Duolingo Lesson: Wednesday 22nd July: Hebrew Determiners:

zeh_determiner_demonstrative_colon_this-copy-1.docx

zeh_determiner_demonstrative_colon_this-copy.pdf

Introduction:

At present, that I may one day be able to read the Hebrew Bible, or Tanakh, or “Old Testament” in its original Hebrew, I am studying Modern Hebrew, for free, via the Duolingo App. I employ this gamified app so as to learn a form of Hebrew that is more similar to Classical/Biblical Hebrew than it is dissimilar. I can, therefore, through the employment of Brown, Driver Briggs and wiktionary, leverage this addictive, and free gamified app so as to learn some Classical/Biblical Hebrew. According to Hector Avalos in The End of Biblical Studies (2007), even though biblical studies is both a dying and oversubscribed [1] profession, nevertheless there is a shortage of talent and competency for the few lecturing positions available. At PhD level, Avalos recommends that those wishing to lecture, should know at least four languages among the following:

 Latin, Greek, Hebrew, German, Aramaic and Syriac,

to some degree of fluency, and that, ideally, one would also be able to decipher some French, Coptic, and Akkadian, as well.

Therefore, wishing eventually to lecture Philosophy of Religion[2] at a PhD level, some day, I am actively trying to learn Latin, Greek, Hebrew, German and Aramaic and Syriac. Aramaic and Syriac are dialects of the same language. The gamified nature of Duolingo is enabling me to build up competency in a lot of the above-mentioned languages.

In this article, I examine some instances of Hebrew determiners.

Body:

 

Masculine Singular Form:

The Hebrew word, infrā:

 

זֶה

is a ‘determiner,’ which means:

‘this (masculine, singular)’

. The Hebrew word, suprā, when transliterated into the alphabet used by English speakers, appears thus:

‘zēh.’

The word, suprā, when its phonemes be transcribed phonetically into the International Phonetic Alphabet appears thus:

/zeː/

The word, suprā, whenspelled with Hebrew letters, appears thus:

‘zayin, segol; hey.’

In Biblical Hebrew, we employ the phrase:

הַדָּבָר הַזֶּה

or, when transliterated into the alphabet that English speakers use:

‘had͡ħd͡ħāb͡hā́r hazzḗh;’

‘had͡ħ-d͡ħāb͡hā́r haz-zḗh;’

to mean:

‘this thing.’

The phrase suprā—when its phonemes be transcribed, employing, in so doing, the International Phonetic Alphabet—appear thus:

/had.daː.ˈvaːr haz.ˈzeː/

The phrase, suprā, when spelled using Hebrew letters appears thus:

‘hey, pathach; daleth, dagesh forte, qamats; veith, qamats; reish. hey, pathach; zayin, segol; hey.’

Feminine Singular Form:

The Hebrew word, infrā:

זֺאת

is a determiner which means:

 ‘this (feminine, singular).’

The Hebrew word, suprā, when transliterated into the letters of the alphabet used by English speakers, appears thus:

‘zōʔt͡h.’

. The Hebrew word, suprā, when the phonemes, which comprise it, are transcribed into the International Phonetic alphabet, appears thus:

/zoˑʔθ/

/ˈzoˑʔ.θə/

. The word, suprā, when spelled using Hebrew letters, appears thus:

‘zayin, defective cholam; aleph; tau.’

.

Conclusion:

Having examined these Modern-Hebrew determiners—encountered by means of the Duolingo app—and thereupon examining the Classical-Hebrew equivalents of these two determiners, we can now confidently proceed in our studies of Modern Hebrew, employing Duolingo as an instrument in this endeavor.

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[1] That is to say that there are many more post-graduates who wish to lecture biblical studies than there exist accredited universities, colleges, and seminaries with lecturing positions available.

[2] I prefer to call this field: “Philosophy of Religion” rather than to call it: “Theology.” Philosophy of Religion does not assume the existence of God, whereas Theology does. ‘Philosophy of Religion’ is a more neutral term for this field that both theists and atheists can accept.

The Elements of Euclid in Greek and Latin

I was trying to parse my way through an edition of The Elements in Greek and Latin:

https://archive.org/details/euclidisoperaomn01eucluoft/page/x

The name of The Elements in Ancient Greek is:

Στοιχει̃a

or, when transliterated:

Stoicheĩa

.

The Ancient-Greek word, τὰ στοιχει̃α or, when transliterated ‘tà stoicheĩa,’ is a plural form of the 2nd-declension neuter verb, τὸ στοιχει̃ον genitive: του̃ στοιχείου or, when transliterated: ‘tò stoicheĩon,’ genitive: ‘toũ stoicheíou.’

The Ancient-Greek word, ‘tò stoicheĩon,’ can mean ‘an element in a set.’

Figure 1: The elements of this set are alpha, beta, gamma and delta.

The Ancient-Greek word, ‘tò stoicheĩon,’ is formed from the Ancient-Greek masculine noun, ὁ στοι̃χος genitive: του̃ στοίχου or, when transliterated, ‘ho stoĩchos,’ genitive: ‘toũ stoíchou,’ which means ‘steps,’ or ‘a flight of stairs;’ and the Ancient-Greek 2nd-declension neuter nominal suffix, ‘-eĩon,’ genitive: ‘-eíou’ which denotes ‘a means (of),’ ‘an instrument of;’ etc.

Figure 2: a ‘stoĩchos’ or ‘series of steps.’

The term, ‘stoĩchos,’ according to Wiktionary, may be traced back to the indo-european word:

*steigʰ

, which means:

‘climb.’

Hence, etymologically, the Ancient-Greek term, ‘stoicheĩa,’ can be said to mean: ‘the means of climbing up;’ ‘the means of stepping up;’ ‘the means of ascent;’ etc.

This is highly instructive, as, in truth, Elements is a book that is a Jacob’s ladder, of sorts, by which one can ascend, element by element, into the heavens of mathematical knowledge.

Figure 3: With The Elements of Euclid, we advance in our mathematical knowledge element by element. Each element is, conceptually, like a rung, heaving us upwards to Mathematical prowess; to an implicit knowledge of Euclidean Geometry.

The Ancient-Greek word for ‘bone.’

Figure 1: I drew this bone in inkscape.

τὸ οστέον Genitive: τοῦ οστέου ‘tò ostéon’ Genitive: ‘toû ostéou.’ The Ancient-Greek word for ‘bone.’ We derive the medical prefix ‘osteo-‘ from this. ‘osteoarthritis’ for instance is an inflammation of the joints caused by an inflammation of the bones at the joint. Learning Greek makes one better able to understand and remember biological terms.

Integer Division in Python.

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integer_division_python

(Click the below link for a pdf version of this blog-post)

integer_division_python

 

Figure 1:  The Division symbol.  This symbol is used as a Division Operator in Mathematics, but not as a Division Operator in programming languages such as Python.

What goes on, Arithmetically, in Division?

Division, in Arithmetic, is one of the four elementary operations.  We ought to examine what occurs, arithmetically, in integer division.

 

Let us take the equation:

8 ÷ 4 = 2

.  We pronounce the above equation, in English, as:

Eight divided by four is equal to two.

In the above equation, the integer, 8, is the dividend.  The integer, 8, is what is being divided up 4 ways.  I looked up the word ‘division’ in a Latin dictionary[1], and its transliterated equivalent gave:

‘to distribute,’

as a definition.  8 elements, the dividend, is being distributed amongst 4 sets, leaving 2 elements – the quotient – in each set.

At the end of the financial year, a portion of a company’s profits is divided up between the company’s shareholders.  This money that is divided up is termed a ‘dividend.’  The term, ‘dividend,’ comes from the Latin gerundive phrase, ‘dividendum est,’ which means ‘that which must be divided.’  In the above equation, it is the integer, 8, that must be divided.

In the above equation, the:

÷

symbol is termed ‘the division operator.’  To restate: ‘operator’ is Latin for ‘worker.’  It is the division operator that facilitates the ‘operation’ or ‘work’ of division.  In Python, we use the:

/

, or forward-slash symbol, as a division operator.  In Python, the division operator is known as a ‘binary operator’ as it takes two operands.  The operands, in question, are:

8

, the dividend, and:

4

, the divisor.

In the Python equation:

> > >8 / 4

2.0

> > >

The dividend, 8, and the divisor, 4, are the two operands that the binary operator:

/

takes.

 

Figure 2:  In python, we use the / symbol as a division operator.  This is common to most programming languages.  In the above example, we have divided 8 by 4, and have got the quotient, 2.0.

Let us return to the equation:

8 ÷ 4 = 2

In the above equation,

4

is termed ‘the divisor.’  In Latin, the ‘-or’ suffix denotes the agent, or doer of an action.  It is the:

4

that is doing the dividing.  8 is being divided by 4.

In the equation:

8 ÷ 4 = 2

the:

=

, or “equals sign,” is termed ‘the sign of equality.’  The sign of equality or equality operator tells us that 8 divided by 4 is equal to 2.

In the equation:

8 ÷ 4 = 2

, 2 is termed ‘the quotient.’  The quotient[2] is simply the result of division.

The result of 8 being divided 4 ways is 2, so, therefore, 2 is the quotient.

If we were doing ‘Sums’ in primary school, then:

2

, the quotient, would be our answer.

Integer Division in Python

In this section, we shall program a simple Integer-Division Calculator in Python.

Figure 3:  In the above-depicted program, we have programmed a simple Integer-Division Calculator that requests the user to input a dividend and a Divisor.  The Integer-Division Calculator then returns a quotient.

Figure 4:  What the Integer-Division Calculator, as depicted in Figure 3, outputs when we, the user, input the Dividend, 8, and the Divisor, 4.  As we can see, the program outputs the quotient, 2.

Glossary

divide

• verb.

3. [with object] [MATHEMATICS] find how many times (a number) contains another: 36 divided by 2 equals 18.

• [no object] (of a number) be susceptible of division without a remainder: 30 does not divide by 8.
• find how many times (a number) is contained in another: divide 4 into 20.

<ORIGIN> Middle English (as a verb): from Latin divider ‘force apart, remove’.  the noun dates from the mid 17^th century.[3]

<ETYMOLOGY>  From the Latin 3^rd-conjugation verb, ‘dīvidō dividere, dīvīsī, dīvīsum,’ which means, ‘to divide;’ ‘to separate.’  From the Latin inseparable particle, ‘dĭs,’ or ‘dis-’ which means ‘in two;’ and the Latin 2^nd-declension verb, ‘videō vidēre, vīdī, vīsum,’ which means ‘to see.’  The etymological sense of the preceding seems to be ‘to arrange something such that it appear in two.’

dividend

• 1. a sum of money paid regularly (typically annually) by a company to its shareholders out of its profits (or reserves).
     • a payment divided among a number of people, e.g. winners in a football pool or members of a cooperative.
     • an individual’s share of a dividend.
     • (dividends) a benefit from an action or policy: buying a rail pass may still pay dividends.
  2. [MATHEMATICS] a number to be divided by another number.

<ORIGIN> late 15^th century (in the general sense ‘portion, share’): from Anglo-Norman French dividend, from Latin dividendum ‘something to be divided’, from the verb divider (see DIVIDE).[4]

<ETYMOLOGY>  From the Latin gerundive, ‘dīvidendum est,’ which means ‘that which must be divided.’  From the Latin 3^rd-conjugation verb, ‘dīvidō dividere, dīvīsī, dīvīsum,’ which means, ‘to divide;’ ‘to separate.’  From the Latin inseparable particle, ‘dĭs,’ or ‘dis-’ which means ‘in two;’ and the Latin 2^nd-declension verb, ‘videō vidēre, vīdī, vīsum,’ which means ‘to see.’  The etymological sense of the preceding seems to be ‘to arrange something such that it appear in two.’

 

 

division

• noun. [mass noun]
  1. the action of separating something into parts or the process of being separated: the division of the land into small fields | a gene that helps regulate cell division.
     • the distribution of something separated into parts: the division of his estates between the two branches of his family.
     • [count noun] an instance of members of a legislative body separating into two groups to vote: the new clause was areed without a division.
     • [LOGIC] the action of dividing a wider class into two or mor subclasses.
  2. the process of dividing one number by another.
     • [MATHEMATICS] the process of dividing a matrix, vector, or other quantity by another under specificrules to obtain a quotient.

 

<ORIGIN> late Middle English: fromOld French devisiun, from Latin divisio(n-), from the verb dividere (see DIVIDE).[5]

<ETYMOLOGY>  From the Latin 3^rd-declension Feminine noun, ‘dīvīsiō, dīvīsiōnis,’ which means ‘a division,’ ‘a distribution.’

 

 

divisor

• noun. [MATHEMATICS] a number by which another number is to be divided.
  • a number that divides into another without a remainder.

<ORIGIN>  late Middle English: from French diviseur or Latin divisor, from dividere (see DIVIDE).[6]

<ETYMOLOGY>  From the Latin 3^rd-declension masculine noun, ‘dīvīsor, dīvīsōris,’ which means ‘one who distributes.’

 

 

 

equation

• 1. [MATHEMATICS] a statement that the values of two mathematical expressions are equal (indicated by the sign =)
  2. [mass noun] the process of equating one thing with another: the equation of science with objectivity.
     • (the equation) a situation in which several factors must be taken into account: money also came into the equation.
  3. [CHEMISTRY] a symbolic representation of the changes which occur in a chemical reaction, expressed in terms of the formulae of the molecules or other species involved.

<PHRASES>

• equation of the first (or second etc.) order [MATHEMATICS] an equation involving only the first derivative, second derivative, etc.

<ORIGIN> late Middle English: from Latin aequatio-(n-), from aequare ‘make equal’ (see EQUATE).[7]

<ETYMOLOGY> from the Latin 1^st-and-2^nd-declension adjective, ‘æqua, æquus, æquum,’ which means ‘equal;’ and the 3^rd-declension nominal suffix, ‘-tiō, (-tiōnis),’ which denotes a state of being.  Therefore, etymologically, an ‘equation’ is ‘a state of being equal.’  Etymologically, therefore, an ‘equation’ is a mathematical statement that declares terms to be equal.

 

operator

4. [MATHEMATICS] a symbol or function denoting an operation (e.g. ).[8]

<ETYMOLOGY>  From the 3^rd-declension masculine Latin noun, ‘ŏpĕrātor, ŏpĕrātōris,’ which means ‘operator,’ ‘worker.’  The Latin 3^rd-declension noun, ‘opus, operis,’ which means ‘work,’ ‘labour.’  From the Latin 1^st-conjugation verb, ‘operō, operāre, operāvī, operātor;’ and the 3^rd-declension nominal suffix, ‘-or,       (-ōris)’ which denotes a performer of an action.  Etymologically, as regards Mathematics, it is the operator that is said to perform the work of the operation.

operation

• noun.
  • [mass noun] the action of functioning or the fact of being active or in effect: restrictions on the operation of market forces | the company’s first hotel is now in operation.

4. [MATHEMATICS] a process in which a number, quantity, expression, etc., is altered or manipulated according to set formal rules, such as those of addition, multiplication, and differentiation.

<ORIGIN> late Middle English: via Old French from Latin operatio(n-), from the verb operari ‘expend labour on’ (see Operate)[9]

 

<ETYMOLOGY>  From the Latin 3^rd-declension feminine noun, ‘ŏpĕrātĭo, ŏpĕrātĭōnis,’ which means ‘a working,’ ‘a work,’ ‘a labour,’ ‘operation.’  From the Latin 1^st-declension deponent verb ‘operor, operāre, operātus sum,’ which means ‘to work,’ ‘to labour,’ ‘to expend labour on;’ and the Latin 3^rd-declension nominal suffix, ‘-iō, (-iōnis),’ which denotes a state of being.  Etymologically, therefore, as regards Mathematics, an ‘operation’ is a ‘mathematical work;’ ‘mathematical working;’ a ‘mathematical labour.’  The mathematical work that would be carried out depends on the operator.  For instance, if the operator be a plus sign, then the mathematical work to be carried out would be addition.  Addition is a type of operation.

 

 

 

 

 

 

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[1]  dīvīsiō ōnis, f

[VID-], a division, distribution…

Latin English Lexicon: Optimized for the Kindle, Thomas McCarthy, (Perilingua Language Tools: 2013) Version 2.1  Loc 32190

See GLOSSARY

[2]  See the chapter, TWO WAYS OF CONCEPTUALISING DIVISION https://mathsandcomedy.com/2016/06/29/one-way-of-conceptualising-division/

https://mathsandcomedy.com/2016/07/03/another-way-of-conceptualising-division/

[3] Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc 202778

[4]  ibid.  Loc 202820

[5]  Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc 202998

[6] ibid. Loc 203079

[7]  ibid.  Loc 234861

[8]  ibid.  Loc 493860.

[9] ibid.  Loc 493797

An Etymological Introduction to Trigonometry

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an_etymological_introduction_to_trigonometry

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an_etymological_introduction_to_trigonometry

Figure 1:  The mathematician, George Boole (1815-1864), was self-taught and fluent in Latin, Ancient-Greek, and Hebrew by the age of 12.  I will be 30 in less than a month, and I am not even close to being fluent in any of these languages.  However, I still cultivate an interest in these languages in some measure of poor imitation of the great man.  It is certainly a great irony that subjects thousands of years old, such as Ancient-Greek and Latin, can make something so modern, such as Computer Programming, so much easier.  If you have an interest in Science Fiction, you will notice that even in the far-flung future, scientists will name their bionic monsters after letters of the Ancient-Greek alphabet.  The letter ‘Sigma,’ or Σ seems to be a favourite of Science-Fiction writers.  In Ratchet and Clank: A Crack in Time, the Robot Junior Caretaker of the Great Clock is called Sigma 0426A.

Figure 2:  Ecstasy tablets, very often, have the Ancient-Greek Majorscule, Sigma, stamped into them.  So it is not only Computer Programming that a knowledge of Ancient-Greek will make easier: it will also give you a head start in Pharmacy!

I shall be studying QQI Level-V Videogame development in September.  One of the modules of which this course comprises is called:

Mathematics for Programming

.

A huge part of this Maths module is Trigonometry.  This is why I wish to develop an implicit knowledge of the fundamentals of Trigonometry, now, prior to beginning the module formally, in September.

The purpose of this article is to take a look at the etymological meaning of some of the key terms pertaining to Trigonometry.

‘Trigonometry’

The term, ‘trigonometry’ is derived from four root words:

1. ‘trí’ This is the Ancient-Greek Cardinal Numeral, 3.
2. ‘tó gónu’ This is an Ancient-Greek third-declension neuter noun, which means ‘the knee;’ ‘the corner;’ ‘the vertex.’
3. ‘tó métron.’ This is an Ancient-Greek second-declension neuter noun, which means ‘the measurement.’
4. ‘-y.’ This is a noun-making suffix.  It comes from the Latin substantive-adjective 2^nd-declension neuter plural suffix ‘ [i]-a.’

Figure 3:  Etymologically, ‘Trigonometry’ is the study of the measurement of three-cornered polygons, or triangles.

The four root words, or etymons, listed above, when considered together, give us an etymological definition of ‘Trigonometry:’

The study of the measurement of three-cornered polygons.

The study of the measurement of polygons with three vertices.

The study of the measurement of triangles.

Now that we have the term ‘Trigonometry’ broken down, etymologically, let us now consider the Trigonometric term, ‘equilateral.’

‘Equilateral’

Figure 4:  An equilateral triangle.  An equilateral triangle has sides of equal length, and angles of equal magnitude.  Each of an equilateral’s interior angles is equal to 60º in magnitude.

The term, ‘equilateral,’ can be broken down, etymologically, into three root words:

1. ‘æqua, æquus, æquum.’ This is a 1^st-and-2^nd-declension Latin adjective that means ‘equal.’
2. ‘latus, lateris.’ This is a 3^rd-declension neuter Latin noun that means ‘side.’
3. ‘-ālis, -āle.’ This is a 3^rd-declension Latin adjectival suffix.

The three root words, or etymons, listed above, when considered together, give us an etymological definition of ‘equilateral:’

 

of [triangles] that possess equal sides[1]

Now that we have the term ‘equilateral’ broken down, etymologically, let us now consider the Trigonometric term, ‘isosceles.’

‘Isosceles’

Figure 5:  An isosceles triangle.  An isosceles triangle has 2 sides equal in length, and two angles equal in magnitude.

Figure 6:  An isosceles triangle has two ‘legs’ or sides equal in length.

The term, ‘isosceles,’ can be broken down, etymologically, into two root words:

1. ísos.  This is an Ancient-Greek adjective that means ‘equal,’ ‘the same,’ ‘proportionate.’
2. tό skéllos.   This is an Ancient-Greek third-declension neuter noun that means ‘leg.’

It is funny how, in Ancient-Greek, the sides of triangles are called ‘legs’ and the corners of triangles are called ‘knees!’

The two root words, or etymons, listed above, when considered together, give us an etymological definition of ‘isosceles:’

A triangle [that possesses two sides] that are equal in length.

A triangle [that possesses two sides] that are the same in measurement.

A triangle [that possesses two sides] that are proportionate.

Now that we have the term ‘isosceles’ broken down, etymologically, let us now consider the Trigonometric term, ‘scalene.’

‘Scalene.’

Figure 7:  A Scalene Triangle.  As we can see from the above diagram, a scalene triangle is one which possesses 3 sides, all of unequal length; and 3 interior angles, all of unequal magnitude.

Figure 8:  The Trigonometric term, ‘scalene’ is derived from the Ancient-Greek adjective, ‘skălēnos,’ which means ‘unequal.’

The term, ‘scalene,’ can be broken down, etymologically, into the root word:

1. ‘skălēnḗ, skălēnos, skălēnón’ This is a 1^st-and-2^nd-declension Ancient-Greek adjective that means: ‘uneven,’ ‘unequal.’

 

When we consider the root word, or etymon, listed above, then we can come to the following etymological definition of ‘scalene:’

[of a triangle whose sides are] of unequal [length.][2]

 

 

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[1]  Et sequitur: equal angles.  It follows, according to mathematical logic, that if a triangle’s sides be all equal in length that its interior angles will, likewise, be all equal in magnitude.

[2]  Et Sequitur: and whose interior angles are unequal in magnitude.  It follows, according to mathematical logic, that if a triangle’s sides be all unequal in length that its interior angles will, likewise, be all unequal in magnitude.

The Mathematical Distinction that Exists between Precision and Accuracy.

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Introduction:

In everyday common parlance, the terms ‘precision’ and ‘accuracy’ are synonyms. However, this is not so in Mathematical jargon. In mathematical jargon, there exists an important difference in meaning between the terms ‘precision’ and ‘accuracy.’ It is the purpose of this chapter to explicate this difference in meaning.

Body:

If one should derive:

π

to eleven decimal places by dividing 22 by 7:

22/7

, then the result of this calculation:

3.14285714286

will be more precise than:

π

derived properly – i.e. through differentiation – to eight decimal places:

3.14159265

, but the latter answer will be more accurate than the former.

In mathematics, the term, ‘precision,’ denotes how many decimal places the result of a calculation can run to[1], whereas the term, ‘accuracy,’ denotes how close to the correct answer the result of a calculation is.

In mathematics, the term, ‘precision’ denotes how many significant digits that a mathematician should use to render a quantity, whereas the term ‘accuracy’ denotes how close to the correct quantity the quantity rendered in digits is.

An Etymological Definition:

The English term, ‘precision’ comes from the Latin 3rd-declension feminine noun, ‘praecīsiō, praecīsiōnis,’ which means a ‘cutting off[2] .’ After how many significant digits ought we to cut the answer off?

The verb, ‘caedere,’ can also mean ‘to kill[3] .’ After how many significant digits do we kill off the trail?

After our dividing 22 by 7:

22/7

, we cut the answer off after 11 significant digits following the decimal point:

3.14285714286

.
We use a total of 12 significant digits in our rendering of:

π

.

After arriving at:

π

, properly – i.e. through differentiation – we cut the answer off after 8 significant digits following the decimal point:

3.14159265

.

We use a total of 9 significant digits in our rendering of:

π

.

In the first case, we employ 12 significant digits in our rendering of:

π

, and, in the latter case, we employ 9 significant digits in our rendering of:

π

. Therefore, again, to restate, the former rendering of:

π

is more precise than the latter, however, the latter rendering of:

π

is more accurate than the former.

Precision in Python:

It is possible to modify the precision of π, in Python, by applying formatting[4]

Figure 1:  We have, here, created a program that prints out π with varying degrees of precision; from the most precise: with 6 significant figures trailing the decimal point; to the least precise: with 0 significant figures trailing the decimal point.

Figure 2:  What the previous Python script outputs.

Epilogue: What is π?

Figure 3:  The iconic symbol.  π is the sixteenth letter of the Ancient-Greek Alphabet.  This is its minuscule form.  It is conjectured that the Ancient-Greek letter, π, was employed so as to represent the length of a circle’s circumference, as the letter, ‘pi’ can be taken as a contraction of the term, ‘perimeter.’

π comes into play with the radians of Trigonometry, a crucial component of Computing Mathematics, so we may as well digress a little and ask ourselves what π actually is.

 

π symbolises and denotes the ratio that exists between the length of a circle’s diameter and the length of a circle’s circumference.

 

Figure 4:  π is equal to the ratio that exists between the length of a circle’s diameter, and the length of a circle’s circumference.

The ratio:

Diameter : Circumference

can be expressed as the ratio:

1 : 3.14159…

Glossary:

accuracy

• noun.

(plural. accuracies)

     [mass noun] the quality or state of being correct or precise:  we have confidence in the accuracy of the statistics.

 

• TECHNICAL the degree to which the result of a measurement, calculation, or specification conforms to the correct value or standard: the accuracy of radiocarbon dating | [count noun] accuracies of 50-70 per cent. Compare with PRECISION. [1]

<ETYMOLOGY>  From the Latin 3^rd-declension Latin noun, ‘accurātiō, accurātiōnis,’ which means ‘accuracy,’ ‘carefulness.’  From the Latin preposition, ‘ad,’ which means ‘towards;’ and the Latin 1^st-declension feminine noun, ‘cūra, cūrae,’ which means ‘care;’ and the Latin 3^rd-declension nominal suffix, ‘-ātiō’ which denotes a state of being.  The etymological sense of the English term, ‘accuracy,’ therefore, is ‘the state of being oriented towards carefulness.’

 

 

accurate

• adjective.

1. (especially of information, measurements, or predictions) correct in all details; exact: accurate information about the illness is essential.
   • (of an instrument or method) capable of giving accurate information: an accurate thermometer.
   • providing a faithful representation of someone or something: the portrait is an accurate likeness of Mozart.
2. (with reference to a weapon, missile, or shot) capable of or successful in reachingthe intended target: reliable, accurate rifles | a player who can deliver long accurate passes to the wingers.

<DERIVATIVES> late 16^th century: from Latin accuratus ‘done with care’, past participle of accurare, from ad- ‘towards’ + cura ‘care’.[2]

 

<ETYMOLOGY>  From the Latin 1^st-conjugation verb, ‘accūrō, accūrāre, accūrāvī, accūrātum,’ or ‘adcūrō, adcūrāre, adcūrāvī, adcūrātum,’ which means ‘to give close attention to,’ ‘to be careful.’[3]

From the Latin preposition, ‘ad,’ which means ‘towards,’ and the Latin 1^st-declension feminine noun, ‘cūra, cūrae,’ which means ‘care.’

precise

• adjective.

marked by exactness and accuracy of expression or detail: precise directions | I want as precise a time of death as I can get.

• (of a person) exact, accurate, and careful about details: the director was precise with his camera positions.
• [attributive] used to emphasize that one is referring to an exact and particular thing: at that precise moment the car stopped.

<DERIVATIVES> preciseness noun.

<ORIGIN> late Middle English: from Old French precis, from Latin praecis- ‘cut short’, from the verb praecidere, from prae ‘in advance’ + caedere ‘to cut’[4].

 

<ETYMOLOGY> From the Latin 1^st-and-2^nd-declension adjective, ‘praecīsa, praecīsus, praecīsum,’ which means ‘broken off,’ ‘abrupt.’  From the Latin verb, ‘praecīdō, praecīdere, praecīdī, praecīsus,’ which means ‘to cut off in front,’ ‘cut off.’[5]

From the Latin preposition, ‘prae,’ which means ‘before,’ ‘beforehand;’ and the Latin 3^rd-conjugation verb, ‘caedō, caedere, cecīdī, caesum,’ which means ‘to cut.’  The etymological sense of ‘precise’ – like ‘concise’ – is ‘cut off.’

 

 

precisely

in exact terms; without vagueness: the guidelines are precisely defined.

• exactly (used to emphasize the complete accuracy or truth of a statement): at 2.00 precisely, the phone rang | kids will love it precisely because it will irritate their parents.
• used as a reply to confirm or agree with a previous statements: ‘You mean it was a conspiracy?’ ‘Precisely.’ .[6]

 

precisian

chiefly ARCHAIC a person who is rigidly precise or punctilious, especially as regards religious rules.

<DERIVATIVES> precisianism noun.[7]

precision

• [mass noun]

the quality, condition, or fact of being exact and accurate: the deal was planned and executed with military precision.

• [as modifier] marked by or adapted for accuracy and exactness: a precision instrument.
• TECHNICAL refinement in a measurement, calculation, or specification, especially as represented by the number of digits given: a technique which examines and identifies each character with the highest level of precision | [count noun] a precision of six decimal figures.

Compare with ACCURACY.

<ORIGIN> mid 18^th century: from French precision or Latin praecīsiō(n-), from praecīdere ‘cut off’ (see PRECISE).[8]

<ETYMOLOGY>  From the Latn 3^rd-declension feminine noun, ‘praecīsĭo, praecīsĭōnis,’ which means ‘a cutting off,’ ‘the piece cut off.’  In rhetoric, ‘praecīsĭo,’ means ‘a breaking off abruptly.’  In Late Latin, ‘praecīsĭo,’ can mean ‘an overreaching.’ [9]

 

radian

[GEOMETRY] a unit of measurement of angles equal to about 57.3°, equivalent to the angle subtended at the centre of a circle by an arc equal in length to the radius.[10]

<ETYMOLOGY>  From the Scientific Latin 1^st-and-2^nd-declension adjective, ‘radiāna, radiānus, radiānum’ which means ‘of the radius,’ ‘concerning the radius,’ ‘denoting the radius.’  From the Latin 2^nd-declension masculine noun, ‘radius, radiī’ which means ‘a geometer’s rod[11] [for measuring the distance between the centre of a circle and the circumference],’ and the Latin 1^st-and-2^nd-declension adjectival suffix,      ‘-iāna, -iānus, -iānum,’ which means ‘of,’ ‘concerning,’ ‘denoting.’  The etymological sense of the English noun ‘radian’ is ‘that unit of measurement of angles that concerns radiuses.’

 

 

[1]  Oxford University Press.  Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc 4388.

 

[2]  Oxford University Press.  Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc 4388.

[3] Perlingua Language Tools.  www.perlingua.com   Version 2.1 (Kindle Edition.)  2013.  Latin English Lexicon.  Thomas Mc Carthy.  Loc. 1075.

[4] Oxford University Press.  Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc. 554162.

[5] Perlingua Language Tools.  www.perlingua.com   Version 2.1 (Kindle Edition.)  2013.  Latin English Lexicon.  Thomas Mc Carthy.  Loc. 76264.

 

[6] ibid.  Loc. 554172

[7] ibid.  Loc. 554179

[8]  ibid.  Loc. 554191

[9]  Perlingua Language Tools.  www.perlingua.com   Version 2.1 (Kindle Edition.)  2013.  Latin English Lexicon.  Thomas Mc Carthy.  Loc. 76264.

[10]  Oxford University Press.  Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc. 578311.

[11]  Perlingua Language Tools.  www.perlingua.com   Version 2.1 (Kindle Edition.)  2013.  Latin English Lexicon.  Thomas Mc Carthy.  Loc. 87154.

 

---

[1]

See the Oxford Dictionary of English’s TECHNICAL definition of ‘precision’ in the glossary below.

[2]

From the Latin preposition ‘prae,’ which means ‘before,’ and the Latin 3rd-conjugation verb, ‘caedō, caedere, cecīdī, caesum,’ which means ‘to cut.’

[3]

For instance, a ‘suicide’ is a man or woman who kills himself/herself. From the Latin 1st-and-2nd-declension possessive adjective, ‘sua, suus, suum,’ which means ‘his, her, its;’ and the Latin 3rd-conjugation verb, ‘caedō, caedere, cecīdī, caesum,’ which means ‘to kill.’ The etymological sense of ‘suicide,’ therefore is a man or woman who kills himself/herself.

[4]

See the blogpost: Formatting Numbers in Python.

The Epistemology of Algorithms.

Below is a Word-Document Version of this blog post:

final_epistomology_recovered_algorithms

Below is a pdf Version of this blog post:

final_epistomology_recovered_algorithms

---

Figure 1:  The Ancient-Greek word ‘EPISTEME’ which means ‘knowledge’ wrought into the Blacksmith’s monument outside Monaghan Courthouse. Monaghan is such a cultured little burg!

In science and philosophy, Epistemology is the study of knowledge, and what constitutes knowledge.

 

In Computer programming, we have to think epistemologically about knowledge; what constitutes knowledge; and what forms it may take.

 

In Computer programming, knowledge is deemed to have two forms:

1. Declarative,
2. Imperative.

The term, ‘imperative,’ denotes a command. ‘Imperative Knowledge’ is knowledge that instructs one on how to do something by giving him/her a set of commands.

 

If I told you that porridge consisted of oats and heated water, then this would be ‘declarative knowledge.’

 

If, instead, I gave you a set of instructions on how to make porridge such as:

RECIPE:

 

INGREDIENTS:

 

• Oats
• Water

 

METHOD:

 

Measure out 80 grams of oats. Measure out 160 millilitres of water. Combine the oats and water in a pot. Heat the pot over a hob until it reaches boiling point, stirring all the while. Keep the oats-and-water mixture at boiling point for three minutes. Take the porridge off the hob. Serve.

 

then the above would be an example of imperative knowledge.

 

Above, we see the two types of knowledge in action: declarative and imperative. The declarative form of knowledge tells you what porridge is. The imperative form of knowledge consists of a series of instructions that enables you to make porridge.

 

As you can see, the verbs that I use in telling you how to make porridge are, grammatically, in the imperative mood:

 

‘measure…’

‘combine…’

‘heat…’

‘keep…’

‘take…’

‘serve…’

 

In grammar, the imperative mood denotes a verb in its command form.

 

A series of commands that enables one to prepare a foodstuff is termed a ‘recipe.’  Very often, Computer Scientists will refer to algorithms as ‘recipes.’

In cookery, a recipe is a series of commands that allows one to prepare a foodstuff.

In computer science, an algorithm – or recipe – is a series of commands that allows one to solve a computational problem.

In computer science, an algorithm – or recipe – is a series of commands that allows one to accomplish a task computationally.

 

 

Glossary:

declarative

• adjective.

of the nature of or making a declaration: declarative statements.

[GRAMMAR] (of a sentence or phrase) taking the form of a simple statement.

[COMPUTING] denoting high-level programming languages which can be used to solve problems without requiring the programmer to specify an exact procedure to be followed.

noun.

a statement in the form of a declaration.

[GRAMMAR] a declarative sentence or phrase.

<DERIVATIVES> declaratively adverb. [1]

<ETYMOLOGY> from the Latin 1st-and-2nd-declension adjective, ‘dēclārātīva, dēclārātīvus, dēclārātīvum,’ which means ‘pertaining to the making quite clear.’ From the Latin 1st-conjugation verb, ‘dēclārō, dēclārāre, dēclārāvī, dēclārātum,’ which means ‘to explain,’ ‘to make quite clear,’ and the Latin 1st-and-2nd-declension adjectival suffix ‘-īva,    -īvus, -īvum,’ which means ‘of,’ ‘concerning,’ ‘pertaining to.’ From the Latin prefix ‘dē-’ which expresses intensive force, and the Latin 1st-conjugation verb, ‘clārō, clārāre, clārāvī, clārātum,’ which means ‘to brighten,’ ‘to illuminate,’ ‘to clarify.’

epistemology

[mass noun] [PHILOSOPHY] the theory of knowledge, especially with regard to its methods, validity, and scope, and the distinction between justified belief and opinion.

< DERIVATIVES> epistemological adjective. epistemologically adverb. epistemologist noun.

         < ORIGIN> mid 19th century: from Greek episteme ‘knowledge’, from epistathai ‘know, know how to do’.[2]

<ETYMOLOGY> From the Ancient-Greek Feminine noun, ‘hē épistḗmē,’ which means ‘knowledge,’ and the Ancient-Greek Masculine noun, ‘ho lógos,’ which denotes a ‘study.’ Therefore, the English term, ‘epistemology’ can be said, etymologically, to mean ‘the study of knowledge. The Ancient-Greek Feminine noun, ‘hē épistḗmē,’ which means ‘knowledge’ can be broken down, a little further, into the Ancient-Greek preposition, ‘epí,’ which means ‘above,’ or ‘over,’ and the Ancient-Greek verb, ‘hístēmi,’ which means ‘to stand.’ Hence, ‘hē épistḗmē,’ at root, means ‘above-standing,’ ‘over-standing.’ In English, the term ‘knowledge’ is more-or-less synonymous with the term, ‘understanding.’ The Ancient-Greeks did not “understand:” instead they were inclined to “above-stand;” they were inclined to “over-stand.” Etymologically, therefore, the English term, ‘epistemology’ can be said to mean ‘the study of over-standing,’ ‘the study of above-standing.’

 

 

 

 

imperative[3]

• adjective.

1. of vital importance; crucial: immediate action was imperative | [with clause] it is imperative that standards are maintained.
2. giving an authoritative command; peremptory: the bell pealed again, a final imperative call.
   • [GRAMMAR] denoting the mood of a verb that expresses a command or exhortation, as in come here!

• noun.
  1. an essential or urgent thing: free movement of labour was an economic imperative.
     • a factor or influence making something necessary: the biological imperatives which guide male and female behaviour.
  2. [GRAMMAR] a verb or phrase in the imperative mood.
     • (the imperative) the imperative mood.

<DERIVATIVES> imperatival adjective. imperatively adverb. imperativeness noun.

<ORIGIN> late Middle English (as a grammatical term): from Late Latin imperativus (literally ‘specially ordered’, translating Greek prostatikē enklisis ‘imperative mood’), from imperare ‘to command’, from in- ‘towards’ + parare ‘make ready’.[4]

<ETYMOLOGY> from the Latin 1st-and-2nd-declension adjective, ‘impĕrātīva, impĕrātīvus, impĕrātīvum,’ which means ‘pertaining to the command;’ ‘of the command.’ From the Latin 1st-conjugation verb, ‘imperō, imperāre, imperāvī, imperātum,’ which means ‘to command,’ ‘to order,’ and the Latin 1st-and-2nd-declension adjectival suffix ‘-īva, -īvus,              -īvum,’ which means ‘of,’ ‘concerning,’ ‘pertaining to.’ From the Latin prefix ‘in-’ which expresses the concept of ‘unto,’ ‘toward,’ and the Latin 1st-conjugation verb, ‘parō, parāre, parāvī, parātum,’ which means ‘to make ready,’ ‘to prepare.’ The etymological sense, therefore, of the English adjective, ‘imperative’ is: ‘concerning the command;’ ‘pertaining to the command;’ ‘of the command;’ ‘concerning the order;’ ‘pertaining to the order;’ ‘of the order;’ ‘concerning the making ready of;’ ‘pertaining to the making ready of;’ ‘of the making ready of;’ etc.

 

 

 

 

[1] Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010. Loc178909.

[2] Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010. Loc 234206

[3] ibid. Loc 345797

 

Hexadecimal

Figure 1:  Today’s Blog-post is brought to you by the number, 16.  I drew the above image in Microsoft Paint.

 

Figure 2:  On today’s show, we are going to teach you how to Count – geddit?  because the above is a picture of The Count from Sesame Street? – in sixteens.

The term, ‘hexadecimal¹,’ refers to a base-sixteen number system. A hexadecimal number system uses sixteen distinct symbols so as to represent numerical quantities. These 16 symbols are:

0_sixteen = 0 _ten
1_sixteen = 1 _ten
2_sixteen = 2 _ten
3_sixteen = 3 _ten
4_sixteen = 4 _ten
5_sixteen = 5 _ten
6_sixteen = 6 _ten
7_sixteen = 7 _ten
8_sixteen = 8 _ten
9_sixteen = 9 _ten
A_sixteen = 10 _ten
B_sixteen = 11 _ten
C_sixteen = 12 _ten
D_sixteen = 13 _ten
E_sixteen = 14 _ten
F_sixteen = 15 _ten

Let us now, for the sake of comprehension, equate the denary² whole numbers, 0_ten to 15_ten to their equivalents in Hexadecimal:

0 _ten = 0_sixteen
1 _ten = 1_sixteen
2 _ten = 2_sixteen
3 _ten = 3_sixteen
4 _ten = 4_sixteen
5 _ten = 5_sixteen
6 _ten = 6_sixteen
7 _ten = 7_sixteen
8 _ten = 8_sixteen
9 _ten = 9_sixteen
10 _ten = A_sixteen
11 _ten = B_sixteen
12 _ten = C_sixteen
13 _ten = D_sixteen
14 _ten = E_sixteen
15 _ten = F_sixteen

Sixteen is equal to two to the power of four:

16 _ten =2^4 _ten

In Computer science, a byte is a combination of 8 binary digits, or bits. In Computer Science, we humorously term a combination of 4 binary digits – or half a byte – a ‘nibble.’

Every possible nibble, or permutation of four binary digits, can be represented by a single hexadecimal symbol/number.

0000 _two = 0 _sixteen
0001 _two = 1 _sixteen
0010 _two = 2 _sixteen
0011 _two = 3 _sixteen
0100 _two = 4 _sixteen
0101 _two = 5 _sixteen
0110 _two = 6 _sixteen
0111 _two = 7 _sixteen
1000 _two = 8 _sixteen
1001 _two = 9 _sixteen
1010 _two = A _sixteen
1011 _two = B _sixteen
1100 _two = C _sixteen
1101 _two = D _sixteen
1110 _two = E _sixteen
1111 _two = F _sixteen

Let us now, for sake of comprehension, express each single-digit hexadecimal number, and equate it to its equivalent nibble:

0 _sixteen = 0000 _two
1 _sixteen = 0001 _two
2 _sixteen = 0010 _two
3 _sixteen = 0011 _two
4 _sixteen = 0100 _two
5 _sixteen = 0101 _two
6 _sixteen = 0110 _two
7 _sixteen = 0111 _two
8 _sixteen = 1000 _two
9 _sixteen = 1001 _two
A _sixteen = 1010 _two
B _sixteen = 1011 _two
C _sixteen = 1100 _two
D _sixteen = 1101 _two
E _sixteen = 1110 _two
F _sixteen = 1111 _two

A Byte, as alluded to above, is two nibbles, we can, therefore, express each byte as a combination of two hexadecimal digits.

There are 256 possible bytes, and 256 possible permutations of two-digit hexadecimal numbers.

0000-0000_two = 00_sixteen
0000-0001_two = 01_sixteen
0000-0010_two = 02_sixteen
0000-0011_two = 03_sixteen
0000-0100_two = 04_sixteen
0000-0101_two = 05_sixteen
0000-0110_two = 06_sixteen
0000-0111_two = 07_sixteen
0000-1000_two = 08_sixteen
0000-1001_two = 09_sixteen
0000-1010_two = 0A_sixteen
0000-1011_two = 0B_sixteen
0000-1100_two = 0C_sixteen
0000-1101_two = 0D_sixteen
0000-1110_two = 0E_sixteen
0000-1111_two = 0F_sixteen

0001-0000_two = 10_sixteen
0001-0001_two = 11_sixteen
0001-0010_two = 12_sixteen
0001-0011_two = 13_sixteen
0001-0100_two = 14_sixteen
0001-0101_two = 15_sixteen
0001-0110_two = 16_sixteen
0001-0111_two = 17_sixteen
0001-1000_two = 18_sixteen
0001-1001_two = 19_sixteen
0001-1010_two = 1A_sixteen
0001-1011_two = 1B_sixteen
0001-1100_two = 1C_sixteen
0001-1101_two = 1D_sixteen
0001-1110_two = 1E_sixteen
0001-1111_two = 1F_sixteen

0010-0000_two = 20_sixteen
0010-0001_two = 21_sixteen
0010-0010_two = 22_sixteen
0010-0011_two = 23_sixteen
0010-0100_two = 24_sixteen
0010-0101_two = 25_sixteen
0010-0110_two = 26_sixteen
0010-0111_two = 27_sixteen
0010-1000_two = 28_sixteen
0010-1001_two = 29_sixteen
0010-1010_two = 2A_sixteen
0010-1011_two = 2B_sixteen
0010-1100_two = 2C_sixteen
0010-1101_two = 2D_sixteen
0010-1110_two = 2E_sixteen
0010-1111_two = 2F_sixteen

0011-0000_two = 30_sixteen
0011-0001_two = 31_sixteen
0011-0010_two = 32_sixteen
0011-0011_two = 33_sixteen
0011-0100_two = 34_sixteen
0011-0101_two = 35_sixteen
0011-0110_two = 36_sixteen
0011-0111_two = 37_sixteen
0011-1000_two = 38_sixteen
0011-1001_two = 39_sixteen
0011-1010_two = 3A_sixteen
0011-1011_two = 3B_sixteen
0011-1100_two = 3C_sixteen
0011-1101_two = 3D_sixteen
0011-1110_two = 3E_sixteen
0011-1111_two = 3F_sixteen

0100-0000_two = 40_sixteen
0100-0001_two = 41_sixteen
0100-0010_two = 42_sixteen
0100-0011_two = 43_sixteen
0100-0100_two = 44_sixteen
0100-0101_two = 45_sixteen
0100-0110_two = 46_sixteen
0100-0111_two = 47_sixteen
0100-1000_two = 48_sixteen
0100-1001_two = 49_sixteen
0100-1010_two = 4A_sixteen
0100-1011_two = 4B_sixteen
0100-1100_two = 4C_sixteen
0100-1101_two = 4D_sixteen
0100-1110_two = 4E_sixteen
0100-1111_two = 4F_sixteen

0101-0000_two = 50_sixteen
0101-0001_two = 51_sixteen
0101-0010_two = 52_sixteen
0101-0011_two = 53_sixteen
0101-0100_two = 54_sixteen
0101-0101_two = 55_sixteen
0101-0110_two = 56_sixteen
0101-0111_two = 57_sixteen
0101-1000_two = 58_sixteen
0101-1001_two = 59_sixteen
0101-1010_two = 5A_sixteen
0101-1011_two = 5B_sixteen
0101-1100_two = 5C_sixteen
0101-1101_two = 5D_sixteen
0101-1110_two = 5E_sixteen
0101-1111_two = 5F_sixteen

0110-0000_two = 60_sixteen
0110-0001_two = 61_sixteen
0110-0010_two = 62_sixteen
0110-0011_two = 63_sixteen
0110-0100_two = 64_sixteen
0110-0101_two = 65_sixteen
0110-0110_two = 66_sixteen
0110-0111_two = 67_sixteen
0110-1000_two = 68_sixteen
0110-1001_two = 69_sixteen
0110-1010_two = 6A_sixteen
0110-1011_two = 6B_sixteen
0110-1100_two = 6C_sixteen
0110-1101_two = 6D_sixteen
0110-1110_two = 6E_sixteen
0110-1111_two = 6F_sixteen

0111-0000_two = 70_sixteen
0111-0001_two = 71_sixteen
0111-0010_two = 72_sixteen
0111-0011_two = 73_sixteen
0111-0100_two = 74_sixteen
0111-0101_two = 75_sixteen
0111-0110_two = 76_sixteen
0111-0111_two = 77_sixteen
0111-1000_two = 78_sixteen
0111-1001_two = 79_sixteen
0111-1010_two = 7A_sixteen
0111-1011_two = 7B_sixteen
0111-1100_two = 7C_sixteen
0111-1101_two = 7D_sixteen
0111-1110_two = 7E_sixteen
0111-1111_two = 7F_sixteen

1000-0000_two = 80_sixteen
1000-0001_two = 81_sixteen
1000-0010_two = 82_sixteen
1000-0011_two = 83_sixteen
1000-0100_two = 84_sixteen
1000-0101_two = 85_sixteen
1000-0110_two = 86_sixteen
1000-0111_two = 87_sixteen
1000-1000_two = 88_sixteen
1000-1001_two = 89_sixteen
1000-1010_two = 8A_sixteen
1000-1011_two = 8B_sixteen
1000-1100_two = 8C_sixteen
1000-1101_two = 8D_sixteen
1000-1110_two = 8E_sixteen
1000-1111_two = 8F_sixteen

1001-0000_two = 90_sixteen
1001-0001_two = 91_sixteen
1001-0010_two = 92_sixteen
1001-0011_two = 93_sixteen
1001-0100_two = 94_sixteen
1001-0101_two = 95_sixteen
1001-0110_two = 96_sixteen
1001-0111_two = 97_sixteen
1001-1000_two = 98_sixteen
1001-1001_two = 99_sixteen
1001-1010_two = 9A_sixteen
1001-1011_two = 9B_sixteen
1001-1100_two = 9C_sixteen
1001-1101_two = 9D_sixteen
1001-1110_two = 9E_sixteen
1001-1111_two = 9F_sixteen

1010-0000_two = A0_sixteen
1010-0001_two = A1_sixteen
1010-0010_two = A2_sixteen
1010-0011_two = A3_sixteen
1010-0100_two = A4_sixteen
1010-0101_two = A5_sixteen
1010-0110_two = A6_sixteen
1010-0111_two = A7_sixteen
1010-1000_two = A8_sixteen
1010-1001_two = A9_sixteen
1010-1010_two = AA_sixteen
1010-1011_two = AB_sixteen
1010-1100_two = AC_sixteen
1010-1101_two = AD_sixteen
1010-1110_two = AE_sixteen
1010-1111_two = AF_sixteen

1011-0000_two = B0_sixteen
1011-0001_two = B1_sixteen
1011-0010_two = B2_sixteen
1011-0011_two = B3_sixteen
1011-0100_two = B4_sixteen
1011-0101_two = B5_sixteen
1011-0110_two = B6_sixteen
1011-0111_two = B7_sixteen
1011-1000_two = B8_sixteen
1011-1001_two = B9_sixteen
1011-1010_two = BA_sixteen
1011-1011_two = BB_sixteen
1011-1100_two = BC_sixteen
1011-1101_two = BD_sixteen
1011-1110_two = BE_sixteen
1011-1111_two = BF_sixteen

1100-0000_two = C0_sixteen
1100-0001_two = C1_sixteen
1100-0010_two = C2_sixteen
1100-0011_two = C3_sixteen
1100-0100_two = C4_sixteen
1100-0101_two = C5_sixteen
1100-0110_two = C6_sixteen
1100-0111_two = C7_sixteen
1100-1000_two = C8_sixteen
1100-1001_two = C9_sixteen
1100-1010_two = CA_sixteen
1100-1011_two = CB_sixteen
1100-1100_two = CC_sixteen
1100-1101_two = CD_sixteen
1100-1110_two = CE_sixteen
1100-1111_two = CF_sixteen

1101-0000_two = D0_sixteen
1101-0001_two = D1_sixteen
1101-0010_two = D2_sixteen
1101-0011_two = D3_sixteen
1101-0100_two = D4_sixteen
1101-0101_two = D5_sixteen
1101-0110_two = D6_sixteen
1101-0111_two = D7_sixteen
1101-1000_two = D8_sixteen
1101-1001_two = D9_sixteen
1101-1010_two = DA_sixteen
1101-1011_two = DB_sixteen
1101-1100_two = DC_sixteen
1101-1101_two = DD_sixteen
1101-1110_two = DE_sixteen
1101-1111_two = DF_sixteen

1110-0000_two = E0_sixteen
1110-0001_two = E1_sixteen
1110-0010_two = E2_sixteen
1110-0011_two = E3_sixteen
1110-0100_two = E4_sixteen
1110-0101_two = E5_sixteen
1110-0110_two = E6_sixteen
1110-0111_two = E7_sixteen
1110-1000_two = E8_sixteen
1110-1001_two = E9_sixteen
1110-1010_two = EA_sixteen
1110-1011_two = EB_sixteen
1110-1100_two = EC_sixteen
1110-1101_two = ED_sixteen
1110-1110_two = EE_sixteen
1110-1111_two = EF_sixteen

1111-0000_two = F0_sixteen
1111-0001_two = F1_sixteen
1111-0010_two = F2_sixteen
1111-0011_two = F3_sixteen
1111-0100_two = F4_sixteen
1111-0101_two = F5_sixteen
1111-0110_two = F6_sixteen
1111-0111_two = F7_sixteen
1111-1000_two = F8_sixteen
1111-1001_two = F9_sixteen
1111-1010_two = FA_sixteen
1111-1011_two = FB_sixteen
1111-1100_two = FC_sixteen
1111-1101_two = FD_sixteen
1111-1110_two = FE_sixteen
1111-1111_two = FF_sixteen

Thus, as regards Computer Programming, Hexadecimal is sometimes dubbed “a shorthand for binary.” It is much easier, and it is much more conducive to accuracy, for a human being to low-level program by entering in permutations of two Hexadecimal Digits, than for him/her to low-level program by entering in permutations of eight binary digits. It is possible to low-level program in hexadecimal by using a hexadecimal editor, often referred to as a “hex editor.”

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¹ The term ‘hexadecimal’ is derived from the Ancient-Greek Cardinal Number, ‘héx,’ which means ‘six,’ and the Ancient-Greek Cardinal Number, ‘déka,’ which means ‘ten.’ When we affix the Latin 3rd-declension suffix, ‘-ālis, -āle’ to the numbers, ‘héx,’ and ‘déka,’ – which, when combined make the Latin prefix, ‘hexadecima-‘ which denotes 16 – we get the Latin 3rd-declension adjective, ‘hexadecimālis, hexadecimāle,’ which means ‘of 16;’ ‘relating to 16;’ etc. Thus, the English adjective, ‘hexadecimal,’ possesses the etymological sense: ‘of [base] 16;’ ‘relating to [base] 16;’ etc.

² The base-10 or decimal numbers that we ordinarily use on a day-to-day basis.

Classical Hebrew and a Galaxy Far Far Away.

I never got into the Star Wars franchise of films. I believe that the only Star Wars film that I have ever watched from start to finish was Phantom Menace. I know that Star Wars aficionados detest this film, but I remember really enjoying it.

Like most writers, I hope to, one day, complete a screenplay. I saw the Phantom Menace screenplay in a charity shop and bought it for dirt cheap.

Figure 1: The Phantom-Menace screenplay that I bought, a while back, in a charity shop.

I am teaching myself Classical Hebrew at the minute. The O’Reilly Dictionary asserts that Irish-Gaelic and Classical Hebrew are related languages. This would be a fascinating thing to research.

Figure 2: The O’Reilly Irish-English Lexicon from 1864.

A friend of mine has asked my help in writing a book that explores the linguistic and cultural similarities that existed between the Ancient Gaels and the Ancient Hebrews.

The way that I teach myself Classical Hebrew is by following a course on Youtube. In particular, I am following a course taught by Doctor Bill Barrick. Dr Barrick really gets into the nuts and bolts of Hebrew Grammar, which is what I like about his course in preference to many others.

Learning a dead language is difficult. Learning a dead language that has practically zero words in common with English – unlike Greek and Latin, say – is doubly difficult.

Classical Hebrew is a useful language to learn, even for purely secular purposes. As a Canaanite Language (1.) it is related to other Ancient Canaanite languges, such as Egyptian Hieroglyphics, and Classical Arabic, and Modern languages spoken in the Middle East, such as Modern Arabic.

For example, the Hebrew word for ‘head’ is ‘rōsh.’

The Aramaic (2.) word, the for ‘head’ is ‘rēsh.’

The Arabic word for ‘head’ is ‘ra’as.’

But learning a dead language, like Classical Hebrew, a language that one, especially in Ireland, is very unlikely to use, ever, in conversation, is extremely difficult. I remember when in Switzerland, on holiday, I was immersed in French and German. At night, prior to drifting off to sleep, I would hear the phonemes of French and German re-echo in my mind. A few months in such an immersion, and I would have become fluent. Such an immersion, although not totally impossible in Classical Hebrew (3)., is still not an easy task.

Modern Hebrew, from what I can gather, is a totally artificial construct. It was invented in the 1800s. They pronounce some phonemes in an Ashkenazic style, and other phonemes in a Sephardic style. Modern Hebrew uses an artificial compromised pronunciation. They have also, largely, abandoned the syntax of Ancient Hebrew. Modern Hebrew is essentially Hebrew words arranged in English syntax. English is very prepositional, so Modern Hebrew had to invent a load of prepositions, in the 1800s, that were never used, neither amongst the Ancient Hebrews, nor in Contemporary Jewish Ghettos. Certain Orthodox Jews find Modern Hebrew, for all the reasons listed above, blasphemous, and refuse to speak it.

So learning a dead language, such as Classical Hebrew, is a difficult task. One method that Doctor Bill Barrick has so as to overcome some of these difficulties, is to relate Ancient Hebrew words to modern-day entities.

I had been doing this myself, independently, with Ancient Greek.

I have a JVC cinema system, for example, and, thereupon, I fastened a sticker with the Ancient-Greek word:

κίνημα

or ‘kínēma,’ the Ancient-Greek word for ‘motion’ whence we derive the English word ‘cinema’ which describes ‘motion pictures.’

Doctor Bill Barrick would relate Ancient-Hebrew terms with the phenomena of modernity.

One phenomenon of Modernity to which he attached a Classical-Hebrew term just so happened to be Star Wars.

Figure 3: C3PO.

Doctor Bill Barrick theorised that the planet ‘Endor,’ the planet infested with Sasquatches known as ‘Ewoks,’ derived its name from the Ancient-Hebrew words, ‘Ayin’ and ‘Dor.’

Ayin Dor would translate to ‘Eye/Spring of Generation.’

The Ancient Hebrews used the term ‘eye’ so as to mean ‘natural water-spring.’ To the Ancient Hebrews, the earth, or ‘Ha-arets (4.) ‘ was a big eye, that would well up with water in places.

This is another benefit to learning languages. Not only does one learn the language itself, but one is also acquainted with the concepts of the culture that gave rise to that language.

Speaking of American Sci-Fi franchises, although I am a man, soon to be thirty, who is single, and who lives, for the most part, with his parents (5.) , I never got into Star Trek either.

Recently, prior to passing away, Leonard Nimoy, the actor who played, Spok, said that the Trekker live-long-and-prosper hand symbol was based on the Hebrew character, shin.

Figure 4: Leonard Nimoy giving the live-long-and-prosper handsign.

Figure 5: The 21^st character of the Hebrew Alphabet, Shin. Shin means ‘teeth.’ The shin symbol represents that which devours, especially fire and romantic love.

Below are links to Word documents that contain the words, ‘Ayin’ and ‘Dor’, their spellings, and their meanings.

ayin_eyes_spring

dor_generation

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(1.) Classical Hebrew’s linguistic classification.

(2.) The language of ancient Babylonia and Persia.

(3.) Modern-day Samaritans, for example, speak a form of Hebrew very close to Classical Hebrew, but I have no interest in packing my bags to go off to Samaria to see them.

(4.) ‘Erets’ in Hebrew means ‘land, country, earth, planet earth.’ It is ‘Haarets’ in its definite form. Hence the newspaper, Haaretz.

(5.) I am alluding to a quip made by Patrick Stewart in Ricky Gervaise’s sitcom, Extras.

 

Ancient Languages; Recent Technological Innovations.

Figure 1: An iPad.  I drew this with oil pastels and oil paints.

I am fascinated by Ancient Languages.

Tablets were used in the Ancient World.  There is a scene in Cecil B. De Mille’s 1959 film, Ben Hur, where Masala, the Roman antagonist, confirms a hefty wager against Judah Ben Hur, by imprinting his ring into Sheikh Ilderim’s Clay tablet.  Masala bets that he will win a chariot race against Judah in the Jerusalem Circus.  He loses his bet and his life in the attempt.

It amazes me that tablets were used in the Ancient World to convey and show information; they fell out of fashion for a long while; and then, only in the last ten years, they have become as popular as ever they were in the Ancient World.

The Latin word for ‘tablet’ is the feminine, first-declension noun, ‘tabula, tabulae.’  From the Latin word ‘tabula’ we derive the English verb, ‘to tabulate,’ which is the arrangement of analysed statistical data.

The Ancient-Hebrew  word for ‘tablet’ is the masculine noun, ‘lúach,’ or ל֫וּחַ in Hebrew script.  When Judah Ben Hur saw Sheikh Ilderim’s lúach, he would have smiled, wryly, as Masala took the bait.  Now we had a chariot match on our hands!

The Ancient-Greek word for ‘tablet’ is the masculine, third-declension noun, ‘hó pínach, toũ pínakos,’ or ‘ ὁ πίναξ , τοῦ πίνακος ‘ in Ancient-Greek script.

Perhaps when Aristotle was observing nature; researching the world’s first biology book, the ‘Historia Animālium;’ he recorded his observations in one such ‘pínach.’