beenary numbers https://m.phys.org/news/2018-06-scientists-bees-concept.html
On Fri, 8 Jun 2018 07:40 'Bo Jacoby' via Chat, <c...@jsoftware.com> wrote: > Cardinal numbers (0, 1, 2, . . .) are including 0 (zero). > Ordinal numbers (1, 2, 3, . . .) are starting with 1 (first). There is no > "zeroth". > There is arithmetic of cardinal numbers (including the J verbs + * ^ ! ) , > but there is no arithmetic of ordinal numbers. > The codes of the UDC are important numerical objects, but they are neither > integers, nor decimal fractions, nor rational numbers, nor real numbers, > nor complex numbers, nor quaternions, nor vectors, nor matrices, nor > functions, nor operators. They have been neglected by mathematicians. > A new kind of numbers must be considered. I dubbed them 'ordinal > fractions' . > A cardinal number, such as 'one', counts a set. > An ordinal number, such as 'the first', identifies an element in a set. > A cardinal fraction, such as 'one half', measures a part of a totality. > An ordinal fraction, such as 'the first half', identifies a part of a > totality. > Consider for simplicity the binary, rather than the decimal, notation. > one = 1 = 0001. The digit positions, right to left, indicate ones, twos, > fours, and eights, and the digit values are one-digit binary cardinal > numbers, 0 and 1. > the first = 1 = 0001. This is the cardinal number corresponding to the > ordinal number in question. > one half = 0.1 = 0.1000. The digit positions after the binary point > indicate halfs, fourths, eights, and sixteenths, and the digit values are > one-digit binary cardinal numbers, 0 and 1. > the first half = ????? > My solution to this problem is > the first half = 1 = 1000 > the second half = 2 = 2000 > > the first fourth = 11 = 1100 > > the second fourth = 12 = 1200 > > the third fourth = 21 = 2100 > > the fourth fourth = 22 = 2200 > > the odd fourths = 01 = 0100 > the even fourths = 02 = 0200 > the sixteenth sixteenth = 2222 > Note that the digit positions indicate halfs, fourths, eights, and > sixteenths, and the digit values are either 1 meaning first, and 2 meaning > second, or 0 meaning both. 1000 means: first half, both fourths, both > eights, both sixteenths. 'both' goes without saying, just as 0 goes without > saying. 1000 = 1 = first half. That is one reason for choosing 0 for > 'both'. > I did not know the words hyponymy and hypernymy. Thanks! That is just what > I need. > In logic I let 1 and 2 represent True and False. 0 means unknown or > unimportant. > > The Transylvanian problem: > 0001 Minna is human > > 0002 Minna is vampire > 0010 Minna is sane > 0020 Minna is insane > 0100 Lucy is human > 0200 Lucy is vampire > 1000 Lucy is sane > 2000 Lucy is insane > Check the 2^4 ordinal fractions from 1111 to 2222 against the data. (I > have not done it) > Thanks! Bo. . > > > > > > > > > > > > > > > > > Den 5:58 fredag den 8. juni 2018 skrev Donna Y <dy...@sympatico.ca>: > > > Can we agree on definitions > > Ordinal numbers and Cardinal numbers are Natural numbers which do no > include the number 0. The Natural numbers are well ordered. > Whole numbers are the Natural numbers and 0. 0 is the least element of the > Whole numbers. > Integers are Whole numbers and Negative signed Natural numbers. (-n + n= > 0 Zero is not a positive or a negative integer—0 has no sign.) The set of > integers has no least element. > Real numbers are continuous and complete and can be rational or > irrational—rational numbers are integers and fractions, irrational numbers > cannot be expressed as a ratio of two integers. > Imaginary numbers are not real—they exist in another dimension—root > negative 1 or i, complex numbers have real and imaginary components. > > Tables are two dimensional arrays. > > The basic structure of UDC is hierarchy but it could be viewed in other > ways—as you said yourself. > > Are you using tables where Rows are records and Columns are attributes? Is > there a primary key? > > I am not sure where your Ordinal Fraction comes in but a computer > application of UDC would need full integration of information retrieval > (IR) features into a database management system (DBMS). > > Right truncation specifies hypernomy (is a—as in number theory is a subset > of mathematics)—I copied this table but from my view forms of higher degree > is not a subset of diophantine equations. > > Table 1: > > 5: mathematics and natural sciences > 51: mathematics > 511: number theory > 511.5: diophantine equations > 511.57: forms of higher degree > > What is the precise reason you chose to use 0 as a wild card?—why not * or > # or & or … ? What advantages are derived by using 0? For example when you > use boolean logic the 0 and 1 can represent False and True and then the > result vector of 0 and 1 can be used for selection. > > hat does this even mean? > > > For example: 0=0 and 0>1 and 1<0 and 10<>01 and 1><2. (meaning that the > whole is equal to the whole, and the whole comprises the first part, and > the first part is part of the whole, and the first half is compatible with > the odd fourths, and the first part is disjoint with the second part). > > The notation for ordinal fractions makes ordinal fraction arithmetic > easy, just as the notation for cardinal numbers makes cardinal number > arithmetic easy. > > Keep asking! > > > Maybe you can show how Ordinal Fractions can be applied to the problem > below: > > PUZZLE BREAK > > Inspector Craig Visits Transylvania > Inspector Craig of Scotland Yard was called to Transylvania to solve some > cases of vampirism. Arriving there, he found the country inhabited both by > vampires and humans. Vampires always lie and humans always tell the truth. > However, half the inhabitants, both human and vampire, are insane and > totally deluded in their beliefs: all true propositions they believe false, > and all false propositions they believe true. > The other half of the inhabitants are completely sane: all true statements > they know to be true, and all false statements they know to be false. Thus > sane humans and insane vampires make only true statements; insane humans > and sane vampires make only false statements. > Inspector Craig met two sisters, Lucy and Minna. He knew that one was a > vampire and one was a human, but knew nothing about the sanity of either. > Here is the investigation: > Craig (to Lucy): Tell me about yourselves. > Lucy: We are both insane. > Craig (to Minna): Is that true? > Minna: Of course not! > From this, Craig was able to prove which of the sisters was the vampire. > Which one was it? > — From Logician Raymond Smullyan > > > Donna Y > dy...@sympatico.ca > > > > On Jun 7, 2018, at 5:55 PM, 'Bo Jacoby' via Chat <c...@jsoftware.com> > wrote: > > > > > > "You do not show how to access particular rows or columns or elements > from a table". > > The table, and the table name, is addressed by 00. > > The left column, and the left column header, is addressed by 01. > > The right column, and the right column header, is addressed by 02. > > The upper row, and the upper row header, is addressed by 10. > > The upper left table entry, and its data content, is addressed by 11. > > The upper right table entry, and its data content, is addressed by 12. > > The lower row, and the lower row header, is addressed by 20. > > The lower left table entry, and its data content, is addressed by 21. > > The lower right table entry, and its data content, is addressed by 22. > > > > "without knowing the number of rows or columns." > > In the example there are two rows and two columns. > > If you need a third row, call it 30. > > > > "Why not the concept of arrays with an index?" > > Arrays may have different shapes. Any ordinal fraction has the shape > (_$9). > > Arrays have elements. Ordinal fractions don't. > > > > Only array elements contains data. Any ordinal fraction may contain data. > > > > Arrays may have subarrays. Any ordinal fraction has subordinate ordinal > fractions. > > Arrays and atoms have names. Ordinal fractions don't. > > > > "the set of Natural numbers begin with 1 yet we use base 10 > representation that uses 0." > > > > Cardinal numbers and ordinal fractions have similarities and > differences. > > Cardinal number 0 (meaning "nothing") is not the same thing as ordinal > fraction 0 (meaning "everything"). > > > > Cardinal number 1 (meaning "one") is not the same thing as ordinal > fraction 1 (meaning "first part"). > > > > Using "0" for wild card character does not get along with using "0" for > counting to ten. > > A cardinal number is represented by a right-justified sequence of digits > with a finite number of nonzero digits. The cardinal number 1 may be > written 00001. > > > > An ordinal fraction is represented by a left-justified sequence of > digits with a finite number of nonzero digits. The ordinal fraction 1 may > be written 10000. > > > > "However this was not an easy system in which to do arithmetic so I > cannot see how your base 9 system could be either." > > Cardinal numbers, A and B, are ordered such that either A=B or A<B or > A>B. For example: 0=0 and 0<1 and 1>0 (meaning "zero is equal to zero" , > and "zero is fewer than one", and "one is more than zero"). > > > > Ordinal fractions, A and B, are ordered such that either A=B or A<B or > A>B or A<>B or A><B. For example: 0=0 and 0>1 and 1<0 and 10<>01 and 1><2. > (meaning that the whole is equal to the whole, and the whole comprises the > first part, and the first part is part of the whole, and the first half is > compatible with the odd fourths, and the first part is disjoint with the > second part). > > The notation for ordinal fractions makes ordinal fraction arithmetic > easy, just as the notation for cardinal numbers makes cardinal number > arithmetic easy. > > Keep asking! > > Bo. > > > > > > > > > > > > > > > > > > > > > > > > > > > > Den 18:35 torsdag den 7. juni 2018 skrev Donna Y <dy...@sympatico.ca > >: > > > > > > UDC is a library classification system akin to the Dewey decimal > system—the creators collaborated with Dewy. UTC is also used for data. > > > >> Every number is thought of as a decimal fraction with the initial > decimal point omitted, which determines the filing order. > > > > I am not sure why you say it cannot handle tables. > > > >> Concepts are organized in two kinds of tables in UDC:[27] < > https://en.wikipedia.org/wiki/Universal_Decimal_Classification#cite_note-UDC_Structure-27 > > > >> Common auxiliary tables (including certain auxiliary signs). These > tables contain facets of concepts representing, general recurrent > characteristics, applicable over a range of subjects throughout the main > tables, including notions such as place, language of the text and physical > form of the document, which may occur in almost any subject. UDC numbers > from these tables, called common auxiliaries are simply added at the end of > the number for the subject taken from the main tables. There are over > 15,000 of common auxiliaries in UDC. > >> The main tables or main schedules containing the various disciplines > and branches of knowledge, arranged in 9 main classes, numbered from 0 to 9 > (with class 4 being vacant). At the beginning of each class there are also > series of special auxiliaries, which express aspects that are recurrent > within this specific class. Main tables in UDC contain more than 60,000 > subdivisions. > > > > Can you show exactly what is gained by your “ordinal fraction”? > > > > Also—the set of Natural numbers begin with 1 yet we use base 10 > representation that uses 0. > > > > However in the 4 BCE the Greeks used their letters to represent numbers > from one to nine with no zero: > > > > alpha beta gamma delta epsilon digamma zeta eta theta > > > > They didn’t need to use 0 for higher values because much like Romans > they had symbols for higher values. > > > > However this was not an easy system in which to do arithmetic so I > cannot see how your base 9 system could be either. > > > > You suddenly use 0 when you illustrate tables. You do not show how to > access particular rows or columns or elements from a table but instead use > vague > > terms upper, lower, left, right without knowing the number of rows or > columns.. > > > > Why not the concept of arrays with an index?. > > > > Maybe you could explain what I am missing. > > > > Donna Y > > dy...@sympatico.ca > > > > > >> On Jun 7, 2018, at 3:47 AM, 'Bo Jacoby' via Chat <c...@jsoftware.com> > wrote: > >> > >> Ordinal Fractions is an improvement to the idea behind the Universal > Decimal Classification (UDC). > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
