number, represented by said letter, expressing the ratio of the circumference of a perfect circle to its diameter. The value of pi has been calculated to many millions of decimal places, to no readily apparent purpose: no perfect circles or spheres exist in nature, since matter is composed of atoms and therefore lumpy, not smooth. Nature
herself sometimes takes to rounding off the more extreme decimals of numbers when they get sufficiently small, as Prof. Heisenberg has pointed out. However, the continued extension of pi provides a harmless exercise of computer power which would otherwise be misused playing Quake or surfing pointless web sites.
He was referring to the difference between the values of pi for different dimensions. The question he was addressing was whether pi was the same for every dimension. He offered a value for 3D, a different value for 2D, and said you could calculate the margin of error.
"Those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded."