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Infinity beyond experience
1. Infinity beyond experience
Some people talk about God being
"infinite". What does that mean?
Does
"infinity" exist?
In what sense might
"infinity" exist?
potential "infinity" (abstract, theory, etc.)
actual "infinity" (concrete, practice, etc.)
2. Infinity
Matthew 5:26 Verily I say unto thee, Thou shalt by no means come out thence, till thou hast paid the uttermost farthing. [kjv]
αμην λεγω σοι ου μη εξελθης εκειθεν εως αν αποδως τον εσχατον κοδραντην [gnt]
The Greek translated as
"uttermost" is that of
"last". Is there ever a
"last" "payment"?
Incorrect idea: Infinity is like a number so large that there are no numbers beyond it.
Correct idea: Infinity is like a number so large that there is always a number beyond it.
3. Death by taxes
Certainty? In this world nothing is certain but death and taxes.
Benjamin Franklin (American scientist, inventor, philosopher, statesman) .
Which gets worse over time?
☐ Death gets worse over time.
☐ Taxes get worse over time.
He does not possess wealth; it possesses him. Benjamin Franklin.
What does Jesus say about taxes (yokes of compulsion) by religious institutions?
4. Cars
The "
INFINITI" car is made by the luxury division of the Nissan Motor Company in Japan.
5. Gödel and incompleteness
Kurt Gödel stunned the mathematical world in 1931 by proving that it is impossible to find a consistent mathematical system that will allow all possible truths to be decided. This is called the
incompleteness Theorem.
Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.
The incompleteness theorem of
Kurt Gödel (Austrian logician, mathematician, philosopher) says that, for any formal proof system that includes arithmetic, there exist true statements that cannot be proven within the system. Part of Gödel's motivation was the belief that
there is no finite description of truth. That is, truth is infinite.
6. To infinity and beyond
7. Infinity
The term "
infinity", represented by "
∞" (figure eight on its side) is often used to refer to a large but unspecified quantity/number.
The "
all" of "
infinity" would be a lot.
The first use of the infinity symbol as what today is described as a figure eight on its side is from 1655 by John Wallis. It is not clear how he arrived at this symbol.
Mathematics: -infinity to +infinity
Computers: finite representation, possibility for overflow
The infinite, as described by Plato and related by Aristotle, can mean infinitely big or infinitively small (through division).
8. Unbounded infinity
9. Compass directions
10. Diagram
11. Buzz Lightyear
Buzz Lightyear from Toy Story: "
To infinity and beyond".
Can one go "beyond" infinity?
Can one go "110%"?
Is the earth finite or infinite?
Is the universe finite or infinite?
Is time finite or infinite?
12. Infinite things
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe. Albert Einstein's (Physicist)
13. God is infinite
When one says that "
God is infinite" it means that, being outside of time and space (as we know it), God is not subject to the restrictions that we face in living in time and space (as we know it).
The phrase "
forever and ever" can be taken to mean "
until the end of time and then after that".
The modern Greek word for "
infinity" is
"άπειρο" (A-pee-ro) ≈ "infinity".
It comes from the negation prefix «
α» and «
πείρο» which has to do with experience.
The modern Greek word "πείραμα" (PEE-ra-ma) ≈ "experiment" - something that comes out of ("ex") experience.
The modern Greek word "εμπειρία" (ehm-pee-REE-a) ≈ "experience" from which we get the word "empirical".
14. Unbounded
The Greek word/prefix «
άπειρο» appears in the Bible. Do any of the Bible verses relate to any concept of "
infinity" as in "
to that which is not yet experienced".
The English word
"eternal" comes, through French, from the Latin word
"aeternus" ≈ "lasting forever, unending" which comes from the Latin word
"aevum" ≈ "age".
15. Hebrews 5:13 Inexperienced
Hebrews 5:13 For every one that useth milk is unskilful in the word of righteousness: for he is a babe. [kjv]
πας γαρ ο μετεχων γαλακτος απειρος λογου δικαιοσυνης νηπιος γαρ εστιν [gnt]
The same ancient Greek word that means
"unlimited" or
"infinite" can mean, depending on context,
"inexperienced".
16. Hebrews 5:13
KJV: For every one that useth milk is unskilful in the word of righteousness: for he is a babe.
Greek: πας γαρ ο μετεχων γαλακτος απειρος λογου δικαιοσυνης νηπιος γαρ εστιν
Latin: omnis enim qui lactis est particeps expers est sermonis iustitiae parvulus enim est
Tyndale: For every man that is feed with mylke is inexperte in the worde of rightewesnes. For he is but a babe.
17. James 1:13 Temptation
James 1:13 Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man: [kjv]
μηδεις πειραζομενος λεγετω οτι απο θεου πειραζομαι ο γαρ θεος απειραστος εστιν κακων πειραζει δε αυτος ουδενα [gnt]
The the following verse in James, the translation of «
απειραστος» appears like the Greek word for "
infinite" but is the word for "
examination" that is often translated, through the Latin, as "
temptation".
18. James 1:13
KJV: Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man:
Greek: μηδεις πειραζομενος λεγετω οτι απο του θεου πειραζομαι ο γαρ θεος απειραστος εστιν κακων πειραζει δε αυτος ουδενα
19. Numbers 14:23
Numbers 14:23 Surely they shall not see the land which I sware unto their fathers, neither shall any of them that provoked me see it: [kjv]
η μην ουκ οψονται την γην ην ωμοσα τοις πατρασιν αυτων αλλ η τα τεκνα αυτων α εστιν μετ εμου ωδε οσοι ουκ οιδασιν αγαθον ουδε κακον πας νεωτερος απειρος τουτοις δωσω την γην παντες δε οι παροξυναντες με ουκ οψονται αυτην [lxx]
surely they shall not see the land, which I sware to their fathers; but their children which are with me here, as many as know not good or evil, every inexperienced youth, to them will I give the land; but none who have provoked me shall see it. [bs3]
Here, the
LXX (Septuagint) differs from the
HOT (Hebrew Old Testament).
20. Numbers 14:23
KJV: Surely they shall not see the land which I sware unto their fathers, neither shall any of them that provoked me see it:
Hebrew: אם יראו את הארץ אשר נשבעתי לאבתם וכל מנאצי לא יראוה׃
Greek: η μην ουκ οψονται την γην ην ωμοσα τοις πατρασιν αυτων αλλ η τα τεκνα αυτων α εστιν μετ εμου ωδε οσοι ουκ οιδασιν αγαθον ουδε κακον πας νεωτερος απειρος τουτοις δωσω την γην παντες δε οι παροξυναντες με ουκ οψονται αυτην
Brenton: surely they shall not see the land, which I sware to their fathers; but their children which are with me here, as many as know not good or evil, every inexperienced youth, to them will I give the land; but none who have provoked me shall see it.
21. Jeremiah 2:6
Jeremiah 2:6 Neither said they, Where is the LORD that brought us up out of the land of Egypt, that led us through the wilderness, through a land of deserts and of pits, through a land of drought, and of the shadow of death, through a land that no man passed through, and where no man dwelt? [kjv]
και ουκ ειπαν που εστιν κυριος ο αναγαγων ημας εκ γης αιγυπτου ο καθοδηγησας ημας εν τη ερημω εν γη απειρω και αβατω εν γη ανυδρω και ακαρπω εν γη εν η ου διωδευσεν εν αυτη ουθεν και ου κατωκησεν εκει υιος ανθρωπου [lxx]
And they said not, Where is the Lord, who brought us up out of the land of Egypt, who guided us in the wilderness, in an untried and trackless land, in a land which no man at all went through, and no man lived there? [bs3]
22. Jeremiah 2:6
KJV: Neither said they, Where is the LORD that brought us up out of the land of Egypt, that led us through the wilderness, through a land of deserts and of pits, through a land of drought, and of the shadow of death, through a land that no man passed through, and where no man dwelt?
Hebrew: ולא אמרו איה יהוה המעלה אתנו מארץ מצרים המוליך אתנו במדבר בארץ ערבה ושוחה בארץ ציה וצלמות בארץ לא עבר בה איש ולא ישב אדם שם׃
Greek: και ουκ ειπαν που εστιν κυριος ο αναγαγων ημας εκ γης αιγυπτου ο καθοδηγησας ημας εν τη ερημω εν γη απειρω και αβατω εν γη ανυδρω και ακαρπω εν γη εν η ου διωδευσεν εν αυτη ουθεν και ου κατωκησεν εκει υιος ανθρωπου
Brenton: And they said not, Where is the Lord, who brought us up out of the land of Egypt, who guided us in the wilderness, in an untried and trackless land, in a land which no man at all went through, and no man lived there?
23. Zechariah 11:15
Zechariah 11:15 And the LORD said unto me, Take unto thee yet the instruments of a foolish shepherd. [kjv]
και ειπεν κυριος προς με ετι λαβε σεαυτω σκευη ποιμενικα ποιμενος απειρου [lxx]
24. Zechariah 11:15
KJV: And the LORD said unto me, Take unto thee yet the instruments of a foolish shepherd.
Hebrew: ויאמר יהוה אלי עוד קח לך כלי רעה אולי׃
Greek: και ειπεν κυριος προς με ετι λαβε σεαυτω σκευη ποιμενικα ποιμενος απειρου
Latin: et dixit Dominus ad me adhuc sume tibi vasa pastoris stulti
Luther: Und der Herr sprach zu mir: Nimm abermal zu dir Geräte eines törichten Hirten.
Spanish: Y me dijo Jehová: Toma aún el apero de un pastor insensato;
25. Songs
There are some songs about counting and, as a consequence, ideas of
"infinity".
26. Ecclesiastes 1:15
Ecclesiastes 1:15 That which is crooked cannot be made straight: and that which is wanting cannot be numbered. [kjv]
διεστραμμενον ου δυνησεται του επικοσμηθηναι και υστερημα ου δυνησεται του αριθμηθηναι [lxx]
Can we smooth out a fractal and still have a fractal? Do we try to smooth out crooked things?
Can we go "
beyond infinity"?
27. Ecclesiastes 1:15
KJV: That which is crooked cannot be made straight: and that which is wanting cannot be numbered.
Hebrew: מעות לא יוכל לתקן וחסרון לא יוכל להמנות׃
Greek: διεστραμμενον ου δυνησεται του επικοσμηθηναι και υστερημα ου δυνησεται του αριθμηθηναι
Latin: perversi difficile corriguntur et stultorum infinitus est numerus
Wycliffe: Weiward men ben amendid of hard; and the noumbre of foolis is greet with outen ende.
28. Song: In Christ there is no east or west
Psalms 103:12 As far as the east is from the west, so far hath he removed our transgressions from us. [kjv]
καθ οσον απεχουσιν ανατολαι απο δυσμων εμακρυνεν αφ ημων τας ανομιας ημων [lxx]
The words to "
In Christ there is no east or west" were written by English poet/author William Arthur Dunkerley (1852-1941) in 1908 for an exhibition in London for the theme "
the orient in London".
The Latin word
"orientem" ≈ "east" and is the source of the English word "
orient". At one time, the top of maps were the direction east.
It was published in 1913, a year before the start of World War I, based on Galatians 3:28. During World War I, his hymn book "
Hymns for men at the front" sold
8,000,000 (eight million) copies.
29. Jeremiah 1:5 Life
Jeremiah 1:5 Before I formed thee in the belly I knew thee; and before thou camest forth out of the womb I sanctified thee, and I ordained thee a prophet unto the nations. [kjv]
προ του με πλασαι σε εν κοιλια επισταμαι σε και προ του σε εξελθειν εκ μητρας ηγιακα σε προφητην εις εθνη τεθεικα σε [lxx]
… formarem … utero … vulva … [v]
When does life begin?
When does life end?
What exactly is time?
30. Jeremiah 1:5
KJV: Before I formed thee in the belly I knew thee; and before thou camest forth out of the womb I sanctified thee, and I ordained thee a prophet unto the nations.
Hebrew: בטרם אצורך בבטן ידעתיך ובטרם תצא מרחם הקדשתיך נביא לגוים נתתיך׃
Greek: προ του με πλασαι σε εν κοιλια επισταμαι σε και προ του σε εξελθειν εκ μητρας ηγιακα σε προφητην εις εθνη τεθεικα σε
Latin: priusquam te formarem in utero novi te et antequam exires de vulva sanctificavi te prophetam gentibus dedi te
31. Infinity does not exist in reality
Infinity appears to be a man-made illusion.
Time is not infinite (begin and end to time due to thermodynamics)
Space is not infinite (darkness of space explanation).
God is outside of time and space.
Information is outside of time and space.
(many notes and details omitted due to time constraints)
32. The beginning and end of time
Both the Bible and current scientific thought (since the end of the 19th century) agree that there is a
beginning to time and an
end to time as we know it. The two viewpoints disagree on the time scale.
Modern secular view: Due to the 2nd law of thermodynamics, about 1900, it was recognized that there must be a beginning of time and an end of time.
33. Pentagram
Can we create an image that
appears to never end?
Computer/Information science can be thought of as the search for finite representations of (potentially) infinite objects.
more finite space (takes less space)
more finite time (runs faster)
Computation is inherently related to information and randomness (e.g.
AIT (Algorithmic Information Theory)).
34. How it is done
35. Finite representations of infinite objects
1 How many dots are red?
2 Ratio of integers as counts
3 Infinite rational approximation
4 Finite rational approximation
5 Finite representation
Computer/Information science can be defined as the search for
finite representations of (potentially)
infinite objects.
Is this possible? Does it make sense?
36. Real numbers
|
3.
1415926535
8979323846
2643383279
5028841971
6939937510
5820974944
5923078164
0628620899
8628034825
3421170679
...
|
Chaitin states in his book Meta Mathematics that Émile Borel, in 1927, "pointed out that if you really believe in the notion of a real number as an infinite sequence of digits 3.1415926..., then you could put all of human knowledge into a single real number",
Chaitin refers to this Borel number concept as "Borel's amazing know-it-all real number".
|
37. Matthew 5:26 Uttermost
Matthew 5:26 Verily I say unto thee, Thou shalt by no means come out thence, till thou hast paid the uttermost farthing. [kjv]
αμην λεγω σοι ου μη εξελθης εκειθεν εως αν αποδως τον εσχατον κοδραντην [gnt]
The Greek for
"uttermost" is that of
"last" as in the
"last days" and is the first part of the English word
"eschatology".
A joke about "
consultants" is that their primary objective is to "
extend" the "
consulting contract".
Will the "
last payment" ever happen if those who are being "
paid" make a "
profit" or otherwise "
subsist" on those "
payments"? The phrase "
last farthing" does not mean there will be a "
last farthing".
Prank:
In a group setting, put a new member (as initiation) under a blanket and tell them they need to take off something (e.g., clothing) that they do not need and hand it to you.
[band camp initiation]
38. End of page
The saying of Buzz Lightyear in Toy Story "To infinity and beyond!" is more figurative than literal.
A better idea of Infinity is that it means "unbounded" or "unlimited".
