The Path to (Original) Biblical Expertise

There are four competencies for an expert on the original meaning of the Bible.

• knowledge of the relevant languages
• knowledge of the relevant historical background
• knowledge of the relevant history of interpretation
• hermeneutical competency

1. A New Testament expert must know Greek. A Hebrew Scriptures expert must know Hebrew and/or Aramaic. A New Testament expert is normally expected to know Hebrew as well, since such knowledge can be relevant for some NT interpretation.

An OT scholar will often know some of the associated Semitic languages: Aramaic, Ugaritic, Akkadian.

2. Historical background is extensive. For a NT scholar, there is Jewish history, intertestamental history, Greco-Roman history. There are extensive bodies of literature--Apocrypha and Pseudepigrapha, rhetoricians, Oxyrhynchus papyri, Dead Sea Scrolls, Philo and Josephus, perhaps the relevant rabbinic literature, although it is later. There is socio-cultural knowledge.

For an OT scholar there are inscriptions and the key Ancient Near Eastern collections.

3. The history of interpretation primarily refers to the scholarship of the last two hundred years and especially the last few decades. Pre-critical interpretation is of a different sort. It may be helpful spiritually but usually is not of much help for determining the original meaning.

It goes without question that a real biblical scholar will know about manuscripts and how to determine how the most likely initial reading. The true scholar will know source hypotheses. He or she will have an up to date sense of genre and how oral tradition works. They will know how redaction works. Further they will know how to analyze narratives as stories. They will know how to bring sociology and anthropology to bear on interpretation.

4. Finally, an original meaning biblical expert will be able to operate with historical-cultural excellence. They will resist theological anachronism. They will not have artificial boundaries about what the text can and cannot mean. They will read the text in the light of the world behind the text, not the preoccupations or concerns of the last hundred years. They will bring historical and literary evidence to bear on interpretive questions, and draw the most likely contextual conclusion, not twist the evidence to fit their preconceptions.

4.4 Sin in the Old Testament

See the bottom for previous posts.

4.4 Sin in the Old Testament

4.4.1 Unintentional Sin
Numbers 14:22-31 immediately shows us the distance between our Western worldview and that of the Ancient Near East with regard to sin and the need for atonement. The Hebrew word here is ḥaṭa’ (chata’) – do wrong, sin.

• This passage begins with atonement for corporate sins. We tend to see sin only in individualistic terms.
• This passage really only focuses on unintentional sin, while we focus overwhelmingly on intentional sin. There is no atonement in this passage for intentional sin.

I will argue in the next section that the trajectory of Scripture is toward intentional sin and away from the category of unintentional sin. The New Testament has almost nothing to say about unintentional sin. It operates almost entirely from a sense of intentional wrongdoing. Wesley is a fine starting point: "A willful transgression against a known law of God."

I will define sin in terms of the standard of loving God and loving neighbor. Unintentional sin is a valid theological category, but should be understood in terms of unintentionally wronging others or unintentionally dishonoring God. God's concern is with our intentional sins, not our unintentional ones, except insofar as they have adverse consequences toward others.

We should note that while the Law does not provide much room for atonement for intentional sin, the narratives indicate that it is possible. David is forgiven for his affair with Bathsheba and the death of Uriah.

4.4.2 Corporate Sin and Guilt
Corporate sin is not a natural category for Western individualists, although more recent discussions of corporate guilt in terms of things like racism and sexism have revived the older category. Christian confessions often incorporate a corporate confession of sin that goes beyond the individuals or the sum of individuals.

Nevertheless, here even in the Old Testament we see some progression from the collective guilt and punishment of Deuteronomy 5:9-10 to the individual punishment and guilt of Ezekiel 18:2-4 and Jeremiah 31). We tend to modernize these passages, "de- and re-culturize" them so to speak. Corporate guilt is intrinsic to deuteronomistic theology and thus to the Deuteronomistic history of Joshua, Judges, Samuel, and Kings.

I perhaps will want to have an excursus here on deuteronomistic theology and the idea of the Deuterononistic History.

So we see Deuteronomy 5:9-10 in terms of consequences (genetics and environment). I think there was more going on in the OT context. Explain the context of Ezekiel 18.

4.4.3 Sin and Uncleanness
a. Although sin and uncleanness are distinct categories in the Pentateuch, there is a certain blurring of the two. Both require cleansing rituals in the OT. (cf. Lev 12-15; Num 19)

I have found Mary Douglas incredibly helpful in getting out of my Western categories and at least in a more likely direction for the categories of the Ancient Near East. Jonathan Haidt has also been very helpful in identifying the "sanctity" category of much human moral thinking (see material on holiness in the chapter on God).

"Dirt is matter out of place." A terd is okay outside. Not so much in the living room. It makes my living room unclean. See food laws (Lev. 11, 17; Deut. 14)

• Fish without fins and scales aren't right. Unclean
• Birds that can't fly aren't right. Unclean
• Blood belongs in and has magical life properties. Unclean if in the wrong place but full of life-giving power if properly channeled.
• Pigs go with Philistines and their gods--defiling. Sheep go with Israel and YHWH, good and scrumptious.
• Male with male doesn't fit. Unclean... abomination (to'evah)

b. I need to do more research on whether Leviticus thinks of the sexual prohibitions in terms of uncleanness rather than sin (Lev. 18). Certainly Numbers has no sacrifice for sexual sins since it has no category for intentional sins at all. In David's case, God caused the baby to die.


Previous "chapters"
Chapter 1: What is Biblical Theology?
Chapter 2: Theology of God
Chapter 3: Creation and Consummation

4.1-3 Sin and the Fall

Friday Science 3c. Hermitians and Fundamental Theorem of Quantum Mechanics

Fifth installment summarizing Susskind's, Quantum Mechanics: The Theoretical Minimum.

Chapter 1: Dirac was much smarter than I (introducing linear algebra).
Chapter 2: Quantum States (a.k.a., more linear algebra)
Chapter 3a: Linear Operators
Chapter 3b: Eigenvectors

More on chapter 3. I increasingly get the sense that this book should have been written somewhat in the reverse order that he did. Typical linear, building block thinking. Most human minds--especially those this book is allegedly written for, like me--work on a "need to know" basis. That's how this book should be written.

1. Made some progress this week in the book. Think I'm further than I've ever been in it, understanding more than I ever had. Probably could handle a re-read. Since I'm making good progress, I'll try just to jot down some notes.

A "Hermitian" conjugate is like the complex conjugate of a matrix. You do two things to a matrix to find its Hermitian conjugate:

• Interchange the rows and columns (so m₂₃ becomes m₃₂)
• Complex conjugate each matrix element.

A Hermitian conjugate is denoted by a dagger. So the Hermitian conjugage of M is M^† . The matrix might have a T in its upper right hand (for "transposed").

• So you might say that M^† = [M^T]*    (transposed and conjugates).
• So if M∣A〉 = B then 〈A∣M^† = 〈B∣

2. A Hermitian operator is one that is equal to its Hermitian conjugate: M = M^†

The eigenvalues of a Hermitian operator are all real.

3. We now get to what Susskind calls the fundamental theorem of quantum mechanics. It amounts to this: "Observable quantities in quantum mechanics are represented by Hermitian operators" (64). Another way to put it is that "The eigenvectors of a Hermitian operator form an orthonormal basis."

Here is my interpretation of how he unpacks it:

• The possible vectors for a Hermitian operator are all of its eigenvectors and their sums.
• The unequal eigenvalues of a Hermitian are orthogonal.
• Even equal eigenvalues can be analyzed as orthogonal. In other words, two eigenvectors can have the same eigenvalue. This is called "degeneracy."
• If a space is N-dimensional, there will be N orthonormal eigenvectors.

4. The Gram-Schmidt procedure is a procedure for teasing out orthonormal sets that relate to degenerated eigenvectors with the same eigenvalues. Here is the procedure:

• Divide vector one by its own length to get the first orthonormal basis of unit length.
• "Project" the second vector onto that unit vector by taking the inner product with it. 〈V₂∣v₁〉. 
• Subtract this from the second vector.
• Then divide the result by the length of the second vector to get an orthonormal basis for the second vector of unit length.

I don't entirely follow, but I'm making progress.

7. Concentrated Hebrews (7:1-28--Melchizedek)

See bottom for previous posts.

d. The Order of Melchizedek (7:1-28)
     1. Overview

• Chapter 7 resumes where 5:10 left off. Jesus is a high priest after the order of Melchizedek. 
• The author's strategy in this central argument of Hebrews (7:1-10:18) is three fold: 1) Christ is a superior priest, 2) in a superior sanctuary, 3) offering a superior sacrifice. So there is no more need for any Levitical system at all for Jesus has not only fulfilled it. He is actually the reality to which it pointed.
• The early Christians understood Psalm 110:1 as a verse about Jesus. The author of Hebrews, perhaps uniquely, understood Psalm 110:4 as about Jesus too. The author understood this verse to say that the Messiah would be a priest after the order of Melchizedek.
• But what is a priest after the order of Melchizedek? This is the question that Hebrews 7 seeks to answer.
• To answer this question, the author goes to the only other passage in the Old Testament (his Scriptures) where Melchizedek is mentioned, namely, Genesis 14. This is thus a kind of gezerah shewah, "catchword" argument.
• There are three basic approaches to Melchizedek: 1) to see him as a Christophany, an appearance of Jesus in the Old Testament, 2) to see him as an archangel of sorts (following the possible lead of 11QMelchizedek), and 3) that Hebrews is doing midrash here, answering an exegetical question in Psalm 110:4 by interpreting the text of Genesis 14.
• I favor the last option. First, there is no indication in Hebrews 7 that Jesus was Melchizedek. Rather, the Genesis text "likens" Melchizedek to Jesus. Second, if Melchizedek were an angel, surely Hebrews would say that Jesus was greater than he. Or why didn't Melchizedek provide atonement. Neither of these options seems likely.
• What does seem likely is that Hebrews is using Genesis 14 to identify what a priest after the order of Melchizedek is. He is doing a midrash on the Genesis text far more than investigating the historical Melchizedek. This distinction is often lost on those who read the Bible in a pre-modern way anyway. 

     2. Characteristics of a Melchizedekian Priest (7:1-3)

• 7:1-3. These verses begin with some preliminary allegorical readings of the Genesis 14 text. What is a priest after the order of Melchizedek? If we take the name Melchizedek as an indication of what such a priest is, then a priest after the order of Melchizedek is a "king of righteousness. If you take the name of the village Salem symbolically, such a priest is a "king of peace."
• 7:3. With regard to Melchizedek, these seem to constitute a non in thora non in mundo argument, "if it is not in the Torah, it does not exist." This exegetical technique allows you to use the silence of the text in order to draw a conclusion. 
• So the Genesis text does not mention a priestly genealogy for Melchizedek. It does not mention when he started or ended serving as a priest. So, following Jewish midrash, we can conclude that a priest after the order of Melchizedek has no priestly father, mother, or genealogy. Such a person does not start or end their service according to a designated plan. 
• These comments are not, in my opinion, meant to suggest that the historical Melchizedek existed from eternity past to eternity future. In that sense, Melchizedek himself was not truly or fully a priest after the order of Melchizedek. Only Jesus is.
• But this allegorical interpretation of the Genesis text tells us what a priest after the order of Melchizedek is. It is a priest who is not from a Levitical parentage. Most especially, it is a priest with an indestructible life who remains in office forever. Not having a beginning of days could be a reference to Christ's pre-existence.
• Jerome Neyrey has argued that 7:3 would have been immediately understood to be divine language indicating that Jesus was divine. Could be, although the context seems much more focused on Jesus' genealogy.

     3. The Greater Priesthood (7:4-10)

• There is a simple "transitive" argument in these verses. Melchizedek was greater than Abraham. Levi was in Abraham. Therefore, Melchizedek was greater than Levi. Therefore, a priest after the order of Melchizedek is greater than a priest after the order of Aaron and Levi.
• 7:4. Abraham gave Melchizedek a tithe, an ancient practice and precedent for all later biblical tithes.
• 7:7. The one who blesses is superior to the one who is blessed.
• 7:8. Throughout this chapter, Jesus' never-ending priesthood is seen as the key feature that makes his priesthood superior to Levi's.

     4. The Change of Law (7:11-19)

• 7:11. Perfection did not come through the Levitical priesthood. Human perfection in Hebrews has to do with real cleansing from sin. In Hebrews 10:1-2 we will see very clearly that perfection in this context for Hebrews has to do with taking away sins.
• For the author, Psalm 110:4 points to a priesthood beyond the Levitical priesthood.
• 7:12. The author understands a change in priesthood to imply a change of law. In Hebrews, the author looks at the Jewish Law almost entirely from the perspective of sacrificial law. That is to say, Hebrews is not interested in the works of Law that Paul was: circumcision, food laws, sabbath observance (this is part of a cumulative argument against Pauline authorship). The Law in Hebrews almost entirely refers to sacrificial law.
• Hebrews understands priesthoods to stand on the foundation of laws. So the Aaronic priesthood was based on the legitimacy of the Jewish (sacrificial) Law. Now, there is a new covenant, which serves as the basis of the Melchizedekian priesthood.
• 7:13-14. Here the author states the obvious. Jesus was from the tribe of Judah, not the tribe of Levi. He doesn't have the right genealogy to be an earthly priest. But as we will see he is qualified to be a heavenly one.
• 7:15-17. This verse is strong evidence that 7:3 is about priestly genealogy rather than eternal ontology. Jesus is qualified by his indestructible life, not his earthly parentage. Psalm 110:4 is quoted again, indicating again the kind of priest that Jesus is.
• 7:18-19. So the earlier sacrificial commandments are now null and void. They didn't actually work (the author will again develop this idea more fully in chapter 10). The Jewish Law did not perfect any worshiper. However, this new priesthood introduces a better hope.  

     4. Confirmed with an Oath (7:20-25)

• 7:20-21. Hebrews already emphasized the oath of Psalm 110:4. Here he does it again. God made no oath about Levitical priests, but he did about Jesus as a priest after the order of Melchizedek. 
• 7:22. This makes Jesus the guarantor of a better covenant. This is the first time that the word covenant has been used in the sermon.
• 7:23-24. Here we have a "singular versus many" argument similar to the one we saw in the first two verses of the sermon. There have been many, many priests. But there is only one priest who continues forever, because he never dies. This is the fourth time the author has mentioned or alluded to Jesus never-ending priesthood.
• 7:25. Jesus thus remains as an atoning intercessor forever. In my opinion, Jesus' intercession in Hebrews relates predominantly to his intercession for the audience's atonement. Again we have the opportunity mentioned for the audience to draw near to God.

5. Conclusion (7:26-28)

• 7:26. The author generalizes in conclusion. The audience has a great high priest: holy, blameless, without stain, set apart from sinners, higher than the heavens. The last comment relates to the fact that Jesus now sits in the highest heaven at God's right hand, which is also, presumably, the heavenly Holy of Holies, which we will encounter in the next chapters.
• 7:27. Jesus does not need to offer a sacrifice for his own sins. He does not have sin (cf. 4:15). 
• You might call this comment a kind of inclusio with 5:3, bringing the high priest part of the argument to an end.
• 7:28. God's oath is again contrasted with the Jewish Law. Jesus as Son is mentioned again. Jesus' perfection is mentioned again (reminds us of 5:10).

I. Sermon Introduction (1:1-2:18)

     A. Exordium (1:1-4)

     B. Celebration of the Enthroned Son (1:5-14)
     C. Background of Salvation (2:1-18)

II. The Argument (3:1-10:18)
     A. Enter into God's Rest (3:1-4:13)

     B. The High Priestly Argument (4:14-10:18)
          1. A Superior Priest (4:14-7:28)
               a. Hold Fast (4:14-16)
               b. Appointed High Priest (5:1-10)

               c. Central Exhortation (5:11-6:20)

6. Concentrated Hebrews (5:11-6:20--Central Exhortation)

See bottom for posts thus far.

c. The Central Exhortation (5:11-6:20)
     1) The Warning (5:11-6:8)

• 5:11. Throughout Hebrews so far, the author has alternated between teaching and preaching. At 5:11 we get the most pointed warning yet to the audience, the central exhortation of the sermon.
• Melchizedek is what sets it off, suggesting that the audience’s weak understanding of Jesus’ atonement stands at the center of their problem. More to come.
• 5:12. They have been believers for some time--should be teachers by now.
• The author shames them by saying they need to go back to the ABCs of faith.
• 5:13. The use of milk-meat is a commonplace of ancient rhetoric (Philo, Epictetus)
• 6:1. They need to go on to maturity, "perfection." (not referring to an instantaneous event, however).
• The author seems to suggest that the items that follow were beginning ABCs for the audience. But these are not things a Jew would have learned when coming to Christ. They are things that a Gentile would have learned when coming to Christ. This is the strongest evidence that the audience may actually be predominantly Gentile.
• 6:1-2. Most of these are common Jewish beliefs: repentance of sinful deeds, faith in God, resurrection, eternal judgment.
• Baptisms, plural, could refer to baptism in water and in the Holy Spirit
• Laying on hands was an early Christian practice of anointing and commissioning for service.
• 6:3-6. These are the key verses in the Bible on the issue of "second repentance." That is to say, can you return to Christ if you have fallen away?
• There are four key interpretations of these verses and others like them in Hebrews (10:26; 12:16-17): a) that it means what it says (if you apostatize, you cannot return), b) that it is an idle threat that would never happen (what's the point of the threat then), c) that they had not really become Christians but only "tasted" a little (Jesus "tasted" death in 2:9 but really died), and d) they only appeared to be Christians but really weren't (if so, Hebrews doesn't know about this possibility).
• The Parable of the Prodigal Son is the central passage on this topic. Anyone who longs to return can. This is true not least because it is the Holy Spirit who empowers repentance (cf. Rom. 2:4). In other words, only God allows a person to have the power to repent (6:3), a power that Wesleyans call "prevenient grace."
• I have found the paradox of Schroedinger's cat helpful here. You don't know whether the cat is alive or dead until you open the box. In a sense, you don't know whether you have ever fallen away until you die. For those who endure to the end, the cat has never ultimately fallen away.
• 6:4-5. Various descriptions of truly coming to Christ: being enlightened, tasting of the heavenly gift, namely partaking of Holy Spirit, tasting of the powers of the coming age and the goodness of the word of God.
• 6:6. To abandon Christ is to crucify him all over again, exposing him to public disgrace (honor-shame language).
• 6:7-8. Hebrews uses a farming image of watering ground. If you keep watering but only get thorns and thistles, eventually you burn the ground.

     2) The Assurance (6:9-20)

• 6:9. In the end, the author does not think the audience is going to fall away or that God is going to abandon the congregation. 
• 6:10. For one, they have been noble in their faithfulness in the past--a striking invocation of merit!
• 6:11-12. They need to endure to the end. This section ends with an inclusio alluding back to their dullness in 5:11.
• 6:13-20. These verses are a "cool-down" after the very pointed exhortation of the previous verses. The author gives words of encouragement that slide back to the topic of Melchizedek in Hebrews 7.
• 6:13-15. Abraham is invoked as an example of how God keeps his promises, namely the promise to multiply his offspring. This is of course a key Pauline text as well. The message is that the audience can keep going knowing that God will keep his promises to them as well, the promise of Christ's return and the setting up of God's kingdom.
• 6:16-18. Here and in Hebrews 7, there is emphasis on God's oath. This is interesting given exhortations elsewhere in the New Testament not to make oaths (e.g., Matt. 5:33-37).
• 6:17-18. What are the two unchangeable things--the oath and God's unlying character? Or is it the promise and the oath?
• 6:18. It is impossible for God to lie. Theologically, I would simply say that God doesn't lie. God can do whatever he wants, but he will never want to lie.
• 6:18-19. Note the emphasis on the hope. The audience has hope. They have an anchor. 
• 6:19-20. The chapter ends with a return to the theme of Jesus as high priest, thus getting us ready for the resumption of the central argument in chapter 7.
• Jesus has gone "within the veil," foreshadowing the imagery of Hebrews 8-10.

I. Sermon Introduction (1:1-2:18)

     A. Exordium (1:1-4)

     B. Celebration of the Enthroned Son (1:5-14)
     C. Background of Salvation (2:1-18)

II. The Argument (3:1-10:18)
     A. Enter into God's Rest (3:1-4:13)

     B. The High Priestly Argument (4:14-10:18)
          1. A Superior Priest (4:14-7:28)
               a. Hold Fast (4:14-16)
               b. Appointed High Priest (5:1-10)

4. Sin and the Fall

Previous posts
Chapter 1: What is Biblical Theology?
Chapter 2: Theology of God
Chapter 3: Creation and Consummation

Chapter 4: Sin and the Fall
4.1 Rule of Faith on the Fall

• God created the world good but with the potential for evil.
• Adam's default state was without sin but capable of sin (posse non peccare).
• Adam and Eve were created in the image of God (imago dei).
• Adam sinned and brought the power of Sin over humanity and the world. The world thus is not as it should be or could be.
• We now sin like Adam. We now die like Adam.

4.2 Genesis and Romans

• Genesis three is an etiology of snakes, wives, and husbands. Debate over whether it is descriptive or prescriptive, whether it is punishment or consequence. Debate over whether it indicates hierarchy as consequence or damaged relationship between wives and husbands. Death seems to be the default to which the Tree of Life was an antidote.
• Romans 5 introduces new terminology and broadens the scope (the Fall plays no real role in the theology of the OT as a whole): sin, disobedience, condemnation, Sin as a power (flesh sometimes mistranslated as sinful nature), cosmic scope (creation in bondage to corruption and decay), death as new element rather than one to which the Tree of Life was the antidote.
• Augustinian elements introduced: original sin, total depravity, sinful nature, 
• 1 Timothy 2 and this text.

4.3 Excursus: The Fall and Evolution

• Clearly unforeseen by the Genesis or Pauline texts, as are strategies such as the gap theory. Whether this fact is fatal or not depends on your understanding of inspiration and/or your understanding of genre. Many would argue that the question is simply beyond the scope of what Genesis 1 meant to address in context. What is the genre of Genesis 1?
• Romans 5 is more difficult for evolution than Genesis 1. Evolution requires lots of death, yet Paul seems to say that death is a consequence of Adam and Eve's sin. Some say Paul is referring to spiritual death, but 1 Corinthians 15 makes this reading difficult.
• Science has of course problematized a literal reading. The most recent difficulty is the human genome, which seems to indicate that the human genetic pool could not have come from one man and one woman at the same time. 
• The most clever solution is that of John Walton, who argues that Adam and Eve were king-priests living in Africa several tens of thousands of years ago before homo sapiens left Africa. As representatives of the human race, they sinned and brought the consequences on the human race as a whole.
• One might then argue that they brought the power of Sin on the earth, including the prevalence of Satan and the demonic over the earth. And while humanity might have enjoyed eternal life, now we die as the progenitors of humanity did.
• This discussion no doubt is not yet over in the church.

3.3.2 Heavenly Beings cont.

Continued from here

3.3.2 YHWH's Allies in the Old Testament

• There are angels in the Pentateuch (rescue Lot, Jacob wrestles)
• Angel of the LORD (e.g., burning bush)
• The destroyer (Exodus)
• The LORD of hosts (YHWH Sabaoth)
• Cherubim (Ark of the Covenant; Garden of Eden)
• Seraphim (Isaiah 6)
• Archangels in Daniel 

3.3.3 YHWH's Enemies in the Old Testament

• There are other gods in the OT, but perhaps we should think of them as demons (Ps. 82; 1 Cor. 10).
• The Satan in Job, Zechariah, 2 Chronicles 21

3.3.4 Heavenly Beings in the New Testament

• Archangels
• Satan 
• Demons and Evil Spirits
• Angelic Judgment (1 Cor. 6; 1 Pet. 3; Rev. 20:10)

3.4 The Redemption/Consummation of Creation

• Intermediate State (2 Cor. 5; Phil. 1; Luke 20; Rev 6)
• Resurrection/Glorified Bodies (Rom 8; 1 Cor. 15; Phil 3)
• Redemption of Creation (Rom 8)

Previous posts
Chapter 1: What is Biblical Theology?
Chapter 2: Theology of God
See the here.

Chapter 3: Creation and Consummation
3.1 The Creation Rule of Faith 1
      Creation Rule of Faith 2

3.2 The Life of Creation
3.3 Heavenly Beings
     3.3.1 The Rule of Faith

Steps to Schrodinger's Equation

On my bucket list is to understanding Schrodinger's wave equation. I'm closer than even. Here are the steps and their components as I currently understand them.

1. The story of Ernst Schrodinger's equation
2. The basic point of the equation
3. Total energy (the Hamiltonian)
    --kinetic energy
    --momentum reformulation
    --potential energy
4. The Wave Equation
    --simple harmonic motion
    --taking derivatives
    --second derivatives
    --implicit differentiation
    --partial derivatives
    --derivatives of transcendental functions
5. The e form of the Wave Equation
    --cos x + i sin x = e to the ix
    --so psi equals e to the i times (kx-omega t)
6. Second derivative of psi function with respect to x
    --derivatives of e
    --Planck's constant and h bar
7. Time Independent Schrodinger Equation
8. Time Dependent Schrodinger Equation
9. The ket version
10. Dirac's relativistic version

Friday Science 3b: Eigenvectors

Fourth installment summarizing Susskind's, Quantum Mechanics: The Theoretical Minimum.

Chapter 1: Dirac was much smarter than I (introducing linear algebra).
Chapter 2: Quantum States (a.k.a., more linear algebra)
Chapter 3a: Linear Operators

So I continue working through chapter 3.

1. I think I have seen the term "eigenvectors" and "eigenvalues" since high school. These are more of the words I have heard for decades... they're familiar... but I haven't had any sense of what they meant (other such words include Fourier analysis, which I know a little now, the "Hamiltonian," and more).

So an eigenvector is one that you can put into a matrix machine and it's just like multiplying the matrix by a number.

So if the following matrix

  

is multiplied by the following vector

The answer for the top row is (1 x 1) + (2 x -1) = 1 - 2 = -1 .

The answer for the bottom row is (2 x 1) + (1 x -1) = 1 .

2. Now what is fun is that multiplying the matrix above by the vector is the same as multiplying the top and bottom of the vector by -1. So we say that the 1, -1 vector is an "eigenvector" of the first matrix and that -1 is the "eigenvalue" that goes along with the eigenvector.

In formal language, an eigenvector of M is a vector  ∣λ〉 such that

M∣λ〉 = λ∣λ〉 

and λ is the eigenvalue.

Not much, but it will have to do this week.

5. Concentrated Hebrews (Hebrews 4:14-5:10)

Posts thus far at the bottom.

B. A Superior Priest (4:14-7:28)
     1. Hold Fast (4:14-16)

• This is a hinge in Hebrews. 10:19-25 says very similar things. It is not exactly an inclusio, since 10:19 begins a new section rather than ending this one.
• The common elements with 10:19-25 include 1) the exhortation for the audience to hold fast to the confession, 2) an exhortation to approach Jesus the high priest, and 3) passage through the heavens/the heavenly sanctuary.
• 4:15. Jesus is again said to be a high priest who can sympathize with our weaknesses (mainly our temptations).
• This is the classic verse indicating that Jesus did not have sin while on earth.

2. Appointed High Priest (5:1-10)

• 5:1. The chapter begins by describing what a high priest is. High priests offer gifts and sacrifices for sins.
• 5:2-3. They have mercy on those who have gone astray. Hint to the audience: Jesus is there for you as you are wavering in your faith. Earthly priests can of course identify with the sinfulness of those who come to them, which is not true of Jesus, who sympathizes with their temptation but not their sin. The earthly high priests have to offer sacrifices for themselves too.
• 5:4. You have to be appointed a high priest. It's not something you can run for. It's not something you can decide to do. You have to have the right lineage and be appointed.
• 5:5-6. These two quotes transition us from the earlier part of Hebrews that focused on Jesus as a Son to the next part which focuses on Jesus as a priest. The quotation of Psalm 2 hearkens back to Hebrews 1:5. Then the author quotes Psalm 110:4 to move to the next phase of the argument: Jesus as priest.
• 5:7. Jesus sounds like a priestly intercessor here, although he will not fully assume this office until after his exaltation (see 5:10). It is natural to think of the Garden of Gethsemane when you read this verse, although it is not actually mentioned.
• Jesus' prayer to be saved "out of" death was heard because of his godliness. This is a reminder that the "faith of Jesus" is a model for us. Hebrews certainly means for Jesus to be a model of faith for the audience. Being saved out of death is likely a reference to Jesus' resurrection, since obviously Jesus did not escape dying.
• 5:8. This can be a puzzling verse. How could Jesus learn obedience? A key is to remember that the author wishes the audience to identify with Jesus here. They are the sons and daughters of God too. They are not too good to undergo suffering since Jesus himself did. He obeyed during a time of persecution, so can they.
• Learning obedience refers to Jesus undergoing an event requiring obedience. It is not about him learning per se, unless perhaps the author is thinking of experiential learning. On the other hand, the author could simply be saying that Jesus obeyed. 
• Of course the New Testament does not teach that Jesus was omniscient while he was on earth (cf. Mark 13:32). As Christians we believe he must have remained omniscient in some sense, but he chose not to access this knowledge fully while he was on earth. I like to think that he didn't access it at all, but played it by the human rules, showing us what is possible through the Holy Spirit. If so, then the additional knowledge he did have on earth came through the Holy Spirit, just as our knowledge can.
• 5:9. The perfection of Jesus in Hebrews, as we saw in chapter 2, is about Jesus being fully ready to serve as our high priest, as the one who reconciles us to God, as the means of our atonement and life. He is not "locked and loaded" for salvation until after he has died, risen, and been exalted at God's right hand.
• Now he is perfected. He is completed as our high priest. He is now our source of eternal salvation, if we will obey him and persist in faith.
• 5:10. Jesus' completion in this area, his perfection, means his full installation as a high priest after the order of Melchizedek, taking up the idea of Psalm 110:4 he mentioned a few verses earlier. 
• This is the occasion for another shift to exhortation, in fact the central exhortation of the letter. The theme of Mechizedek will then be picked up again in chapter 7.

Previous posts:

I. Sermon Introduction (1:1-2:18)

     A. Exordium (1:1-4)

     B. Celebration of the Enthroned Son (1:5-14)
     C. Background of Salvation (2:1-18)

II. The Argument (3:1-10:18)
     A. Enter into God's Rest (3:1-4:13)
          1. A Greater Than Moses (3:1-6)
          2. Hear His Voice Today (3:7-4:11)
               a. Don't Harden Hearts (3:7-19)
               b. Be Diligent to Enter (4:1-10)
          3. The Living Word (4:11-13)

3.2 Humanity and Angels in Creation 1

3.2 The Life of Creation
3.2.1 Humanity in Creation
What was humanity like before the Fall? (discussion of evolution in next chapter)

• good
• not slaves to Sin
• in community with God/holy
• not destined for death
• finite
• image of God
• male and female

3.2.1 The Other Life God Created

• Plants
• Animals
• Micro-organisms
• Other Life in the Universe?

3.3 Heavenly Beings
3.3.1 Rule of Faith

• God created spiritual beings as well as animals and humans (Nicene Creed--things seen and unseen).
• God created them good, but with the capacity to choose, just as humans.
• Satan ("Lucifer") made the wrong choice, as did about a third of the angels (Revelation, Isaiah 14?).
• Fallen angels are demons, the "gods" of the other nations.
• In the first age and the old covenant, angels are ministering spirits sent for those about to inherit salvation (Heb. 1:14).
• Jesus' exorcisms were the beginning of their ouster (Luke 11:20).
• Jesus' death defeated the Devil (Heb. 2).
• Jesus pronounced victory over them after his resurrection (1 Peter 3).
• Christians will judge (fallen) angels (1 Cor. 6:2-3).
• The "lake of fire" was created for them (Revelation).
• Angels will worship God forever (Heb. 12).

Previous posts
Chapter 1: What is Biblical Theology?
Chapter 2: Theology of God
See the here.

Chapter 3: Creation and Consummation
3.1 The Creation Rule of Faith 1
Creation Rule of Faith 2

Friday Science: 3a. Linear Operators

Third installment reviewing Susskind's, Quantum Mechanics: The Theoretical Minimum.

Chapter 1: Dirac was much smarter than I (introducing linear algebra).
Chapter 2: Quantum States (a.k.a., more linear algebra)

1.  So on to chapter 3 (a.k.a., even more linear algebra). This is really as far as I've gotten in the several times I've started plodding through this book. This week I want to summarize a first few pages from chapter 3. It will probably take two more weeks to finish the chapter.

The first half of the chapter is a mathematical interlude. Once again, I think these interludes are most effective after you have introduced a problem you need to solve. Then the math makes sense as a way to solve the problem. Oh well.

2. I think I'm beginning to get a better sense of what bras and kets are. That it is so simple to say is part of my frustration with Susskind's pedagogy. In laypeople's language, a ket like ∣A〉 is a collection of complex numbers (I could explain complex numbers). By convention, they are written in an up and down matrix like this:

We still don't really know why we would want such a collection, but we are calling this a vector.

Bras are written as horizontal collections of complex numbers and are the complex conjugates of the bra equivalent (I could explain complex conjugates). We call them vectors too. They are written like this:

The "inner product" of a bra and a ket is simply the matrix multiplication of the two (I could explain matrix multiplication).

3. Machines and Matrices
So linear operators are basically matrices that bras and kets are multiplied by using matrix multiplication. John Wheeler, a famous twentieth century physicist, called them "machines." Again, Susskind hasn't really given any sense of why we would need these or when we would use them.

But you basically use them to "operate" on bras and kets. For example, here's a linear operator that you might multiply a bra or ket by:

"Operating" this on a bra or ket is like plugging a number into an equation, except we are multiplying a bra or ket by this matrix.

In notation, we might say M∣A〉 = ∣B〉 . The operator M takes the input and spits out the output. ∣A〉 and ∣B〉 are kets.

4. Linear operators 1) relate to observable features in quantum mechanics (=real not imaginary stuff), 2) are like functions--you need to get an output for every imput, 3) multiplying the input by something needs to get the output multiplied by that something, and 4) whether you do the machine on the sum of vectors to begin with or do it on the sum of the outputs, the result should be the same.

Some of the "observables" you use these in relation to include: position of a particle, its energy, its momentum, its angular momentum, or an electric field at a point in space.

I read more than the six pages this post covers (51-56). If I get a chance before next Friday, I may blog some more, but gotta fly.

4. Concentrated Hebrews (Hebrews 3:1-4:13)

So far in this series:

I. Sermon Introduction (1:1-2:18)

     A. Exordium (1:1-4)

     B. Celebration of the Enthroned Son (1:5-14)
     C. Background of Salvation (2:1-18)
___________________
II. The Argument (3:1-10:18)
     A. Enter into God's Rest (3:1-4:13)

1. A Greater Than Moses (3:1-6)

• 3:1. I would say that the argument of Hebrews proper begins here. The author will interrupt it once and twice before he gets going full steam, but the thread of the priestly argument starts here.
• Jesus is called "apostle" and "high priest" of our confession. Scholars debate whether a specific confession is in mind (e.g., "Jesus is the Son of God" or "Jesus is Lord").
• 3:2. God "made" Jesus, often translated as "appointed."
• The angels mediated the first covenant to Moses, and Hebrews 1 has declared Jesus greater than they. Now we get to Moses, the mediator of the old covenant par excellence. And we will see again that Jesus is greater than he.
• 3:3-6 Hebrews makes a word play on the word house. The primary meaning is "household." Moses was a servant in God's household (Num. 12:7). But Jesus was a Son. The Son in a household is more worthy than the servant.
• 3:4. God is the one who built everything. Interesting tension here with 1:2 and 1:10 (cf. also 2:10). I have wondered if this tension suggests that the image of Christ as agent of creation is a metonymy--Christ is God's wisdom, which God used to create the world. 
• 3:5. Moses the servant gave witness to "the things going to be spoken." The things going to be spoken were spoken through Jesus (cf. 2:3).
• 3:6. We are God's household if we hold fast our confidence in what we are hoping for. Hebrews knows nothing of an eternal security. Only those who persist to the end will be part of the kingdom.

2. Hear His Voice Today (3:7-4:11)
     a. Don't Harden Hearts (3:7-19)

• Mentioning Moses raises the question of the wilderness generation. Israel left Egypt, but almost none of them reached the Promised Land of Canaan. The author uses this as a parable for the journey of the audience. They have left Egypt. But they will not make it to the unshakeable kingdom (12:28) unless they persist to the end.
• 3:14. Two verses highlight the conditional nature of their belonging to God's household and their participation in Christ. We have already seen one--3:6. The other is 3:14: "We have become and remain partakers of the Christ if indeed we hold fast the beginning of substance firm until the end." The perfect tense suggests that while they fully became partakers at some point in the past (completed action), that completed result only continues as long as they persist in faith. If they fall away like the wilderness generation, then they cease to be partakers of the Christ.
• 3:7. "as the Holy Spirit says." Hebrews sees Scripture as the mouthpiece of the Holy Spirit. This is not a past word but a living word directly to the audience today ("says").
• 3:7-11. This is a quote of Psalm 95:7-11. The psalm is of course a call to ancient Israel to persist in faith and not be like the wilderness generation before them. Hebrews appropriately reapplies it to his audience as well.
• 3:12. The problem of the wilderness generation was "an evil heart of unbelief." A lack of faith, in other words--a lack of faith that did not move forward to the Promised Land. The audience is also tempted not to continue through with what may lie ahead. Jesus is a sympathetic priest as he was tempted not to go forward with the crucifixion.
• The author implies that the audience may be tempted to "turn away from the living God." Such a worry would especially be appropriate if they were Gentiles who had at one point worshiped dead idols. Jews would not see themselves turning away from the God of Israel.
• The audience is asked to encourage each other to continue in the wilderness every day that is called "today," which is every day. The opposite course is to be hardened in the deceitfulness of sin. When we think of enjoying the "pleasures of sin for a time" (11:25), such sin could involve the pleasure of not being persecuted.
• 3:16. Here is the point. All this wilderness generation left Egypt under Moses. The parallel is that the audience had started in faith with Jesus. They had been enlightened (6:4). They have partaken of the Holy Spirit. They were children of God and had a birthright (12:16). They had appropriated the sacrifice of Christ for sins (10:26).
• In other words, the audience were truly Christians. The fact that they had partaken of Holy Spirit (like Jesus partaking of blood and flesh in 2:14) shows they were true believers. As Paul says, they had passed through the Red Sea--through the waters of baptism (1 Cor. 10:2). The similarity between Hebrews 3 and 1 Corinthians 10 suggests to me that the author knew this text or had heard Paul or a Pauline someone make this argument.
• 3:17-18. But their "corpses fell in the desert." They did not make it to the Promised Land. Indeed, God swore they never would. It seems beyond question that the author is saying you can truly be a Christian and still not make it to heaven and the kingdom of God.
• 3:19. The reason was unbelief. It was their lack of faith. They did not persist to the end.

     b. Be Diligent to Enter (4:1-10)

• 4:1. These verses give the second half of the argument. The "therefore" implies that what follows is a logical consequence of what has preceded. The audience should not be like the wilderness generation. They should enter God's rest.
• 4:2. The author hopes for a contrast in what happens to the audience. The wilderness generation did not have faith. Hopefully, they will.
• 4:3. We who believe enter into God's rest, into Canaan.
• 4:4 The author now makes a catchword argument (gezera shewa) to explain what God's rest is. Psalm 95 says that the wilderness generation would not enter God's rest. This leads the author to ask, "What is the rest of God?" His mind turns to Genesis 2:2, when God rests from creation.
• 4:9. The conclusion of this train of thought will come later. When we enter the rest of God, we are entering a sabbath rest. In the imagery I lean toward this being final, eschatological rest.
• 4:6-7. The author now plays on the timeline of the psalm. Joshua did finally lead God's people into Canaan land. But the psalmist wrote after that. So if the psalmist holds out the promise of God's rest after Joshua, there must be another rest available, the one available to the audience. 
• 4:9-10. A sabbath-rest, a final rest remains for God's people. To enter God's rest is to stop working as God did on the seventh day. It would be easy to take this in a very Reformation way--now rely on faith rather than works. But this reading does not seem to fit Hebrews. It seems anachronistic. Even Paul does not say to stop "works." Works are never seen as bad or something to stop in Paul's writings.
• So perhaps Hebrews is speaking of the eschaton, when we have finally finished our race (12:2) and can stop the effort that is required by faithfulness.  

3. The Living Word (4:11-13)

• 4:11. These verses then conclude the section. We must be diligent to enter God's final rest. We enter it every day that is called "today," and we strive to enter it once and for all in the eschaton.
• The audience does not want to fall by the same example of disbelief as the wilderness generation. The word example here (hypodeigma) is the same one used in 8:5. It seems to have the sense of a biblical precedent here, an example (or perhaps even a type) in the biblical text that points forward to something in the life of the audience or a deeper truth.
• 4:12-13. These verses are about the logos, the "word of God." It would again be anachronistic to take this in reference to the Bible, although theologically the Bible does contain the central words of God. There is also no clear indication that the author has Jesus in mind as the Word of God. The background here seems more in keeping with the book of Wisdom and Philo.
• The word of God in Jewish speculation was the tool of God's creation and of God enacting his will in the world. In Genesis 1, God speaks and it happens. John 1 of course gives us the clearest application of logos background to Christ. In Greek Stoicism, the logos was connected to the Mind that orders all things in the universe, and in Jewish Middle Platonism, that logos became associated with God.
• So the word of God enacts God's will in the world, and 4:12 seems to focus on God's will in judgment. The mention of a sword reminds us of Wisdom 18:15-16 talks about God's word leaping from heaven with a sword in judgment of the Egyptians. So the word of God in judgment of the world is living and active and has a sword that gets to the bottom of things.
• 4:12. The word can tell the difference between soul and spirit. Are these separable? For Philo the spirit was the "soul's soul" and thus part of the soul. It can separate the thoughts and intents of the heart. God knows our true intentions and motives.
• 4:13. The judgment dimension of these verses is clear both from the context, which is about enduring to the end or facing judgment. But this verse also makes it clear. We are entirely known and exposed before God. We cannot hide our hearts. Is there an allusion to the Garden of Eden?
• "His word is for us." Difficult clause to translate. Some render it, "to whom we must give an account." My sense is that it is still talking about God's will in action. God's will faces us and will act on us.

3.2 The Creation Rule of Faith 2

Continuing my notes

Chapter 1: What is Biblical Theology?
Chapter 2: Theology of God
See the previous post.

Chapter 3: Creation and Consummation
3.1 The Creation Rule of Faith

The elements I ended up including in the rule of faith were:

• The triune God is the sole creator.
• God created the universe out of nothing (complete nothingness).
• God created the universe by his Word (see below).
• What he created was good.
• "The heavens declare the glory of God" (Psalm 19:1). In other words, there is a place for natural revelation.

3.2 Tracing Ex Nihilo

• Genesis 1:1-2, comparison with Enuma Elish and other creation stories
• Cf. Isaiah 45:18 should be compared (mention gap theory)
• Cf. Other "mythological" imagery (Isa. 51:9; Ps. 74:13-14)
• The incarnated picture of the world (Psalm 104:2, 6, 14)
• 2 Maccabees 7:14
• Hebrews 11:3

3.3 Creation by God's Wisdom and Word

• Proverbs 8:27-30
• Psalm 33:6
• John 1:3
• 1 Cor. 8:6
• Hebrews 1:2, 10
• Hebrews 11:3
• Colossians 1:15-17

end this sort of section with summary of development of doctrine

3.1 The Creation Rule of Faith 1

Thus far in the outline:

Chapter 1: What is Biblical Theology?
Chapter 2: Theology of God
See the previous post.

Chapter 3: Creation and Consummation
3.1 The Creation Rule of Faith
1. With regard to creation, the Apostle's Creed simply states, "I believe in God, the Father Almighty, maker of heaven and earth." The Nicene Creed only adds, "of all things visible and invisible." The Christians of the centuries have taken these words in the most literal of senses: there is nothing that exists that was not created by God.

As we will see, what is included in the "everything" and what it means to create has perhaps expanded over time. Creating may have merely meant something like "forming" to the Old Testament authors, perhaps even the New Testament authors.

Take 2 Maccabees 7:28, which says, "Look at the sky and the land and when you see all the things in them know that God did not make them out of things that are." Given our current understanding, it would be easy to assume that this verse speaks of creation out of nothing as we think of it. But many would suggest that 2 Maccabees is only arguing that God did not make the world out of already formed materials.

So when someone builds a house, they may buy bricks or planks and other materials in bulk from some business. They are making the house out of things that "are" and forming them into a house. In this interpretation, 2 Maccabees would be suggesting that God made the bricks and planks themselves. He would have made them from more fundamental materials that "do not appear" today (cf. Heb. 11:3).

2. It was in the late 100s AD that the Gnostic controversy seems to have pushed both Jews and Christians to a more radical and consistent understanding of creation out of nothing, creatio ex nihilo. The Gnostics of course believed that matter was evil. Already in the New Testament we find the early stages of this teaching. John 1:14, 6:54, 20:27; 1 John 4:2 all may very well address a rising sense that Jesus could not have been pure if he had flesh. If the underlying materials of the universe are evil, so the Gnostic line of thinking went, then only spirit can be pure, not anything material or made of flesh.

After the Gnostic controversy, creation is no longer just forming but the creation of the underlying raw materials themselves. Creation is now truly out of nothing. The Christians of the centuries pictured creation as God taking empty space and creating material that had not previously existed in any form whatsoever.

After developments in physics in the twentieth century, our sense of what creation out of nothing might mean becomes even greater. Again, the sense that God is the creator has remained constant from Genesis to today. But our sense of what it must mean for God to be creator has possibly changed as our sense of the creation has expanded.

So twentieth century physics introduces two new dimensions to the discussion that no individual in history had apparently thought prior to 1900. The first is Einstein's general theory of relativity, introduced in 1915. Space is no longer a fixed emptiness. Now, space itself can expand and contract. For example, around a massive object like the sun, space gets smaller.

The second is the idea of cosmic inflation. Around 1980, Alan Guth suggested that, in the first .00000000000000000000000000000001 seconds, the universe went from being a point to something close to its current size. In other words, space did not exist before creation. If this theory is correct, then God exists outside and beyond anything we can imagine. He was not "in" space when he created "everything," but his essence is somewhere "outside" this universe and its space...

2.5 God in the New Testament

The book outline so far:

Chapter 1: What is Biblical Theology?
See previous posts for outline

Chapter 2: Theology of God
2.1a The Rule of Faith of God, part 1
2.1b The Rule of Faith of God, part 2
2.2 Progress of the Biblical Understanding of God
2.4 The Old Testament Witness 

2.5 The New Testament Witness

2.5.1 God as Father

2.5.2 God as King

• sovereignty of God

2.5.3 The Righteousness of God

• God as holy, light, perfect

2.5.4 God is love.

2.5.5 God's power, wisdom, and knowledge

2.5.6 God is Spirit

2.4 God in the Old Testament

Trying to outline a future book project while teaching a course in biblical theology. Modifying the outline a little as I go.

Chapter 1: What is Biblical Theology?
1.1 Introduction
1.2 Basic Approaches
1.3 History of Biblical Theology
1.4 This Book's Approach

Chapter 2: Theology of God
2.1a The Rule of Faith of God, part 1
2.1b The Rule of Faith of God, part 2
2.2 Progress of the Biblical Understanding of God
2.4 The Old Testament Witness 

2.4.1 The Oneness of God
So I think I will shuffle the order of presentation a little. Since in class I am almost done with an Old Testament theology of God, let me just present an outline for future filling in.

• Shema needs to feature here, including the covenant relationship of Yahweh with Israel.
• Deuteronomy 32 should be mentioned, especially the text critical issue at 32:8.

2.4.2 The Holiness of God

• The key text here is Isaiah 6. Also interact with passages like Leviticus 11:44 and my sense of what the holiness of God is. Mention Mt. Sinai and Uzzah.

2.4.3 Anthropomorphism in the Old Testament

• Did they take it as such, as most of us do?
• Or did they take it literally, but we should take it metaphorically?
• Or was it literal and we should become open theists and think God has a body?

2.4.4 The Power of God

• An assumption of the divine in general
• Yahweh Sabaoth (e.g., 1 Sam 1:3), God as warrior
• Genesis 18:14; Psalm 24:8
• God as king and judge
• God as creator, Isaiah 55:11

2.4.5 The Knowledge and Presence of God

• Psalm 139 is a locus classicus here. Isaiah 46:9-10
• including the Spirit of God in the Old Testament
• the angel of the LORD and other intermediaries

2.4.6 The Hesed of God

• "The LORD is gracious and compassionate, slow to anger, and abounding in steadfast love (Exod. 34:6; Ps. 103:8, 145:8; Jon. 4:2).
• Toward Israel (Deuteronomy 6), election
• The progressive understanding of Satan

2.4.7 The Wrath of God

• God and the conquest
• God and other nations
• God's wrath toward Israel

2.4.8 Other Pictures of God

• God as father/mother, healer, gardener, shepherd...

2.3.1 The Oneness of God

Thus far in a future book.

Chapter 1: What is Biblical Theology?
1.1 Introduction
1.2 Basic Approaches
1.3 History of Biblical Theology
1.4 This Book's Approach

Chapter 2: Theology of God
2.1a The Rule of Faith of God, part 1
2.1b The Rule of Faith of God, part 2
2.2 Progress of the Biblical Understanding of God

2.3 The Old Testament Witness
2.3.1 The Oneness of God
1. The majority of experts on the Pentateuch believe that the books we now have represent a process of collection and editing of sources that probably did not reach something like their current form until the time after the exile. [1] There is not currently a consensus on exactly what these sources were or how they came together. Meanwhile, many continue to have concerns about Mosaic authorship, not least because the New Testament books seem to operate under this assumption. [2]

In a very real sense, these issues are not of primary concern in our search for a biblical theology. We are affirming by faith that the canonical Pentateuch as it stands is the form that the church has come to see as Scripture. We do not wish to be naive about potential sources or the history of this discussion, but we have already asserted several times that the direction of revealed understanding moves forward toward Christ rather than backward toward sources.

Then God used the Church of the first few centuries to unpack the significance of Christ, who is God's final Word for his creation. And God uses the Church in every age to see the gospel incarnated in every context. Our methodology is thus to dialog with the canonical text in light of the telos of the rule of faith, yet also with an eye to the way God walked with his people through layers of history, text, and tradition.

Whatever the theory, Genesis certainly reflects some of the oldest traditions of the Old Testament about God. We might also mention Judges and 1 Samuel as books that reveal the worship and understanding of God in some of the earliest stages of Israel's history. Chiefly in these earliest stages, we find evidence of polytheism among the people of Israel and we find evidence of henotheism or monolatry.

Henotheism is the belief that there is only one legitimate God, without denying that other gods might exist. We can thus speak of "monolatry" or the belief that you should only worship one God even though others exist. The first of the Ten Commandments (by most Protestant numberings) is worded in a henotheistic way: "You will have no other gods before me" (Exod. 20:3).

From a Christian standpoint, we would of course deny the name "god" to any being but the one true God. However, we can use our model of increasing precision to reconcile these layers of understanding in the following way. There are spiritual forces that are opposed to God. The apostle Paul calls them demons in 1 Corinthians 10:20. We can thus suggest that the other gods that some Israelites falsely worshiped were demonic forces...

[1] See the excursus at the end of this section for a brief history of this source discussion.

[2] I have personally concluded that the New Testament books and perhaps even Jesus himself worked within the assumptions of their day on this issue. That is to say, we should not be surprised to find the assumption that Moses was the author of the Pentateuch because that was the assumption of first century Judaism in general. However, this assumption would seem to be the framework within which God revealed incarnated truths rather than the actual point of the revelations. Indeed, most of the time in the New Testament it is the quotations of Moses that are attributed to Moses rather than the authorship of the Pentateuchal books themselves.

Meanwhile, there is no inductive evidence for Mosaic authorship. For one, the Pentateuch refers to Moses entirely in the third person--the narrator of the Pentateuch is not Moses but speaks about Moses. As long observed, this speaking about Moses includes speaking of his death. Genesis never even mentions Moses. By contrast, there is evidence of varying sources of some kind being put together to form the Pentateuch, even if we are unable to determine exactly what they were.

In short, there are no historical-evidentiary reasons to argue for Mosaic authorship, only traditional and theological ones. An inductive approach will not come to this conclusion. And in fact we can show that this is a tendency in general that has taken place in regard to books like Joshua, 1 Samuel, and Jonah. Tradition had a tendency to ascribe authorship to the main characters of books of Scripture even though those books were anonymous and consistently talked about those individuals in the third person.

Friday Science: Quantum States (chapter 2)

Second installment reviewing Susskind's, Quantum Mechanics: The Theoretical Minimum. Here was the first.

1.  I've read this chapter of Susskind several times. I have some sense of it but continue to find the writing frustrating. I have the sense that it would not be hard to make this material more comprehensible to an invested lay person like me, but it seems written by and for Sheldon. At some point it will more fully click and I will be able to add the necessary paragraphs.

2. Section 2.1 So I understand what he's saying in this first section and can already add the necessary background. There is an almost century old debate in quantum physics about whether quantum uncertainty is due to there being hidden factors or "hidden variables" that would make the quantum world predictable. The majority don't think there are. They just think the quantum world has a fundamental uncertainty built into it.

3. Section 2.2 This section sheds a little light on the first chapter and the bras and kets of linear algebra. Still, it feels like Men in Black where Tommy Lee Jones is mid-conversation with Will Smith after flashing him with the memory thingee.

We still don't know what "spin" is but it is apparently the most fundamental quantum characteristic. For you chemistry buffs, I believe it relates to the final options in the 1s2, 2s2, 3p6 stuff. The two electrons in the s orbital, for example have two different spins. One is said to have a +1/2 spin and the other a - 1/2 spin. Why couldn't he have told us this? Give us something to hold on to, man.

"All possible spin states can be represented in a two-dimensional vector space" (38). That's how he puts it. My interpretation: the final quantum description has only two possible states.

4. So here is how they describe this sort of state, apparently:

∣A〉 = α_u∣u〉 + α_d∣d〉

First impression is of course that this is unnecessarily complicated but I'm sure it's helpful. And I like Dirac so I'll stomach it. But it sure would be nice if someone gave a straightforward explanation. As best I can tell, here's the explanation he never really gives.

a. ∣A〉 is a ket. It is a box in which we put one characteristic of the quantum situation. 

b. There are two possible states for that characteristic. Say it is spin. We might say that spin can be up or down. ∣u〉 is the place we check the "up" box. ∣d〉 is where we check the "down" box." 

These are "basis vectors." They are like the x, y, and z axes in normal geometry, but we can't picture the nature of basis vectors in the quantum world.

I believe up and down are "orthogonal." That is to say, it can't be both. If the state is up, it cannot be down. If it is down, it cannot be up. 

c. α_u and α_d is the value, the component that relates to the up and down. These apparently are complex numbers (that is, they have an imaginary component). I have a hunch they relate to the values of Schrodinger's equation, but making such connections would be far too helpful for Susskind to mention.

I am making the connection because he calls these values, "probability amplitudes," and mentions that their squares are probabilities. I know from elsewhere that this notion relates to Schrodinger's equation, which is about the possible states an electron can be in.

d. The total probability that the spin is either up or down has to equal 1. It is something. α_u*α_u + α_d*α_d has to equal 1, where the * version is the complex complement.

e. "The state of a system" ∣A〉 "is represented by a unit vector" α_u "in a vector space of states" ∣u〉. "The squared magnitudes of the components of the state vector" (α_u*α_u), "along particular basis vectors, represent probabilities for various experimental outcomes" (40).

5. Susskind uses the analogy (I think) of x, y, and z axes. They aren't really spatial coordinates like this. It's an analogy I think to help us understand. What he is trying to picture are quantum categories that are orthogonal to each other just like the x, y, and z axes are orthogonal to each other.

So say the first "axis" we measure is the z axis and then we want to measure the x axis. When we measured the z axis, it had to be either up or down. If we multiply the probability of up times itself and the probability of down times itself and add these two together, it has to equal 1.

If we then move from the z to the x axis, there is half a chance that we will move from it being up to it being right and there is half a chance that it will move from being down to being right. So what value, when multiplied by itself, will yield a half probability of it being right after it being up or down?

∣r〉 = 1/√2∣u〉 + 1/√2∣d〉

Then multiplying this by the equivalent probability for left has to equal 0 because left and right are orthogonal to each other, suggesting the probably for left then has to be:

∣l〉 = 1/√2∣u〉 - 1/√2∣d〉

6. So now he moves on to the y axis. There is a half probability of moving from any of these components to any of the others. For example, there is a half probability that we would go from an "up" state to a "left" state or from a left state to an "in" state. So the probability for "in" times the probability for "left" has to equal 1/2 just like the probability from "up" to "right" needs to be 1/2. As before, the probability of it being both in and out is zero.
I don't quite see how the math works out, but he suggests this means that the probabilities of in and out then turn out to be.

∣i〉 = 1/√2∣u〉 + i/√2∣d〉

∣o〉 = 1/√2∣u〉 - i/√2∣d〉

The reason this seems peculiar to me is because it seems to me that 〈i∣o〉 turns out to be 1 rather than 0, and all the other probability multiplications still have an i in them. Obviously I don't understand something here yet.

7. Another thing I don't understand is what he is calling a phase factor (e^iθ). He says it has unit value and that the vectors can be multiplied by it without changing their values. I'm tucking it away until at some point we see why the heck he's telling us about it.

Once again, he describes a lot of trees but has given us no sense of why any of these things are important or that they relate to anything. Waiting to see the relevance...

2.2 The Progress of the Biblical Understanding of God

Thus far in a future book.

Chapter 1: What is Biblical Theology?
1.1 Introduction
1.2 Basic Approaches
1.3 History of Biblical Theology
1.4 This Book's Approach

Chapter 2: Theology of God
2.1a The Rule of Faith of God, part 1
2.1b The Rule of Faith of God, part 2

2.2 Progress of the Biblical Understanding of God
1. Many sciences make a distinction between precision and accuracy. If something is inaccurate, it is wrong, but a measurement can be more or less precise. If I am trying to hit the side of a barn with a B-B gun, I probably have a fairly large target in mind.

But say that I have painted a series of concentric circles on the side of the barn, down to a bull's eye that is not very big at all. Precision is a matter of how close I get to the bull's eye. If I hit the outermost circle, I have still hit the target, but my aim is not very precise. My shot is accurate, but it is not precise.

In the same way, let me suggest that Abraham's understanding of God was accurate but not nearly as precise as Moses' understanding of God. Let me further suggest that Isaiah's understanding of God was more precise than Moses'. Then Paul's understanding of God was arguably more precise than Isaiah's. And if you would, the understanding of God in the Nicene Creed is more precise perhaps than even Paul's was.

On one level, these understandings do not contradict each other, but they become more and more precise as God clarified and refined the understanding. Joshua 24:2 tells us that Abraham's father and ancestors were polytheists--they worshiped many gods. Genesis and Exodus suggest that Abraham, Isaac, and Jacob worshiped the true God, but they did not yet know him as Yahweh. They knew him as El Shaddai or "God Almighty" (cf. Exod. 6:3).

When Abram met Melchizedek in Genesis 14:17, Melchizedek is said to be the priest of El Elyon (14:19), the priest of "God Most High." Although we immediately and rightly assume that this God is in fact Yahweh, the one true God, it is significant to recognize that El Elyon was the king of the gods in the Canaanite pantheon. That is to say, certainly the Canaanites understood this God to be one among many gods.

The point is that while we have more precise understandings because we stand at the end of the canon and the unfolding of revelation, these understandings were not exactly the same for the biblical authors or the individuals mentioned in the Bible. [1] When we hear about "God Most High," we know this is the only God, Yahweh, the one true God. For Abraham, he was the most appropriate object of worship. For Isaiah, he would have been the only appropriate object of worship. For Paul, he is the only God that truly exists, and other so-called gods are demons (cf. 1 Cor. 10:20).

2. Another possibility to consider is the very real possibility that our understanding of the universe has become greater over time. The natural implication is that our sense of the greatness of God has expanded as well. So Abraham, Moses, Isaiah, Paul, Athanasius (church father at the Council of Nicaea in AD325) and us today--we all believe that God is the greatest Being that exists. But is it not the case that our sense of what the "greatest" might be has increased exponentially since Abraham?

So the "greatest" God for Abraham would surely have been the most powerful, but what would the most powerful Being have been for him? Isaiah 45 may understand the greatness of God on a level that was beyond anything that Abraham might have imagined. Isaiah 55:9 suggests that God is beyond the capacity of human understanding.

Then the New Testament and the early centuries of Christianity wrestled with the Trinity, which was surely beyond anything the Old Testament authors imagined. Similarly, when the doctrine of creation out of nothing crystallized in the late 100s AD, the understanding of God becomes even greater than is clear in Scripture. Now we understand more precisely God as the creator of all matter and not just the one who shaped the chaos that had always been.

I would personally argue that developments in physics in the last century have suggested a universe that is greater than anything a biblical author or an Aquinas or a Luther could have dreamed. Now space--emptiness itself--is something that God must have created. The scope of the universe, the theory of relativity, the strangeness of the quantum world--our conception of greatness has vastly increased. Accordingly, surely our sense of the greatness of the God who made it all out of nothing has become immensely greater.

3. The rest of this chapter aims to follow the progress of biblical understanding about God as it developed within the canon. We do not engage in this investigation as mere analysts of history. We have a theological presupposition. Our theological presupposition is that these developments were moving toward a goal, namely, the rule of faith about God that we set out at the beginning of this chapter. We thus have a theological end point in mind as we process the history of the biblical texts and the more and less precise theological perspectives along the way.

[1] Various scholars debate whether all the people mentioned in the Bible actually existed in history. Such debates are ultimately irrelevant for our point here. We are asserting by faith that God has been walking with humanity since our beginning and that God has been steadily revealing God-self to us over time. What the precise names and dates were of those with whom he walked are irrelevant to this general sense of this unfolding of revelation.

The Parable of the Managers and Administrators

A righteous king went away and left his land in the hands of certain managers and administrators. A first manager gave away lots of money and engaged in a costly war, and there was a great crisis of money in the land at the end of his time. A second manager and he stabilized the land by rescuing the greatest business holders.

But this left the land in even greater debt. So a group of administrators arose saying, "We must be very careful with our money, and bring our spending under control. This is the most important thing." At one point they even shut down the government, saying, "Even though we have said we will pay our vendors, we must not pay them to bring our spending under control."

Then the people of the land chose a very rich manager, and the religious leaders of the land strongly supported him, because they thought he would give them what they wanted. Like the first manager, he gave away lots of money, principally to his rich friends. Curiously, the administrators who had previously complained about the debt of the land were some of his greatest allies. Not only did they vote to increase the debt, but they voted to increase it tremendously.

At the same time, the third manager determined to kick everyone out of his land he could who was not of his kind. He despised the peoples in his land who did not look like him. When it came time to pay the vendors, another group of administrators said, "We must make a way for people to stay here whose parents brought them to this land as children. They have no other place. We will not vote to pay our vendors until they are taken care of."

To be continued...

2. Concentrated Hebrews (Celebration of Son 1:5-14)

Doing notes on Hebrews as I teach a class this semester.

I. Sermon Introduction (1:1-2:18)

     A. Exordium (1:1-4)

_____________________________
B. Celebration of the Enthroned Son (1:5-14)

• These verses are sometimes called a "catena" or "chain" of quotations from the Old Testament. 
• They are structured by way of an inclusio, where words at the beginning and end of a section are similar, saying, "the stuff in the middle goes together." The inclusio are the words, "For to which of the angels did he say at some time" in 1:5 and 13. It's not exactly the same in Greek but strikingly similar.
• 1:5 expands on 1:4, which speaks of Jesus being given a name greater than the angels. The most logical inference from the flow is that this name is "Son," which of course is more of a title than a name.
• 1:5-6. The structure of these two verses is 1) quote, 2) and again, quote, 3) and again, quote.
• 1:5a. This verse quotes Psalm 2, which was a royal psalm but, when read canonically in a fuller sense (sensus plenior), can be taken as a messianic psalm. The king became God's son at the point of his enthronement. So also here, Jesus assumes the throne as God's Son at the time of his exaltation. This timing is supported by the use of this psalm elsewhere (e.g., Acts 13:33) and by the context of 1:3-4.
• As Christians we believe that Jesus was "eternally begotten of the Father." Jesus has always been God's Son for eternity past. We can believe this fact and yet still hear how Hebrews is talking about Jesus' enthronement as another piece of the Christological puzzle.
• 1:5b. This is a quote from 2 Samuel 7:14. In its original context, this verse had Solomon in mind--another instance of a king of Israel being thought of as God's son. But in a fuller sense, these words certainly apply to God's greatest Son for all eternity.
• 1:6. The structure of the quote suggests that the "again" has to do with the fact that this is the third quote and is not talking about when God brings Jesus again into the world at the second coming.
• It is tempting to think of Jesus' birth as the meaning of 1:6. "Angels we have heard on high." However, the previous two verses have been about Jesus' exaltation, and if we look at 2:5, we can argue that Hebrews speaks of the "inhabited world" in relation to the heavenly, eschatological world. For this reason, we have concluded that 1:6 is thinking about when Jesus entered heaven after accomplishing atonement. The angels of heaven bow down when Jesus is enthroned in heaven as he sits at God's right hand.
• If you look at Deuteronomy 32:43, you will be puzzled. It reads, "Rejoice you nations... for he will avenge the blood of his servants." Here is one of several indications that the author is a Greek-speaker rather than someone who read the Bible in Hebrew or Aramaic (a minor argument against Paul as author). The Septuagint here reads, "Rejoice, heavens, and let all the sons of God worship him." "Sons of God" is a way of referring to the angels. So the author seems to be following some Greek version of Deuteronomy here. Of course, the Dead Sea Scrolls read, "let all the gods worship him," so there could have been an earlier Hebrew version in play as well.
• 1:7-12. In Greek, these verses are structured by way of a "men-de" construction. This is an "on the one hand-on the other" type of construction. Thus, 1:7 about the angels is meant to contrast with 1:8-12 about Jesus.
• 1:7. In light of the contrasts that follow, the main point of this quote (Psalm 104:4) would seem to be that angels are transitory and relate to the creation. The author of Hebrews has flipped the sense of the verse, which originally was, "He makes the winds his messengers..."
• 1:8-9. The main point of this quote from Psalm 45:6-7 is that, unlike the angels, who are servants whose role is transitory, Jesus is the divine king whose throne is forever.
• The original psalm was a wedding psalm. The earthly king of Judah is called "God" in a metaphorical sense in Psalm 45, in keeping with the connection between kings and God we have seen in the other quotes. His bride comes out to meet him, along with her virgin companions, and there is hope for children.
• Jesus is also anointed from among his companions, the brothers (and sisters) of Hebrews 2:11-13. Notice that the quote makes a distinction between Jesus as God and God the Father as Jesus' God: "God, your God."
• 1:10-12. This quote contrasts with the transitory ministry of the angels and their connection with the earthly. Meanwhile, Jesus grounds the creation. Remember 1:2 has already said that Christ is the one "through whom God made the worlds." The angels meanwhile are associated with winds and flames. 
• The creation will become old. God will one day wrap it up like a garment. But the years of Jesus as God's Son and as the Lord will never come to an end. His role is eternal. That of the angels is about to change.
• 1:13. The catena ends with a quote from Psalm 110:1, a key verse behind Hebrews. It is the exaltation to God's right hand verse, one that may have been highly generative in the early church as God helped them understand the resurrection.
• 1:14. We have here a clear sense of how Hebrews understands the role of angels in God's plan. They are ministering spirits to humans and the earth in the former age until salvation is fully here. After that, we humans will no longer need their ministry, and they can spend all their time worshiping God with us in the heavenly Jerusalem (12:22).