Thanks to Donna for the interest and for the information.
Ordinal Fractions is an improvement to the idea behind the Universal Decimal
Classification (UDC). Consider this example from wikipedia. 51 Mathematics
510 Fundamental and general considerations of mathematics
511 Number theory
512 Algebra
514 Geometry
517 Analysis
519.1 Combinatorial analysis. Graph theory
519.2 Probability. Mathematical statistics
519.6 Computational mathematics. Numerical analysis
519.7 Mathematical cybernetics
519.8 Operational research (OR): mathematical theories and methods The UDC
has two flaws:
- The digit zero is used for counting. ("Fundamental and general
considerations of mathematics" has number 510, meaning the first subconcept
below "Mathematics".)
- The space is the wild card character. (Number theory, 511, is a subset of
Mathematics, 51.)
So the UDC system is hierarchical, but does not include tables.
Ordinal fractions use zero, not for counting but as wild card character. The
price to pay is that ordinal fractions is not a decimal system. Only the
one-digit ordinal numbers 1 to 9 are used for counting.
Using ordinal fractions the above example may look like this. 5100 Mathematics
5111 Fundamental and general considerations
5112 Number theory
5113 Algebra
5114 Geometry
5115 Analysis
5121 Combinatorics
5122 Graphs
5131 Probability.
5132 statistics
5141 Computational
5142 Numerics
5151 cybernetics
5152 Operational research
5161 theories
5162 methods Tables are expressed like this using ordinal fractions 00 table
01 left column
02 right column
10 upper row
11 upper left
12 upper right
20 lower row
21 lower left
22 lower rightThis elementary structure cannot be addressed by the UDC.
/Bo.
Den 1:32 torsdag den 7. juni 2018 skrev Donna Y <dy...@sympatico.ca>:
Typically you begin at the beginning—the new century begins right after
midnight, right after the last day of the 99th year.
I have no clue why you describe a system where
> Let me tell you how calendars are treated with ordinal fractions. Consider
> the years from 1 to 5000. Any year is a year in a decennium in a century in a
> millenium, The year 2010 is the tenth year in the first decennium in the
> first century in the third millenium.
> (4$10)&#:&.<:2010
> 3 1 1 10
> As 0 is not an ordinal number, ten objects should not be numbered neither
> (i.10) nor (>:i.10) , but (10#.>:2 5#:i.10)
>
> The year 2010 is the fifth year of the second half of the first decennium of
> the first half of the first century of the first half of the third millenium.
> 10#.(7$5 2)&#:&.<:2010
> 3111125
> This ordinal fraction corresponds to a condition like this:
> (M=3)*.(D=1)*.(C=1)*.(L=1)*.(X=1)*.(V=2)*.(I=5)
> Digit zero is position-filler, so 3110000 is "the 21st century",
> corresponding to the condition (M=3)*.(D=1)*.(C=1).
> There are
> 5000 = */7$5 2
> individual years from 1 to 5000, and
> 34992 = */>:7$5 2
> subsets are adressable as ordinal fractions. The total number of subsets of a
> 5000-set is 2^5000, so being an ordinal fraction is an exclusive property of
> a subset.
> This offers a simplification of data structures. The J concepts of arrays,
> sparse arrays, and boxed arrays, are unified as ordinal fractions. Also
> relational databases are simplified, because there is only one method of
> adressing, rather than at least three.
In decimal years the 9th year would roll into the 1st decade and 2010 is 2 0 1
0 not 3 1 1 1o—it is into the third millennium by one decade
In your example the year is just decimal number—if you wanted for some reason
not to use 0 as a placeholder you could say
2 millennia and 1 decade which is one decade into the third millennia.
Measuring a time in weeks, days, hours, minutes, seconds, and milliseconds is
mixed-radix—but in that system. Each digit has its associated base:
Each week is 7 days, each day is 24 hours, each hour is 60 minutes...
You can’t throw in months and years because those are not integer multiples of
weeks.
A mixed radix numeral system--non-standard positional numeral systems in which
the numerical base varies from position to position.
Decimal fractions were introduced by Stevin in 1585. Each digit has base 10.
On the one hand decimal fractions could not even express ⅓—on the other hand
you could determine an approximation—on the other hand
decimal fractions give a deeper understanding of numbers.
I read you paper (or introduction). You move between the concept that ordinals
do not include zero, to wanting to point to a position that is between two
points
on a scale, to using a 3vl logic equivalent to P3 where the truth values are
True, False and both (slightly different from SQL which is a K3 system with
True, False and unknown). I do
not follow how you want to use your “ordinal fraction” here—perhaps by
introducing a concept from fuzzy logic but it uses real numbers (decimals)
between 0 and 1.
According to Lukasiewicz statements about the past and present are true or
false and cannot be altered but statements about the future are contingent—you
might have a measure of probability.
There are terms used to describe data (as first described in 1946 for Social
Science to create rules for statistical analysis):
Nominal (for example an ID number or Phone number or Hockey jersey number)
Ordinal (such as rank of students by height—the students can be ordered but the
difference in height between ranks is unequal)
Interval (there is a set interval as with temperatures in degrees C--the
intervals between each degree value are equal and values can be ordered)
Because of leap years and leap seconds an interval of i year is not exactly
equal for all years—that has to be considered in calculations according to how
results are to be used
Ratio (Like net worth where 0 means no money)
These categories were created to emphasize how different numerical data should
be handled—numbers representing calendar and time data can require special
handling too.
Donna Y
dy...@sympatico.ca
> On Jun 6, 2018, at 3:01 PM, 'Bo Jacoby' via Chat <c...@jsoftware.com> wrote:
>
> Interesting! Is the zeroth century from year -99 to year 0, or from year -100
> to year -1, or from year 0 to year 99?
>
> Den 20:54 onsdag den 6. juni 2018 skrev Donna Y <dy...@sympatico.ca>:
>
>
> Notice the the year 0 in Astronomical year numbering is
>> Fred Espanak of NASA <https://en.wikipedia.org/wiki/NASA> lists 50 phases of
>> the moon within year 0, showing that it is a full year, not an instant in
>> time.
>
> This zero in not nothing. It is like 0 degrees in C or F thermometers but not
> Kelvin where absolute 0 is meant to represent Absolute Zero with the
> molecules not moving. (only recently they have talked of temperatures below
> Absolute Zero since it is an average and they are now capable of sorting
> molecules
>> the team also adjusted the trapping laser field to make it more
>> energetically favourable for the atoms to stick in their positions. This
>> result, described today in Science1
>> <https://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146#b1>,
>> marks the gas’s transition from just above absolute zero to a few
>> billionths of a Kelvin below absolute zero.
>> https://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146
>
>> the sub-absolute-zero gas is that it mimics 'dark energy', the mysterious
>> force that pushes the Universe to expand at an ever-faster rate against the
>> inward pull of gravity.
>
>> Interval: Numerical values without a true zero point. The idea here is the
>> intervals between the values are equal and meaningful, but the numbers
>> themselves are arbitrary. 0 does not indicate a complete lack of the
>> quantity being measured. IQ and degrees Celsius or Fahrenheit are both
>> interval.
>>
>
>
> Donna Y
> dy...@sympatico.ca
>
>
>> On Jun 6, 2018, at 5:00 AM, PR PackRat <hhpack...@gmail.com> wrote:
>>
>> On 6/5/18, Jose Mario Quintana <jose.mario.quint...@gmail.com> wrote:
>>> Let us do it the other way around; pick two dates with a similar timespan
>>> using the BC/AD world standard.
>>> How many years, months and days have passed between them? Does the
>>> question even make sense? Forget about it. Let us try another one: how
>>> many days have elapsed? Can you show us how to perform the calculations in
>>> J?
>>
>> I have a slight background in astronomy and how it has a Julian day
>> number for every date.
>> You "win". See the Wikipedia article, "Astronomical year numbering"
>> <https://en.wikipedia.org/wiki/Astronomical_year_numbering>.
>>
>> Harvey
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