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Models and reality
1. Models and reality
A model is an abstraction (interpretation) of reality that can be used for prediction and/or understanding.
In the
math phase, negative numbers, infinities, etc., can be used to make the math work. Problems arise when trying to inverse map resulting negative numbers, infinities, etc., into the real world or reality.
Essentially, all models are wrong, but some are useful. George Box, Statistician.
The best material model of a cat is another, or preferably the same, cat. Norbert Wiener (and A. Rosenblueth).
A model is a useful fiction.
2. Model build
To discredit an opinion, one can find errors in the opinion. The same does not work well with a model. If a model does explain
all phenomena sufficiently well, one needs to find a better model that handles those phenomena.
In desperation, those tied to
opinion may question whether a model
exists to explain the phenomena (even when presented with a model).
Note that some, such as
flat earthers, may not accept any model but rely primarily on their
opinion.
3. Aristotle: Opinion and knowledge
English: These considerations make it clear that it is impossible to have opinion and knowledge at the same time about the same object; otherwise one would apprehend that the same thing both could and could not be otherwise. (Loeb#391, p. 171)
Greek: Φανερὸν δ' ἐκ τούτων ὅτι οὐδὲ δοξάζειν ἅμα τὸ αὐτὸ καὶ ἐπίστασθαι ἐνδέχεται.ἅμα γὰρ ἂν ἔχοι ὑπόληψιν τοῦ ἄλλως ἔχειν καὶ μὴ ἄλλως τὸ αὐτό· Aristotle: Posterior Analytics [89a]
One destroys an opinion posing as knowledge by pointing out invalid logic, assumptions, etc. If a model explains some, but not all, phenomena, one cannot discredit the model by pointing out what it does not explain. One really needs to come up with a better model. Example:
Older model: Newtonian physics (still valid in many respects)
Newer model: quantum and/or relativistic physics
4. Text meanings
There are many ways to obtain the possible meanings of text. It assumed that the creator of the text had one or more meanings in mind. Such text cannot arise by chance. Here are some ways to attempt to obtain the possible meanings.
☐ literal meaning - acts as a distractor
☐ figurative meaning (many meanings, opinion-based, go figure)
☐ code word meaning (few meanings, constraint-logic based)
☐ simple play on word meaning (verification, continuity, authentication)
☐ extended play on word meanings (Spoonerisms, etc. deeper verification, etc.)
☐ modified meaning based on possible non-verbal communication
The language used can affect the inferred meaning.
☐ original Greek (Hebrew/Aramaic excuse, Koine excuse, idiom excuse)
☐ modified Latin meanings (which changed Greek meanings - deliberate or well-meaning)
☐ modified English meanings (which propagated and/or changed Latin meanings)
☐ change of English over time
5. Multiple models
A good computer scientist can create multiple mental models of what is being investigated, coded, etc., and switch between those models at will, without letting one model viewpoint adversely influence another model viewpoint.
Programming: logic, imperative, functional, assembly, etc.
Biblical analysis: literal, figurative, code-word, play on words, etc.
Those unaccustomed to such models often have trouble separating, say, the literal meaning from the figurative meaning.
... more to be added ...
6. Model fit
Whenever one is presented with a logical model, one should take the following steps.
1. Does the logical model fit? How well does it fit? What does it explain and what does it not explain?
2. If the logical model fits, what are the implications and consequences in terms of reality?
Example: Albert Einstein discovered and jump-started the field of quantum mechanics. He never liked the idea. The model fit and he knew it fit.
7. Models
What is a model?
A model is an abstraction of reality.
As a representation of reality,
models are often used to answer or predict specific questions about that reality.
The purpose of data science, for example, is insight.
8. Models: simple
One goal is to create models of what was said that, in a sense, minimize assumptions of what was said while not assuming things that might have been meant. Here is a simple way to think about a model.
A
model is an abstract representation of the real world with a postulated
mapping between the real world and the model (and between the model and the real world).
9. Models: refined
Here is a more refined way to think about a model. A model is an abstraction of reality.
Essentially, all models are wrong, but some are useful. George Box, Statistician.
The best material model of a cat is another, or preferably the same, cat. Norbert Wiener (and A. Rosenblueth).
A model is a useful fiction. George Box, Statistician.
10. George Box
Essentially, all models are wrong, but some are useful. 1976, 1978. George Box, Statistician.
A model is a useful fiction.
11. Norbert Wiener
The best material model of a cat is another, or preferably the same, cat. Norbert Wiener (and A. Rosenblueth).
12. Actors and pastors
It can be a mixed blessing to have a pastor with an acting background.
Actors speak of things imaginary as if they were real, while you preachers too often speak of things real as if they were imaginary. Thomas Betterton (English actor and theater manager during Restoration England) (1635-1710)
Actors (tend to) take an imaginary world and make it seem real.
Pastors (tend to) take a real world and make it seem imaginary.
With a pastor with an acting background, it can be hard at times to separate reality from fiction.
13. Mathematics and reality
Do whole numbers exist?
Do integer numbers exist?
Do real numbers exist?
Does infinity exist?
14. Infinite things
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe. Albert Einstein's (Physicist)
15. Reality
Is God a mathematician?
Is mathematics real or just in the imagination (of man)?
Albert Einstein (English): "As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality". (Albert Einstein, 1879-1955).
Albert Einstein (German): "Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nict sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit" (Albert Einstein, 1879-1955).
16. Map of the world
Is a one to one (1 to 1) model useful? What would make a good 1 to 1 map of the world?
When the map (model) does not match the world (reality) what do you change?
Change the map to fit the reality of the world.
Change your understanding of the world to fit the map.
Some churches and pastors adapt to the reality that will
fill the seats (to support their belly).
17. Implications of a model
A model is said to faithfully reflect the real world if
implications of the model (usually derived via mathematical calculations), when mapped back into the real world, are a sufficient approximation of truth in the real world to be useful.
Models can be deceptive.
18. Day the universe changed
James Burke, science historian, did an interesting video series in the 1980's entitled "
The Day the Universe Changed: A Personal View by James Burke".
The title comes from the philosophical idea that the universe essentially only exists as you perceive it through what you know; therefore, if you change your perception of the universe with new knowledge, you have essentially changed the universe itself. Wikipedia,
http://en.wikipedia.org/wiki/The_Day_the_Universe_Changed
19. Average ocean depth
A model is a simplified representation of something (e.g., a reality).
Models can be deceptive. Take, for example, the depth of the ocean.
20. Average ocean depth
The average ocean depth is over
2 miles deep (
12,200 feet).
On a model globe, the oceans (and highest mountains) would be about the thickness of a piece of paper.
21. On the earth
To see this, consider the following calculations. On the earth:
12,000 feet ocean depth
--------------------------------- = 0.000284 (depth/diameter)
(5,280 feet/mile) * (8,000 miles)
22. On a globe
On a 12-inch globe, this thickness would be as follows.
0.000284 * 12 = 0.0034 inches
23. Ream of paper
Now consider a ream of paper and the thickness of 500 sheets of paper.
(1.5 inches/ream)
----------------- = 0.003 inches/sheet
(500 sheets/ream)
So on a model globe, the oceans (and highest mountains) would be about the thickness of a piece of paper.
24. Descriptive or predictive
Models can be classified as descriptive or predictive.
25. Descriptive models
To describe something is to talk about the attributes/properties of something.
Marketing models tend to be more descriptive than predictive.
26. Predictive models
A
descriptive model is a model that talks about the attributes/properties of something.
To
predict something is to claim that something will happen before it actually happens.
If you predict and you are wrong, you lose credibility.
27. Predicting the future
A
predictive model is a model that can claim what will happen in that model before it actually happens.
The best way to predict the future is to invent it. Alan Kay (American computer scientist)
28. Assumptions
A predictive model should clearly state the assumptions under which the model correctly predicts what will happen.
Engineering models tend to be more predictive than just descriptive.
29. Black box models
An
assumption is something that is to be true for the desired conclusions to be drawn.
When presented with a model, you might have questions about the inner workings of the model.
30. Black box models
A black box model only shows the input and/or output of the model, not the inner workings. A white box or glass box model allows the internals to be known.
An example of a black box model is quantum mechanics. How it works (functionally) is very well understood but why it works is unknown.
31. Functional behavior
A black box model shows the functional behavior of the model. That is, only from the outside without knowing how it works inside.
It acts as a mathematical function where one provides and input and gets an output.
32. Quantum mechanics
Nobody understands quantum theory.
Richard Feynman (American theoretical physicist)
He was including himself.
33. Quantum mechanics as a black box
The famous physicist Richard Feynman, the most famous physicist between the times of Albert Einstein and Steven Hawking, often stated that quantum mechanics is unquestionably correct in that accurate numbers to great precision can be computed from the theory.
On the other hand, according to Feynman, no one understands why quantum mechanics works or how it works inside, but we have a model that can be used to get useful results from the model.
A model such as quantum mechanics can explain what it does but no one is sure how it works, let alone why it works.
34. Referential transparency
Mathematical functions can be considered black boxes that, given an
input, provide an
output. This is much like a computer program. In a
black box function, you cannot see inside. You should not "
judge" or "
separate" based on the internal workings of the box - which you cannot see nor fully understand. Instead, you should "
judge" or "
separate" based on the external behavior of the box.
The principle of
referential transparency can be stated as follows.
If f(x) is equal to g(x) for all x in the domain of concern, then function f is equal to function g.
That is, if
f and
g are provided input
x and both produce output
y, for the domain of concern they can be considered the same.
The Greek word for "
judge" or "
separate" is related to the Greek word for "
barley".
35. Declarative model of creation
The creation account in Genesis, in terms of creation days, provides a declarative model of the creation.
A declarative model of a system is a model that describes the what of a system but not the how (or why) of a system. This term is used in computer science and software engineering (as black box functional testing). At another interesting level, each day of the creation is associated with a declarative statement as God says or speaks (or declares) what is to be done.
36. Black box model for the Trinity
Some people confuse a "
dimension" as a way to look at something with a "
mode" as a heresy. For those, each "
view" from one side of the box may help.
Does it make any difference in practice if we know the exact nature and inner workings of each aspect of the Trinity?
1 Corinthians 13:12 For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known. [kjv]
Each side uses scripture to justify their view. What do we know?
37. Thinking as a black box
A human cannot know exactly what someone else is thinking. Others are like a "
black box" from the outside. The Bible says this. Jesus, however, could know their thoughts.
 |
Details are left as a future topic.
|
... more to be added ...
38. Acts 17:18 Epicurus
Acts 17:18 Then certain philosophers of the Epicureans, and of the Stoicks, encountered him. And some said, What will this babbler say? other some, He seemeth to be a setter forth of strange gods: because he preached unto them Jesus, and the resurrection. [kjv]
τινες δε και των επικουρειων και στωικων φιλοσοφων συνεβαλλον αυτω και τινες ελεγον τι αν θελοι ο σπερμολογος ουτος λεγειν οι δε ξενων δαιμονιων δοκει καταγγελευς ειναι οτι τον ιησουν και την αναστασιν ευηγγελιζετο [gnt]
Epicurus taught the importance of having friends, controlling anger, not having fear, etc.
Having rejected "
logic" as used by the competing Stoics, and in order to investigate and reason about idea and knowledges,
Epicurus introduced what he called "
rules" or a "
canon of truth" named with the ancient Greek word
"κανών" ≈ "rod, pole, bar, standard".
39. Acts 26:22 Epicureans
Acts 26:22 Having therefore obtained help of God, I continue unto this day, witnessing both to small and great, saying none other things than those which the prophets and Moses did say should come: [kjv]
επικουριας ουν τυχων της απο του θεου αχρι της ημερας ταυτης εστηκα μικρω τε και μεγαλω ουδεν εκτος λεγων ων τε οι προφηται ελαλησαν μελλοντων γινεσθαι και μωυσης [gnt]
The ancient Greek word
"ἐπικουρία" ≈ "help, aid" and is used by Paul as a play on words of the Greek philosopher
"Ἐπίκουρος " ≈ "Epicurus" (341-270 BC).
Did Paul first become a "
friend" of those to whom he was "
witnessing"?
Epicurus advocated having "friends" to "help" you and being "self-sufficient".
Paul advocates getting "help" from God.
40. Puzzle pieces and models
Each insight at one place to what Jesus appears to mean from what he says, in context, acts as a puzzle piece to determine what a similar phrase means in another discourse.
Presented by Jesus and recorded by Matthew: Declarative, sometimes top-down backward-chaining, and distributed fault-tolerant and redundant spread-spectrum constraint logic (code) word (and meaning) puzzle.
Inference method: Bottom-up nondeterministic model parse.
Each underlined word has a deep and technical meaning in the field of programming language theory and in computation theory as part of the general field of computer science.
Discuss:
How does a model approach contrast with an opinion-based approach to inferring what is meant in the Bible?
Provide historical examples of both model-based approaches and opinion-based approaches to inferring what is meant in the Bible.
41. Alphabet
An
alphabet is one part of a
first order language and consists of the following with an example for
propositional (truth table)
logic as a simplification of general logic programming (e.g., Prolog logic programming language).
| alphabet |
| symbol |
propositional logic example |
| variables |
X, Y, etc. (upper case) |
| constants |
0=false 1=true |
| functions |
and, or, not, etc. |
| punctuation |
parentheses, etc. |
In the absence of parentheses, precedence rules are used to convert an expression into a tree form of representation.
There are only
2 unary operations of which the only one that changes the result is
not. The
identity operator might be used as a placeholder but is otherwise not very useful.
There are
16 possible binary operations. Some have common names. Some do not. There are no higher order operators as any such operators can be expressed as binary operators in some manner.
42. Formulas
A
formula for propositional logic can be defined recursively as follows.
1. A variable is a formula.
2. A constant is a formula. The only constants are 0 (false) and 1 (true).
3. If X is a formula and op1 is a unary operator, then (op1 X) is a formula.
3. If X and Y are formulas and op2 is a binary operator, then (X op2 Y) is a formula.
43. All binary logical operations
| # |
A=0
B=0 |
A=0
B=1 |
A=1
B=0 |
A=1
B=1 |
Operation |
Usage |
| 0 |
0 |
0 |
0 |
0 |
Always 0 |
False, Contradiction |
| 1 |
0 |
0 |
0 |
1 |
AND |
Conjunction |
| 2 |
0 |
0 |
1 |
0 |
NOT (A IMP B)=NOT B AND A |
Resolution, Inhibition |
| 3 |
0 |
0 |
1 |
1 |
A |
Identity |
| 4 |
0 |
1 |
0 |
0 |
NOT (B IMP A)=NOT A AND B |
Resolution, Inhibition |
| 5 |
0 |
1 |
0 |
1 |
B |
Identity |
| 6 |
0 |
1 |
0 |
1 |
XOR=NOT EQV |
Security |
| 7 |
0 |
1 |
1 |
1 |
OR |
Disjunction |
| 8 |
1 |
0 |
0 |
0 |
NOR |
Not Disjunction |
| 9 |
1 |
0 |
0 |
1 |
EQV=NOT XOR |
Equivalence |
| 10 |
1 |
0 |
1 |
0 |
not B |
Complement, Negation |
| 11 |
1 |
0 |
1 |
1 |
B IMP A=NOT B OR A |
Implication |
| 12 |
1 |
1 |
0 |
0 |
not A |
Complement, Negation |
| 13 |
1 |
1 |
0 |
1 |
A IMP B=NOT A OR B |
Implication |
| 14 |
1 |
1 |
0 |
1 |
NAND |
Build a computer |
| 15 |
1 |
1 |
1 |
1 |
Always 1 |
True, Tautology |
My preference is to number the operations according to binary number order where zero is false and one is true.
44. Wittgenstein and logical operations
Here is the table from Wittgenstein's
Tractatus Logico-Philosophicus, 5.101. This is often cited as
TLP (Tractatus Logico-Philosophicus). He completed it in 1918 (as a Austrian soldier, artillery, Russian front, later Italian front, in World War I) and published it in 1921. An English translation and Latin title was published in 1922.
The German word "Falsch" ≈ "false" abbreviated as "F".
The German word "Wahr" ≈ "true" abbreviated as "W".
The German word "Nicht" ≈ "not".
I created my own table of these operations in graduate school. It was many years until I found out that it had been done long before.
45. Interpretations and models
Precisely defining models in logic can confuse some people.
Definition: An
interpretation of a
first order language L consists of the following.
a. A non-empty set D, called the domain of the
interpretation.
b. For each constant in L, the assignment of an element in D.
c. For each n-ary function in L, the assignment of a mapping form D
n to D.
d. For each n-ary predicate in L, the assignment of a mapping from D
n into { true , false } (or, equivalently, a relation in D
n).
[Aristotle quote]
46. Interpretations and models
Definition: Let I be an
interpretation of a
first order language L and let F be a closed formula of L. Then I is a
model for F if the truth value of F with respect to I is true.
Definition: Let T be a
first order theory and let L be the
language of T. A
model for T is an
interpretation for L which is a
model for each axiom of T.
Some precise ways of dealing with symbols, languages, interpretations, models, etc., can be found in the field of logic programming. The above definitions are on pages 12-13 of: Lloyd, J. (1984).
Foundations of logic programming. Berlin: Springer-Verlag. This book (about 125 pages) was used in a graduate computer science course in logic programming that I took years ago.
Here is a start at a more precise code word model.
Here is a start at a more precise code word model.
47. Code word model
A logical variable represents a semantic concept. Predicates can select the part of the meaning needed for that part of a sentence fragment. Example:
Let X be a code word logical variable.
verb(X) is logical variable X as a verb. Mode, tense, etc., are omitted for simplicity.
noun(X) is logical variable X as a noun. Gender, etc., are omitted for simplicity.
adjective(X) is logical variable X as an adjective.
(and so on)
Suppose
X is the idea of "
salt".
noun(X) is "salt".
verb(X) is "salted".
adjective(X) is "salty".
Given the use of the logical variable for "
salt", an assignment of a value to this logical variable would make sense in each place where that logical variable is used.
Note that in an actual logical programming language (think of Prolog), the implementation would be somewhat different.
Simplified syntax model: noun(X)
Logic programming syntax: X, noun(X)
48. General methodology
General methodology considerations:
Determine original Greek meanings (not always the Bible dictionary meanings)
Account for play on words in Greek and Latin.
Determine verse flow and context for continuity
Recognize distractor verses. In general, separate the literal model from the figurative or code word model.
Account for many-to-one and one-to-many mappings. Multiple code words with the same meaning. Multiple verse groups to one part of a sequence. And so on.
Account for reverse orders (bottom-up vs. top-down), split orders (e.g., of six, with one separate at one end). Pattern matching (abstraction) in general.
Account for self-similarity (fractal-like verse structure), reflexive and recursive references, and infinite regress.
Use (code word) logic and constraint-logic principles.
Use applied (computer science) programming language and computation theory as needed.
49. Verse model progression
Verse model for RC, KP, B, SM, etc.
Daily bread (hidden manna, Sabbath)
LP verse model (debts)
first and last, alpha and omega
Revelation 4-22 (general model addition), 2D model
10C 2D model (order of commandments)
Rich young ruler (insight)
50. Relationships and associations
Technical
relational algebra and
functional dependency definitions using "
⇒" as "
implies" and "
∞" as "
many" as in "
not constrained" (includes
degenerate cases):
if (A ⇒ B) and (B ⇒ A) then A:B is 1:1 (one to one)
if (A ⇒ B) and (not (B ⇒ A)) then A:B is ∞:1 (many to one)
if (not (A ⇒ B)) and (B ⇒ A) then A:B is 1:∞ (one to many)
if (not (A ⇒ B)) and (not (B ⇒ A)) then A:B is ∞:∞ (many to many)
A one-to-many is handled in the same way as a many-to-one (only from the other direction).
Many sheep and one gone astray.
Two or three go to one.
One body and many parts.
Greatest and/or least among many.
Master with many servants, servant with many under him.
[family trees]
51. Connection scalability and conflict
1
2
3
4
5
6
7
8
9
10
+
-
▶
|
In any distributed system, the number of connections grows as the square of the number of nodes (e.g., people).
As the system (of members and groups) grows, there will invariably be
conflict (between people) or
errors (between system components). Fundamental rules:
Love God (individual)
Love neighbor as yourself (members and groups)
Proclaim truth actively but react passively
There needs to be some
conflict resolution protocol between/among processes.
52. Truth
The model to be presented relates to "
truth" as in "
reality".
Opinion truth can be related to what is called "
philosophy" (literally "
love of wisdom") since all opinion truth, to some extent, relies on logical and reality truth.
53. Separation
Note: Hilbert led the way for mathematics to divorce itself from reality in the early 20th century. It appears that, often, philosophy has done the same, but in a different direction.
54. Knowledge over time
Philosophers are people who know less and less about more and more, until they know nothing about everything. Scientists are people who know more and more about less and less, until they know everything about nothing. Konrad Lorenz (Austrian zoologist)
55. Learning
Originally, physicists and philosophers had a great deal in common; they hypothesized about the universe, using the same logic and same set of knowledge. ... Physicists learn more and more about less and less, until someday they'll know everything about nothing. Philosophers know less and less about more and more, until they'll know nothing about everything. Thorpe, D.
Delphi component design. Reading, MA: Addison-Wesley., p. 37.
In the past hundred years, science has become less and less about reality truth (facts) and more and more about opinion truth.
56. Truth and facts
The separation of truth from reality was expressed clearly in the remark by Joe Biden in August 2020 who told people in Iowa that "
we choose truth over facts". This does not make a lot of sense without a model that shows how one can separate truth and reality and where opinion truth can override reality truth.
A future topic will deal with Biblical truth from the perspective of Jesus as translated to Greek and Hebrew truth. For now, this truth has to do with reality truth and not logical or opinion truth.
57. Infallibility
Note: Taking the Bible as a (man-made) logical truth, as in inerrancy and/or infallibility, creates many logical issues that are not relevant to what Jesus or the Bible are saying. To better understand this, one needs a background in error-correcting codes, fault tolerance, information theory and computability. This is left as a future topic.
Question: Why would a creator who designed and created DNA codes with built-in fault-tolerant features require that all texts are man-made perfect instead of being fault-tolerant?
Question: Should God require the same perfectness of us instead of providing a level of fault tolerance? This is, fault tolerance through the saving grace of Jesus Christ - the rules "broken" for us.
58. Table
Here is a table to model related ideas with an emphasis on Biblical ideas.
| Related hierarchy/sequence of ideas |
| opinion truth |
reality truth |
logical truth |
| philosophy |
science |
information/math |
| way |
truth |
life |
| ask |
seek |
knock |
| faith |
hope |
love/work |
| water |
bread |
blood |
| Holy Ghost |
Son |
Father |
| Comforter |
Jesus |
God |
| think |
see |
do |
| hear |
see |
do |
Some of these connections are left as future topics.
Let us see how some of these ideas fit with the verses in John chapters 14, 15, 16 which the
KJV (King James Version) translates as being able to "
ask anything" and it will be done.
What about asking a question?
 |
Details are left as a future topic.
|
59. End of page
