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University students - 1989 MATH battle over function degrees of freedom


What are degrees of freedom in statistical mathematics. explain in ...

6 answers - Aug 3, 2006
Top answer: The degrees of freedom are the number of extra numbers you need to specify your data completely, after you have provided a summary of your data.

degree of freedom (mathematics and statistics) -- Britannica Online ...

In mathematics, any of the number of independent quantities necessary to express the values of all the variable properties of a system. 

 A system composed of a ...........

Nature is comprised of many components. College textbooks describe many of these facets of existence --> biology, physics, chemistry, math, geology, biochemistry,etc.
If Nature has a problem in one of these areas ...it may use humanoids to express that  conflict.

Many authors expressed that concept ...of human messenger vehicles on EARTH LAB ...... EARTH Theater  ...EARTH equations Theater of WAR.
2 major authors  clearly explained  the situation.

Around year 1600

All the world's a stage - Shakespeare Quotes

www.enotes.com › LiteratureShakespeareShakespeare Quotes
Shakespeare Quotes - All the World's a Stage. ... And all the men and women merely players; They have their exits and their entrances, ... Shakespeare wrote As You Like It. 

Around year 1865

Who Stole the Tarts? | Alice's Adventures in Wonderland, by Lewis ...

Alice's Adventures in Wonderland, by Lewis Carroll: Who Stole the Tarts? ... Here one of the guinea-pigs cheered, and was immediately suppressed by the ...

Here we look at the math and bio-math dimensions   of Nature and the EARTH geography  area of a major math battle .....the 1989 battle of Tiananmen Square, China.

Thus we have in 1989.......the Shakespeare performance in China

year 1600 ---> All the World's a Stage. ... And all the men and women merely players; They have their exits and their entrances

year 1989  ---> All the World's a Stage at Tiananmen Square . ... And all the men and  and women merely players (Chinese university students); They have their exits and their entrances (the entrance of the  Chinese ARMY  on  JUNE 4 ,1989 into the Tiananmen Square  WORLD STAGE).

Humans are symbolic processors. We process language symbols.  In the geography country of China, Asia that would comprise the Chinese language,  arithmetic, geometry, philosophy, history, etc. 
Humans are subsets embedded within the many dimensions  of Nature and Nature's multi-faceted FORMATS of expression.

Tiananmen   Square  
www.infoplease.com/spot/tiananmen.htmlA massive demonstration for democratic reform, begun on Tiananmen  Square by Chinese students in  April, 1989 .........

Let's try to understand this EVENT .....in the context of  our existence on EARTH's geography surface that  can be explained in terms of   mathematical-physics space/time  AND  our human interaction with math and statistics.

Hotelling's T-squared distribution -

In statistics Hotelling's T-squared distribution is  important because it arises as the distribution of a  set of statistics which
are natural generalisations of the .
The distribution - Hotelling's T-squared statistic - Hotelling's two-sample T ...

Let's  look at the data sample of Nature's.  Nature's  social engineering  experiment was  comprised of students and other groups in China, Asia in  year 1989

Beijing Hotel - Wikipedia, the free  encyclopedia

en.wikipedia.org/wiki/Beijing_HotelThe Raffles Beijing Hotel, occupies two of the former blocks of the Beijing Hotel ... Many foreign journalists were based in the hotel during the spring of 1989.

We see that  the EARTH LAB identifiers  HOTEL  + humanoid earthLING groups  +  Tiananmen Sqaure  provides an ideal  geography location with proper noun identifiers for Nature.        Nature sees the symbolic/conceptual  data stream  ---->  HOTEL  + LING + Tiananmen Square -->  thus giving  Nature the ideal pointer to   HOTELLING's T-square  statistical  TEST setting.

The event ..... had various issues and  people involved.

In April 1989, triggered by the death of deposed Communist Party General Secretary Hu
, a liberal reformer, mass gatherings and protests took  place in and around Tiananmen Square.[5] At its   height, some half a million protesters assembled there. The  demonstrations,  consisting of local working residents as well as  students,[6] called  for government accountability, freedom of the press, freedom of  speech, and the   restoration of workers' control over industry.[7]   Peaceful protests also occurred in other cities, such as Shanghai and Wuhan, while looting and rioting broke out in Xi'an   and Changsha.[8]

The movement lasted for about seven weeks. The government   initially   attempted to appease the protesters through concessions, but a    student-led hunger strike galvanized support for the    demonstrators around the country. Ultimately, Deng Xiaoping and other party elders resolved to     use force to suppress the movement.[9]
   authorities declared   martial   law on 20 May.
Thus we see the concepts that led up to the JUNE Fourth incident.   Nature's social engineering INTELLECT and it's bio-math tolerance ellipse reached some breaking  point ...and the Chinese ARMY was called in on JUNE, 1989.

The Tiananmen Square protests of 1989, also known as the June Fourth
Incident in Chinese,[1] were   popular demonstrations crushed by China's army on 4 June 1989,  when China's
leaders ordered the army to force the protesters out of Tiananmen Square in Beijing. On their way to the Square, soldiers   killed protesters in unknown numbers, and the crackdown became known as the
Tiananmen Square Massacre or the June 4 Massacre

Tiananmen Square massacre   takes place — History.com This Day ...  
On June 41989,
however, Chinese troops and security police stormed through Tiananmen
, firing indiscriminately into the crowds of protesters. Turmoil ...

BBC   ON THIS DAY | June 4 | 1989:
Massacre in Tiananmen  Square

Massacre in Tiananmen
. Several hundred civilians have been shot dead by the Chinese army
during a bloody military operation to crush a ...

We have the empirical data of the bio-math  EVENT,  that provides CLUES about the Earth and its cities and populations .....as elements of sample space.  Thus, we see the statistical  TESTING done by NATURE as it reviews society quality control.      
This concept is used  in the  manufacturing of widgets  on a production line...say 10,000 widgets a day.  For every batch of 1,000 widgets.... a sample of  20 widgets is examined for quality control ....... and then  if ERRORS are detetcted .... decisions are made whether to accept or reject the batch of 1000 widgets.

Nature's bio-chemistry engineers and language engineers manufactured the human,  the Central Nervous System symbolic processor, and the foundations of thought and logic..   Nature is very inetrested in the quality control.  Thus Tiananmen Square is one example of Nature's TEST. 

Let's summarize the MATH CLUES and their relationship to the 1989 situation.

CLUE ---> EARTH geography  location LINK to symbolic life......math  equation identifier NOUNS

EarthLINGS ---> ling's T-squared distribution -
Beijing HOTEL  ---> Hotel    T-squared distribution -  Wikipedia, 
Tiananmen Sqaure ---> Hotelling's T-squared distribution

Beijing Hotelling's_Tiananmen-squared_distribution
Beijing Hotelling's_Tiananmen-------red_blood  distribution on June 4,1989

In statistics Hotelling's T-squared distribution is   important because it arises as the distribution of a set of statistics which are   natural generalisations of the ... 
The distribution - Hotelling's T-squared statistic - Hotelling's two-sample T ...

CLUE ---> key word student ........ their involvement in the TEST Hotelling's <i>T</i>  squared 
www.itl.nist.gov/div898/handbook/pmc/section5/pmc543.htmHotelling's T squared. Hotelling's T2
distribution, A multivariate method that is the multivariate
counterpart of Student's-t and which also forms the basis for certain 

CLUE --->  Chi-square translates to ...maps to ...China Tiananmen Square

Two-Sample Hotelling's  T-Square 
sites.stat.psu.edu/~ajw13/stat505/fa06/11.../01_2sampHotel.htmlNow we are ready to define
the Two-sample Hotelling's   T-Square test statistic. ... this test statistic will be   approximately
 chi-square distributed with p degrees of 

CLUE----> Two -sample   ...... 2 groups ...students VS government

Two-Sample Hotelling's T-Square 
sites.stat.psu.edu/~ajw13/stat505/fa06/11.../01_2sampHotel.htmlNow we are ready to define the Two-sample Hotelling's  T-Square test statistic

CLUE--> mean --> English word can have additional definitions ..as = mean / nasty / cruel
Hotelling's  T-Square 
Hotelling's T-square is a statistic for a
multivariate test of differences between the mean values of
two groups. The null hypothesis is that centroid s don't  differ ..

CLUE -> Centroid --> applied math --> Central Communist Party of China

Hotelling's T-Square is the most common,
traditional test where there are two ... The T-Square result   will still have the same F value, degrees of freedom, and ...   F-test shows the centroid (vector) of means of the   dependent variables is not the ...

Thus we see an interesting puzzle about our relationship with Nature's mathematics and statistics dimensions. 

Below, a display of a  IRON TANK  with a vector of means ...nasty artillary cannon  ......messages for  THINK TANK