Ciaran Mc Ardle's Blog
https://codepen.io/Valerius_de_Hib/posts/feed/
ennospam@codepen.ioCopyright 2019
2019-02-02T11:55:56-07:00
The Famous Syllogism in Greek, Latin and English:
https://codepen.io/Valerius_de_Hib/post/the_famous_syllogism_in_greek_latin_and_english
https://codepen.io/Valerius_de_Hib/post/the_famous_syllogism_in_greek_latin_and_englishCiaran Mc Ardle

The Famous Syllogism^{[1]} in Greek, Latin and English:

Introduction:

Quite early on, in his Mathematical Analysis of Logic, George Boole–whence in programming and computer science we derive the datatype name, ‘Boolean’– introduces this famous syllogism to us, his readers.

Body:

In Ancient Greek:

ὁ Σωκράτης ἐστιν ἄνθρωπος.

πάντης ἄνθρωποι ἐστι θνητοί.

οὖν ὁ Σωκράτης ἐστι θνητός.

When Transliterated:

ho Sōcrátēs estin ánthrōpos.

pántēs ánthrōpoi esti thnētoí.

oũn ho Sōkrátēs esti thnētos.

In Latin:

Sōcratēs est homō.

Omnēs hominēs sunt mortālēs.

Ergō, Sōcratēs est mortālis.

In English:

Socrates is a man.

All men are mortal.

Therefore, Socrates is mortal.

Conclusion:

The Ancient-Greek term, ὁ λόγος or, when transliterated, ‘ho lógos,’^{[1]} means–within the context of logic– ‘statement,’ or ‘argument.’

The Latin 1^{st}-and-2^{nd}-declension adjectival suffix, ‘-ica, -icus, -icum’ means ‘of,’ ‘about,’ ‘concerning,’ ‘pertaining to,’ etc.

Hence, etymologically, ‘logic’ is ‘the study of the truth or falsehood of statements and arguments.’

Conventional arithmetic or Conventional Algebra has quantity for its subject. George Boole developed an algebra, or an arithmetic that had logic as its subject.

Indeed, in his book, The Laws of Thought he terms this ‘arithmetic’ or ‘algebra’ of his ‘a calculus of logic’ by which he meant ‘a system whereby the truth or falsehood of statements/arguments could be analysed.’

Glossary:

calculus (ˈkælkjʊləs) nounplural-luses

a branch of mathematics, developed independently by Newton and Leibniz. Both differential calculus and integral calculus are concerned with the effect on a function of an infinitesimal change in the independent variable as it tends to zero.

any mathematical system of calculation involving the use of symbols

logic an uninterputed formal system. Compare formal language (sense 2)

(plural-li (ˈkælkjʊˌlaɪ) ) pathology a stonelike concretion of minerals and salts found in ducts or hollow organs of the body[C17 from Latin: pebble, stone used in reckoning, from calx small stone, counter]

calcular(ˈkælkjʊlə) adjective relating to calculus

calculous (ˈkælkjʊləs) or calculary(ˈkælkjʊlərɪ) of or suffering from a calculus. Obsolete form: calculose

calculus of variations a branch of calculus concerned with maxima and minima of definite integrals.^{[1]}

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The Famous Syllogism in Greek, Latin and English:
2019-02-02T11:55:56-07:00
Introduction to Syllogistic Logic:
https://codepen.io/Valerius_de_Hib/post/introduction-to-syllogistic-logic
https://codepen.io/Valerius_de_Hib/post/introduction-to-syllogistic-logicCiaran Mc Ardle
The Syllogism Stated:

Premise 1:

Socrates is a man.

Premise 2:

All men are mortal.

Necessarily Inferred Conclusion:

Socrates is mortal.

The Syllogism Stated in Terms of Set Theory:

Let:

S

equal the set of Socrates.

Let:

H

equal the set of men.

Let:

M

equal the set of mortal beings.

Socrates is a man.

Sōcratēs est homō.

All S are H.

Hence:

S ⊂ H

.

All men are mortal.

Omnēs hominēs sunt mortālēs.

All H are M.

Hence:

H ⊂ M

.

Given that M is a superset of H:

M ⊃ H

and given that H is a superset of S:

H ⊃ S

, then we can necessarily infer that M is a superset of S:

M ⊃ S

.

The set of Mortal Beings contains Socrates as an element therein.

Hence we can conclude that Socrates, his being an element of the set of Mortal beings, by virtue of his being a member of the set of Men, is mortal.

Ergō Sōcratēs est mortālis.

S ⊂ M

.

Summary I:

S ⊂ H

AND:

H ⊂ M

and so THEREFORE:

S ⊂ M

.

Summary II

M ⊃ H

AND:

H⊃S

and so THEREFORE:

M ⊃ S

.

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Introduction to Syllogistic Logic:
2019-01-22T22:18:31-07:00
The Classics can make STEM easier: Latin names of Formal Logic (Boolean) Symbols
https://codepen.io/Valerius_de_Hib/post/the_classics_can_make_stem_easier_latin_names_of_formal_logic_boolean_symbols
https://codepen.io/Valerius_de_Hib/post/the_classics_can_make_stem_easier_latin_names_of_formal_logic_boolean_symbolsCiaran Mc Ardle

Introduction

It is my contention that the knowledge of Latin and Greek make STEM^{[1]} easier to learn. A huge number of STEM terms are derived from Greek and Latin.

The etymology of STEM:

The acronym, ‘stem’ conjures up the image of the ‘stem of a plant.’ This in turn conjures the image of ‘growth.’ Learning STEM, one grows his/her career; his mathematical and scientific knowledge; and even his own finances and the economy.

The English word, ‘stem’ is derived from the Ancient-Greek 3rd-declension neuter noun, τὸ στέμμα Genitive: τοῦ στέμματος or, when transliterated 'tò stémma,' Genitive: ‘toũ stémmatos.’

The term ‘science’ is derived from the Latin 1st-declension feminine noun, ‘scientia,’ which means ‘knowledge.’

Sir Francis Bacon, who worked on the development of the scientific method once remarked:

Nam et ipsa scientia potestās est.

Science/Knowledge is power.

The term ‘technology’ is derived from the Ancient-Greek 1^{st}-declension feminine noun, ἡ τέχνη Genitive: τῆς τέχνηs or, when transliterated: ‘hē téchnē’ Genitive: ‘tē̃s téchnēs;’ which means ‘art’ ‘artisanship,’ ‘technical ability,’ etc. and the Ancient-Greek suffix, -λογία or, when transliterated: ‘logía’ which denotes a ‘study.’ Etymologically, therefore, ‘technology’ is ‘the study of technical skils;’ ‘the study of technical abilities;’ etc.

The term ‘engineering’ is derived from the Latin prefix ‘in-’ which, in this instance, means ‘in’ ‘into;’ and the 2^{nd}-declension masculine noun, ‘genius’ Genitive: ‘geniī,’ which means ‘begotten spirit‘ ‘daemon’ ‘geni.’ The etymological idea, here, is ‘giving life to machinery’ or, in Latin:

‘pōnere deum in māchinam’

or:

‘placing a god into the machine’

.

The term, ‘mathematics,’ is derived from the Ancient-Greek 3^{rd}-declension neuter noun τὸ μάθημα Genitive: τοῦ μαθήματος or, when transliterated, ‘tì máthēma’ Genitive:toũ mathēmatos,’ which means ‘lesson.’ In Koine Greek, the disciples of Jesus are called ὁι μαθηταί or, when transliterated ‘hoi mathētai.’ The disciples, etymologically ‘learned from [Jesus].’ The term ‘discipulus’ in Latin means ‘disciple,’ ‘learner,’ ‘pupil’ etc. The Latin 3^{rd}-conjugation verb ‘discō, discere, didicī, discitum’ means ‘to learn.’ We can observe that the academic term ‘discertation’ or, etymologically ‘a piece of scholarship’ is derived from this verb.

Vel Symbol:

In Formal Logic this symbol represents ‘disjunction.’ The equivalent in Boolean Algebra is ‘Inclusive Or.’ ‘vel’ is Latin for ‘or.’ One sees this quite a bit in liturgical rubrics^{[2]}.

The Wedge Symbol

In Formal Logic this symbol represents “conjunction.” The equivalent in Boolean Algebra is "And." In Latin, 'ac' or 'atque' is 'and.' Sometimes this symbol is called this. One sees this quite a bit in ecclesiastical Latin.

‘I announce to ye a great joy: we have a Pope!, the most eminent and most revered [forename] of the most holy Roman Church, Cardinal [surname], who hath placed upon himself the name [regnal name].’

In the offertory the priest prays:

‘...prō fidēlibus christiānīs vīvīs atque dēfūnctīs...’

‘...for all faithful Christians living and dead...’

In The Young Pope (2016), a Cardinal, disfavoured by Pius XIII/Jude Law, prays this in the frozen wilderness of Alaska, to whence he was banished.

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The Classics can make STEM easier: Latin names of Formal Logic (Boolean) Symbols
2019-01-21T13:45:49-07:00
The Hebrew Word For Father:
https://codepen.io/Valerius_de_Hib/post/the_hebrew_word_for_father
https://codepen.io/Valerius_de_Hib/post/the_hebrew_word_for_fatherCiaran Mc Ardle
<![CDATA[
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L'chaim': My first 100 Hebrew Words | av

The Hebrew Word for Father:

In this chapter, we are going to examine the Hebrew word, אָב or ‘āv.’

Body

The Hebrew word for ‘father’ is:

אָב

Which is pronounced:

/ʔaːv/ , /ʔa:v/

, and which can be transliterated as:

‘āv’

In Phoenecian, or “Paleo-Hebrew” it is spelt:

According to this intriguing website on Ancient Hebrew this word, pictographically, means “the strength of the house;’ ‘The leader (aluph)^{[1]} of the house (beith).’ He says that in Classical Hebrew thought, each person was said to be blessed with three fathers:

a biological father: ‘the strength of a household;’ ‘the leader of a household;’

a priest: ‘leader of the house of God;’

God: ‘the leader of the Universe.’

In Biblical Hebrew, ‘the patriarchs;’ or ‘the fathers;’ or ‘Abraham, Isaac and Jacob;’ are called the:

In classical Hebrew, a little goes a long way. By our learning of the word, אָב or ‘āv,’ we have gained a more or less implicit understanding of Ancient-Hebrew and Phoenecian culture, as regards how they view concepts such as Godpatriarchy and fatherhood.

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The Hebrew Word For Father:
2019-01-14T03:48:19-07:00
Arrow Functions in ECMA Script 6:
https://codepen.io/Valerius_de_Hib/post/arrow-functions-in-ecma-script-6
https://codepen.io/Valerius_de_Hib/post/arrow-functions-in-ecma-script-6Ciaran Mc ArdleECMA Script 6 | Arrow Functions =>

Arrow Functions in ECMA Script 6:

Introduction:

Arrow functions allow us to store functions as Constants and Variables.

Body:

The following piece of code allows us to save an arrow function that squares 10 as a const:

const square_function = (x)=>x*x;

We can better understand what is being expressed in the above statement by saying it aloud in English:

square_function is an identifier, which represents an address in memory, and which names the data contained within this piece of memory, and which in this instance is a constant – i.e. its value cannot change at runtime^{[1]} – which contains a function that takes a parameter, x, and which applies a squaring operation to this parameter.

When it comes to the mathematics of functions, it is more proper to say that a function is applied to a parameter.

Below is a button that employs the attribute onclick so as to square 10 and then to print the result or square to the screen:

The above button employs the following piece of HTML/JavaScript code so as to have the function, square_functionapplied to the argument, 10, and then to have the result or return value of this function printed to the screen:

When the above button is pressed, the above-described code causes the number 100 to be printed to the screen.

Conclusion:

I really enjoy the functional aspects of the more recent versions of Javascript such as ECMA script 6.

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Arrow Functions in ECMA Script 6:
2018-09-17T01:28:19-07:00
Let Us Fly off on a Tangent
https://codepen.io/Valerius_de_Hib/post/let-us-fly-off-on-a-tangent
https://codepen.io/Valerius_de_Hib/post/let-us-fly-off-on-a-tangentCiaran Mc ArdleLet us fly offf on a tangent.

Let Us Fly Off On a Tangent:

<p>To <em>fly off on a tangent</em> idiomatically, is to digress so radically, such that the topic that one now speaks of is only related to the previous topic – prior to the digression – by having only the point that spurred the tangent in common.</p>
<p>In mathematics, a ‘tangent’ is a line that only has a single point in common with the circumference of a circle.</p>
<p>The tangent line <em>touches</em><a name="referenced_material_i" href="#footnote_i">[1]</a> the circle’s circumference at a single point, and is perpendicular to the radius of the circle.</p>
<p>The angles that the tangent makes with the radius are right, i.e. of magnitude 90°.</p>
<figure id="tangent_svg">
<svg xmlns="http://www.w3.org/2000/svg" version="1.1" Viewbox="0,0,500, 500">
<!--For Absolutes Use Commented OUt SVG Tag Below: -->
<!--<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="500" height="500">-->
<title>Tangent</title>
<desc>A tangent line</desc>
<g class="tangent_image" transform=" translate(150,220)">
<g class="scale_by_100" transform="scale(100,100)">
<circle id="my_circle" cx="0" cy="0" r="1" stroke-width="0.01" stroke="#000000" fill="transparent"></circle>
<line id="radius" x1="0" y1="0" x2="1" y2="0" stroke-width="0.01" stroke="#000000" ></line>
<circle id="my_center" cx="0" cy="0" r="0.025" stroke-width="0.01" stroke="#000000" fill="#FF0000"></circle>
<circle id="my_tangent_point" cx="1" cy="0" r="0.025" stroke-width="0.01" stroke="#000000" fill="#FF0000"></circle>
<text id="circle_name_a" font-family="Times New Roman" x="-1.1" y="-1.0125" font-size="0.25" fill="#000000" font-style="italic">A</text>
<text id="point_a" font-family="Times New Roman" x="-0.05" y="-0.1" font-size="0.25" fill="#000000" font-style="italic">a</text>
<text id="point_b" font-family="Times New Roman" x=".8" y="-0.1" font-size="0.25" fill="#000000" font-style="italic">b</text>
<line id="tangent" x1="1" y1="-2" x2="1" y2="2" stroke-width="0.01" stroke="#000000" ></line>
<g transform="translate(1,-2.01)">
<g transform="scale(0.1,0.1)">
<path id="line_arrow" d="M0,0 L -0.70710678 0.70710678 L0.70710678 0.70710678 L0,0 z"></path>
</g>
</g>
<g transform="translate(1,2.01)">
<g transform="scale(0.1,0.1)">
<path id="line_arrow" d="M0,0 L -0.70710678 -0.70710678 L0.70710678 -0.70710678 L0,0 z"></path>
</g>
</g>
<circle id="my_tangent_point_x" cx="1" cy="-1" r="0.025" stroke-width="0.01" stroke="#000000" fill="#FF0000"></circle>
<text id="point_x" font-family="Times New Roman" x="1.1" y="-1" font-size="0.25" fill="#000000" font-style="italic">x</text>
<circle id="my_tangent_point_y" cx="1" cy="1" r="0.025" stroke-width="0.01" stroke="#000000" fill="#FF0000"></circle>
<text id="point_y" font-family="Times New Roman" x="1.1" y="1" font-size="0.25" fill="#000000" font-style="italic">y</text>
<g class="right_boxes">
<rect fill="transparent" stroke-width="0.01" stroke="#000000" x="0.9" y="-0.1" width="0.1" height="0.1"></rect>
<rect fill="transparent" stroke-width="0.01" stroke="#000000" x="0.9" y="0" width="0.1" height="0.1"></rect>
</g>
</g>
</g>
</svg>
<figcaption><strong>Figure 1:</strong>  A diagram of a tangent line.</figcaption>
</figure>
<p>In the circle:</p>
<p class="cambria_math_centered"><em>A</em></p>
<p>, the centre is at point:
<p class="cambria_math_centered"><em>a</em></p>
<p>.  The radius of the circle is line segment:</p>
<p class="cambria_math_centered">| <em>a</em> <em>b</em> |</p>
<p>.  The tangent line is:</p>

| xy |

. The tangent line:

| xy |

, only touches the circle:

A

, at a single point, and that point is point:

b

. The tangent:

| xy |

is perpendicular to the radius:

| ab |

. The angle:

∠xba

is a right angle.

. The angle:

∠yba

is a right angle.

<hr/>
<p><a name="footnote_i" href="#referenced_material_i">[1]</a>.  The Latin participle, ‘tangēns, tangent-, ’ means ‘touching.’ Therefore, etymologically, a <em>tangent line</em> is only <em>touching</em> a circle’s circumference at a single point.  The Latin 3<sup>rd</sup>-conjugation verb, ‘tangō, tangere, tetigī, tāctum,’ means ‘to touch.’</p>

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Let Us Fly off on a Tangent
2018-05-08T09:25:30-07:00
A Common Principle of Boolean Algebra as Stated in George Boole's 'Mathematical Analysis of Logic':
https://codepen.io/Valerius_de_Hib/post/a-common-principle-of-boolean-algebra
https://codepen.io/Valerius_de_Hib/post/a-common-principle-of-boolean-algebraCiaran Mc Ardle
A Common Principle of Boolean Algebra: xy = y

Statement of the Common Principle:

Should:

x = U

or, in other words:

x = 1

Then, in Boolean Notation :

xy = y

Or, in formal-logic notation:

x ∧ y = y

.

e.g. 1:

Let:

x = 1

.

Let:

y = 0

.

Hence:

xy = y

Or, in formal-logic notation:

x ∧ y = y

, because:

1 × 0 = 0

, or:

1(0) = 0

, or, in formal-logic notation:

1 ∧ 0 = 0

.

e.g. 2:

Let:

x = 1

.

Let:

y = 1

.

Hence:

xy = y

Or, in formal-logic notation:

x ∧ y = y

, because:

1 × 1 = 1

, or:

1(1) = 1

, or, in formal-logic notation:

1 ∧ 1 = 1

.

Addendum:

You may read George Boole's Mathematical Analysis of Logic, for free at Project Gutenberg

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A Common Principle of Boolean Algebra as Stated in George Boole's 'Mathematical Analysis of Logic':
2018-04-16T06:14:54-07:00
A Geometric Representation of the Square Root of Three.
https://codepen.io/Valerius_de_Hib/post/a-geometric-representation-of-the-square-root-of-three
https://codepen.io/Valerius_de_Hib/post/a-geometric-representation-of-the-square-root-of-threeCiaran Mc Ardle
Place one equilateral triangle on top of an inverted equilateral triangle so as to form a diamond.

If we call the length of side of the equilateral triangles:

1 unit

, then the height of the diamond, by proportion, will be:

√3

.

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A Geometric Representation of the Square Root of Three.
2017-03-08T23:20:47-07:00