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Radical square and other roots
1. Radical square and other roots
2. Radical square and other roots
The English word
"radical" comes from the idea of a "
root" such as the root of a tree.
From about the time of the American Revolution in 1776, the English word
"radical" has meant a desired change in the fundamental or "
root" way in which something has been done.
In ancient Greece, the Greek word for "
root" was used for the mathematical concept of, for example, a square root.
Pythagoras used the square root as part of what is called the Pythagorean theorem.
3. Radical root
Colossians 2:7 Rooted and built up in him, and stablished in the faith, as ye have been taught, abounding there in with thanksgiving. [kjv]
ερριζωμενοι και εποικοδομουμενοι εν αυτω και βεβαιουμενοι τη πιστει καθως εδιδαχθητε περισσευοντες εν αυτη εν ευχαριστια [gnt]
radicati … superaedificati … didicistis … gratiarum … [v]
The ancient Greek word
"ῥίζα" ≈ "root" of a plant and, later, as a math root such as the square root of two. It is related to the Latin word
"radix" ≈ "root" and the English word
"root" from the Old English word
"wyrt" ≈ "root".
The English word
"radical" comes from the Latin word
"radicalis" ≈ "pertaining to the root, having roots".
The Gothic word
"waurts" ≈ "root".
4. Pythagoras and mystery
In about 500 B.C., Pythagoras had a secret society who membership was a mystery to anyone outside the group. It was a closed group and required a special initiation.
Pythagoras had a simple
proof (omitted) to show the irrationality of the
square root of two. This
secret was not to be revealed to anyone outside the group. The punishment for revealing this secret was death.
The Greek word for "
mystery" is based on the Greek word for "
initiation" as in a member to a group that is "
shut" until one is "
initiated". The term "
mystery cult" is still heard today.
Do whole numbers exist? Do real numbers exist? Explain.
5. Euclidean distances
The distance
d between points (x
1, y
1, z
1) and (x
2, y
2, z
2) in a 3-D space is determined as follows.
The above math formula can be written as the following coding expression (as an assignment statement) where
sqrt is the square root function and
pow is the power function.
d = sqrt( pow(x2-x1,2) + pow(y2-y1,2) + pow(z2-z1, 2))
This distance is called the Euclidean distance and uses the Pythagorean theorem. This distance idea is used in many areas of statistics in distributions, error analysis, etc.
6. Square root of a tree
A square root of a tree may not be obvious. How about a cube root? In the Bible:
Mountains represent empires.
Trees represent the human infrastructure of an empire.
The birds represent people who make nests in the tree.
The root represents the human leader of the tree.
A fox may have to settle for a den near the tree root.
7. Squares
The idea of a "
square meal" may have come about from the square plates used to serve food on ships.
The idea of a "
square deal" was part of President Theodore Roosevelt's domestic programs.
The idea of a "
new deal" was from President Franklin Roosevelt using a change to the term "
square deal".
8. Music: George Frederick Root
George Frederick Root (1820-1895) would later use the tune that he wrote for the American Civil War song "
Tramp, Tramp, Tramp" for another song. His pseudo-name was "
Wurzel", German for "
root" (his last name).
By the age of 13, he could play a tune on 13 instruments (and was proud of that fact).
9. Colossians 2:7 Roots
Colossians 2:7 Rooted and built up in him, and stablished in the faith, as ye have been taught, abounding there in with thanksgiving. [kjv]
ερριζωμενοι και εποικοδομουμενοι εν αυτω και βεβαιουμενοι τη πιστει καθως εδιδαχθητε περισσευοντες εν αυτη εν ευχαριστια [gnt]
radicati … superaedificati … didicistis … gratiarum … [v]
Might Paul be making an analogy of Christ as an alternative to the "
square root" and "
mystery" secrets of Pythagoras and Greek philosophy?
10. Rooted and grounded
Ephesians 3:17 That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, [kjv]
κατοικησαι τον χριστον δια της πιστεως εν ταις καρδιαις υμων [gnt]
… rootid … [wy]
… eingewurzelt … [lu]
… radicati … [v]
Note that the phrase translated "
rooted and grounded in love" is in verse 17 in one
GNT (Greek New Testament) version and in verse 18 in the other
GNT version.
The modern Greek word for rooted is based on the modern Greek word
"ρίζα" (REE-za) ≈ "root" which is cognate with the Latin word
"radix" ≈ "root" and the Latin word
"ramus" ≈ "branch" and the Old English word
"wyrt" ≈ "herb, plant".
11. Ephesians 3:17
KJV: That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love,
Greek: κατοικησαι τον χριστον δια της πιστεως εν ταις καρδιαις υμων εν αγαπη ερριζωμενοι και τεθεμελιωμενοι
Latin: habitare Christum per fidem in cordibus vestris in caritate radicati et fundati
Wycliffe: that Crist dwelle bi feith in youre hertis; that ye rootid and groundid in charite,
Luther: und Christum zu wohnen durch den Glauben in euren Herzen, und durch die Liebe eingewurzelt und gegründet zu werden,
12. Radical ideas
To promote something as "
radical", one should clearly point out the root idea that exists and is to be changed. Once this is done, one should clearly point out the new "
radical" idea, how it differs from the "
root" idea, and why the "
radical" new idea is better than the "
root" idea.
Being different is not always better. Sometimes it is necessary and needed. At other times, it is not necessary and may cause unintended side-effects and other damage.
13. Change
The power to change is the power to grow. Change is the law of life. And those who look only to the past or present are certain to miss the future. But change for change's sake can be more damaging to your efforts towards creating an engaged and inspired workforce than no change at all. John F. Kennedy (35 President of the United States)
14. Root of trees
Matthew 3:10 And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire. [kjv]
ηδη δε η αξινη προς την ριζαν των δενδρων κειται παν ουν δενδρον μη ποιουν καρπον καλον εκκοπτεται και εις πυρ βαλλεται [gnt]
To what is Matthew referring?
☐ A person who does not bring forth good fruit (the ultimate "
fish fry").
☐ A human infrastructure (empire, church, etc.) that does not bring forth good fruit where the "
root" is the leader (in for a "
rude" or "
root" awakening).
What could this "
tree" refer to historically?
☐ Rome
☐ Judea under Herod
☐ Israel (as the fig tree)
☐ church (sand infrastructure)
☐ other trees/empires/mountains
15. Matthew 3:10
KJV: And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire.
Greek: ηδη δε και η αξινη προς την ριζαν των δενδρων κειται παν ουν δενδρον μη ποιουν καρπον καλον εκκοπτεται και εις πυρ βαλλεται
Latin: iam enim securis ad radicem arborum posita est omnis ergo arbor quae non facit fructum bonum exciditur et in ignem mittitur
16. Roots in Romans
17. Romans 11:16
KJV: For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.
Greek: ει δε η απαρχη αγια και το φυραμα και ει η ριζα αγια και οι κλαδοι
Latin: quod si delibatio sancta est et massa et si radix sancta et rami
18. Romans 11:17
KJV: And if some of the branches be broken off, and thou, being a wild olive tree, wert graffed in among them, and with them partakest of the root and fatness of the olive tree;
Greek: ει δε τινες των κλαδων εξεκλασθησαν συ δε αγριελαιος ων ενεκεντρισθης εν αυτοις και συγκοινωνος της ριζηςκαι της πιοτητος της ελαιας εγενου
Latin: quod si aliqui ex ramis fracti sunt tu autem cum oleaster esses insertus es in illis et socius radicis et pinguidinis olivae factus es
19. Romans 11:18
KJV: Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee.
Greek: μη κατακαυχω των κλαδων ει δε κατακαυχασαι ου συ την ριζαν βασταζεις αλλ αλλα η ριζα σε
Latin: noli gloriari adversus ramos quod si gloriaris non tu radicem portas sed radix te
20. Branches
21. Romans 11:19
KJV: Thou wilt say then, The branches were broken off, that I might be graffed in.
Greek: ερεις ουν εξεκλασθησαν οι κλαδοι ινα εγω εγκεντρισθω
22. Romans 11:20
KJV: Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
Greek: καλως τη απιστια εξεκλασθησαν συ δε τη πιστει εστηκας μη υψηλοφρονει υψηλα φρονει αλλα φοβου
23. Romans 11:21
KJV: For if God spared not the natural branches, take heed lest he also spare not thee.
Greek: ει γαρ ο θεος των κατα φυσιν κλαδων ουκ εφεισατο μηπως ουδε σου φεισηται φεισεται
24. Love of money
Paul writes to Timothy as Bishop of Ephesus.
1 Timothy 6:10 For the love of money is the root of all evil: which while some coveted after, they have erred from the faith, and pierced themselves through with many sorrows. [kjv]
ριζα γαρ παντων των κακων εστιν η φιλαργυρια ης τινες ορεγομενοι απεπλανηθησαν απο της πιστεως και εαυτους περιεπειραν οδυναις πολλαις [gnt]
radix … [v]
In Greek, the word for "
root" is the first word of the sentence which gives it a special emphasis.
Discuss: What might be the reason why "
root" is the first word of this verse (in the Greek)?
25. 1 Timothy 6:10
KJV: For the love of money is the root of all evil: which while some coveted after, they have erred from the faith, and pierced themselves through with many sorrows.
Greek: ριζα γαρ παντων των κακων εστιν η φιλαργυρια ης τινες ορεγομενοι απεπλανηθησαν απο της πιστεως και εαυτους περιεπειραν οδυναις πολλαις
Latin: radix enim omnium malorum est cupiditas quam quidam appetentes erraverunt a fide et inseruerunt se doloribus multis
Wycliffe: For the rote of alle yuelis is coueytise, which summen coueitinge erriden fro the feith, and bisettiden hem with many sorewis.
Gothic: waurts allaize ubilaize ist faihugeiro, thizozei sumai gairnjandans afairzidai waurthun af galaubeinai jassik silbans gathiwaidedun sairam managaim.
Luther: Denn Geiz ist eine Wurzel alles Übels, welches hat etliche gelüstet, und sind vom Glauben irregegangen und machen sich selbst viel Schmerzen,
26. Daniel 4:14-15
Daniel 4:14 He cried aloud, and said thus, Hew down the tree, and cut off his branches, shake off his leaves, and scatter his fruit: let the beasts get away from under it, and the fowls from his branches: [kjv]
και εφωνησεν εν ισχυι και ουτως ειπεν εκκοψατε το δενδρον και εκτιλατε τους κλαδους αυτου και εκτιναξατε τα φυλλα αυτου και διασκορπισατε τον καρπον αυτου σαλευθητωσαν τα θηρια υποκατωθεν αυτου και τα ορνεα απο των κλαδων αυτου [lxx]
4:15 Nevertheless leave the stump of his roots in the earth, even with a band of iron and brass, in the tender grass of the field; and let it be wet with the dew of heaven, and let his portion be with the beasts in the grass of the earth: [kjv]
πλην την φυην των ριζων αυτου εν τη γη εασατε και εν δεσμω σιδηρω και χαλκω και εν τη χλοη τη εξω και εν τη δροσω του ουρανου κοιτασθησεται και μετα των θηριων η μερις αυτου εν τω χορτω της γης [lxx]
27. Daniel 4:14
KJV: He cried aloud, and said thus, Hew down the tree, and cut off his branches, shake off his leaves, and scatter his fruit: let the beasts get away from under it, and the fowls from his branches:
Hebrew: קרא בחיל וכן אמר גדו אילנא וקצצו ענפוהי אתרו עפיה ובדרו אנבה תנד חיותא מן תחתוהי וצפריא מן ענפוהי׃
Greek: και εφωνησεν εν ισχυι και ουτως ειπεν εκκοψατε το δενδρον και εκτιλατε τους κλαδους αυτου και εκτιναξατε τα φυλλα αυτου και διασκορπισατε τον καρπον αυτου σαλευθητωσαν τα θηρια υποκατωθεν αυτου και τα ορνεα απο των κλαδων αυτου
28. Daniel 4:15
KJV: Nevertheless leave the stump of his roots in the earth, even with a band of iron and brass, in the tender grass of the field; and let it be wet with the dew of heaven, and let his portion be with the beasts in the grass of the earth:
Hebrew: ברם עקר שרשוהי בארעא שבקו ובאסור די פרזל ונחש בדתאא די ברא ובטל שמיא יצטבע ועם חיותא חלקה בעשב ארעא׃
Greek: πλην την φυην των ριζων αυτου εν τη γη εασατε και εν δεσμω σιδηρω και χαλκω και εν τη χλοη τη εξω και εν τη δροσω του ουρανου κοιτασθησεται και μετα των θηριων η μερις αυτου εν τω χορτω της γης
29. End of page
Romans 11:16 For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches. [kjv]
ει δε η απαρχη αγια και το φυραμα και ει η ριζα αγια και οι κλαδοι [gnt]
11:17 And if some of the branches be broken off, and thou, being a wild olive tree, wert graffed in among them, and with them partakest of the root and fatness of the olive tree; [kjv]
ει δε τινες των κλαδων εξεκλασθησαν συ δε αγριελαιος ων ενεκεντρισθης εν αυτοις και συγκοινωνος της ριζης της πιοτητος της ελαιας εγενου [gnt]
11:18 Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee. [kjv]
μη κατακαυχω των κλαδων ει δε κατακαυχασαι ου συ την ριζαν βασταζεις αλλα η ριζα σε [gnt]
Romans 11:19 Thou wilt say then, The branches were broken off, that I might be graffed in. [kjv]
11:20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear: [kjv]
11:21 For if God spared not the natural branches, take heed lest he also spare not thee. [kjv]
