Batten-Number Space:


Visual link to BatNum Java programme

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To start Java Applet -click on icon
(To bring up process menu: right click on Java image  when Applet is running)
Use left mouse button to select menu options
Use browser navigation buttons to close or leave the process window

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Programme Notes:

Basically,  Batten-Number Space plays with "number bases":
i.e. the number of symbols used to represent a number. "10" (in base ten) can be (for example) "1010" in base 2, "101" in base 3, "22" in base 4 -or "20" in base 5 (which means 2*5 + 0)....

Base 5 is of course the system used by both Roman Numerals and the abacus. People often think that Roman Numbers are rather difficult to use -but I suspect they were very efficient for people who use an abacus (which the Romans of course did).

Because we have 5 fingers on each hand (and 5 toes on each foot) people around the world tend to use either base 10 -or base 20.

The number system in the Danish language still use a rudiment of an old numeral system, mainly between 49 and 100:

50  = 2.5 times 20  = half the third times twenty = half tre sinds tyve = today: "halvtreds" (sinds = times)
60  =   3 times  20  = tre sinds tyve = tres
70  = 3.5 times 20  = halv fjerde sinds tyve = halvfjerds
(75 = fem(5) og halvfjerds(70) they place the singular digit first)
80  =    4 times 20  = fire sinds tyve = firs
90  = 4.5 times 20  = halv femte sinds tyve = halvfems
(but 100 is *not* 5 times 20 = femte sinds tyve = fems

(with thanks to Sven Börtz)

The French also work in a similar way: So "seventy" in English becomes "three times twenty plus ten" in French. The English Bible refers to the life of a human as "three score plus ten" (a score being 20).  I understand the Mayan calendar worked with base 60 (and 20)...

In modern times,  we still have 60 seconds in minute and 60 minutes in an hour -and 60 * 6 = 360 degrees in a circle (which is a small miscalculation of the number of days in a year).

The lunar month is  28 days long..... (which is 4 * 7 days)...... \

The ancient (British) pre-metric systems used 16 inches to the foot, 3 feet to the yard, 16 ounces to the pound and 2 Pints to the Quart -and 4 Quarts to the Gallon,

Nowadays, only computers, and the nerds that serve them, use bases other than 10, it seems.....

I believe there is a great conceptual; poverty in modern life!


Operating with different number bases changes the number of "bits" (the number of "places" used to represent the complete number.) One could perhaps consider each "bit" to be a"'dimension of space".


Batten Numbers:

When trying to graphically represent the various bit patterns (which, theoretically can have an infinite number of bits) -I decided that a circle was the best shape to use as a basis, because it could be be divided (theoretically) into an infinite number of degrees. The "bits" could then be represented by the rotational divisions of the circle.

In practice, the difference between the least significant bit and the most significant bit (signifying the difference between 10 and 01) was difficult to see. So the dotted arc-segment was added to indicate the most significant bit -and the direction of rotation downwards.

However, the initial ambiguity suggested that it might be interesting to take the various bit rotations -and translate them back into base 10 numbers. Presumably changing number bases would also change the bit patterns -and the (Batten) set of numbers that have similar bit patterns (in that base -for that number).

Similarly -for each number in the set -there is an "inverse" number that can be formed by subtracting the value of each "bit" from the "base" value (i.e. the maximum value for that bit).



Personally, I find such things somewhat interesting and the (logic of the) structure rather beautiful..... but what does it mean? I've no idea......

Except that the idea of numbers sitting in a row from -infinity to +infinity is only a partial truth....  Numbers have a "spatial" aspect -that is, no doubt, closely related to their mathematical qualities -just as a human's physical characteristics are also relevant to their activities as humans.....

Visual link to BatNum Java programme   Visual link to BatNum java Programme

The menu options:

(when programme is running, right mouse click on the image area to make the control panel visible)

"Mode"
(Set Function type)
"Type"
"Basic Principle"                        -Explores the basic mapping into different bases
"Numbers 0 - 83"                       -Maps the first 84 numbers into selected base                 
"Numbers 80 - 163"                   -Maps the numbers from 80 - 163 into selected base   
"Bases 2 -16"                              -Shows selected number in a variety of bases
"Bits","2 Dimensional Bits"     -Represents 2 bits in 2-Dimensional space
"3 Dimensional Bits"                 -Represents 3 bits in 3-Dimensional space
"Batten Numbers"                     -Explores the "Batten" numbers
"Moire.1"                                      -Changing the spacing creates a new image
"Moire.2"                                      -Changing the spacing creates a new image for a different process


"Values"
(Set Dimensions for figures)
"Dimensions"
"Number"          -Select number (if appropriate)
"Base"                -Select base (if appropriate)
 "Bits"                -Select bits (if appropriate)


"Flow"
     (clear image or reset process)
"Process/Image"
"Clear"       -Removes Existing Image without resetting process
"RESET"    -Removes Existing Image and resets process


Visual link to BatNum Java Programme

---------------------------------------------------------

To start Java Applet -click on icon
(To bring up process menu: right click on Java image  when Applet is running)
Use left mouse button to select menu options
Use browser navigation buttons to close or leave the process window

---------------------------------------------------------

Trevor Batten, Baclayon, 2014

Space for Change
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