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).

Jesus choosing people over the Law

I tweeted/made a Facebook post a couple days ago: "Jesus consistently chose people over the Law." Most agreed and at the moment there are 71 either likes or loves of the post on Facebook with 4 shares.

1. Of course there was some push-back, perhaps from three directions. First, there are those who ideologically over-emphasize continuity between the testaments. To me there is some inability to read the biblical texts in context here. For example, someone is so used to Hebrews that they think Leviticus would have had no problem with it. As one colleague once told me: "I think if the author of Leviticus were to read Hebrews, he would say, 'Of course.'" I think this is highly unlikely and reflects some inability to hear Leviticus on its own historical terms. Leviticus itself gives us no reason to think that its system of atonement was inadequate or insufficient in any way as a system. For a thousand years Jews thought the Levitical system was in fact the system God installed for all time.

So a certain degree of contextual unreflectivity is involved when we cannot see how startling a Gospel of John or Ephesians or Hebrews would have been to many Jews when they were hot off the press. This group wishes to say, "The New Testament is simply showing us what was in reality the actual meaning of the Old Testament from the start."

2. A second group are those who are sympathetic with what we might call the "Jewish roots" movement, for lack of a better word. This is a somewhat sectarian Christian movement (one that could become a cult over time), frequently involving Messianic Jews. If the first group says, "The Old Testament meant what the New Testament says," the second group says, "The New Testament means what the Old Testament says." So the discontinuities between the testaments are not fully appreciated again, but in deference to the Old Testament.

The tendency here is to miss the fact that Paul and other New Testament Christians like John did in fact disregard parts of the Jewish Law. Romans 14 and Colossians 2 imply that Gentiles need not keep the Jewish Sabbath (even though it is one of the 10 commandments). Jesus and Paul clearly did not think the food laws were binding on Gentile Christians. Paul in effect did not expect Gentile believers to keep any part of the Jewish Law that was "Jew-specific" or a "boundary" law.

By the way, I heard about another sectarian movement last week in Indiana (another cult waiting to happen). It reminds me of Marcion. It dismisses those parts of the New Testament that it thinks were not written for Gentiles. It is, in effect, a "Paul only" movement. It ignores the Gospels, for example. A contention point is the fact that Colossians 4 seems to indicate that Luke was a Gentile. Basically, it's a rubbish movement.

3. A third group that pushed back perhaps discerned the reason I posted in the first place. A legalistic strand within Christian America, including my own holiness background, has more in common with the mindset of the biblical Pharisees than with Jesus or Paul. I believe Jesus would approve DACA without a moment's hesitation. I believe this is the true Christian position. If Jesus sat loosely to the Jewish Law, imagine how loosely he would sit to the immigration laws of some random country.

I do believe that the rule of law is important in general in that it preserves in structural form the fundamental principle of "loving your neighbor as yourself." However, not all civil laws are created equal. We should obey the laws of our land in general in keeping with Romans 13. But this is not an absolute (cf. Acts 4). And there are various options with regard to the consequences of law-breaking.

4. In any case, I was asked for examples of Jesus putting people over the Law. Here is an annotated list.

Mark
Mark was written for Gentiles (sorry, "Paul-only" idiots in Logansport). So we might not be too surprised if it is not worried about Jesus appearing to be a scrupulous Law-keeper.

a. In Mark 2, Jesus does not respond to the Pharisees, "My disciples aren't breaking the Law by plucking grain on the Sabbath." His response is in effect, "Didn't David break the Law when his fighting men were hungry?" (2:26). In other words, he wasn't concerned about showing that he was a Law-keeper and accepted the assumption of law-breaking.

b. Of course he ignored the traditions of the elders several times. Eating with sinners (Mark 2 again) and thus making himself unclean, healing on the Sabbath (Mark 3), and letting his disciples eat without washing their hands (Mark 7). We easily dismiss these as "that's just the tradition of the elders," but it would not have felt so easy to dismiss at the time. This would have been experienced as Jesus sitting very loosely to the Jewish Law.

c. Mark interprets Jesus to declare all foods clean in Mark 7:19. Let's just say that this would have been a surprise to Leviticus. Very shocking at the time! Even many Christians experienced this as a flagrant disregard for the Scriptures. See Galatians 2.

Matthew
Unlike Mark, Matthew probably was written primarily with Jewish Christians in view. Matthew doesn't mention that Jesus declared all foods clean when telling about the incident in Mark 7 (cf. Matt. 15). So Matthew does seem concerned to show continuity between Jesus and the Law. However, when it comes to individual instruction in the Law, there is discontinuity:

d. Jesus' fulfilled understanding of the Law in Matthew 5 modified and is in tension with parts of the Law. The Law allows divorce for any reason. Jesus prohibits it, possibly because it is a form of legalized adultery and thus is abusive toward wives.

e. The Law says to keep vows (third commandment). Jesus says not to make vows.

f. The Law says to show no pity but "an eye for an eye a tooth for a tooth." Jesus countermands this rule for individuals.

Luke
g. The Parable of the Good Samaritan, as I understand it, suggest that the Levite and the priest were inappropriate in letting their concerns for purity trump the need to help a person in need.

John
The Gospel of John is a highly symbolic presentation of Jesus, a Message version, if you would. Its author seems to see in Jesus a deeper reality that supercedes practice of the Jewish Law. It also seems to be for a primarily Gentile audience.

h. In John 10:34, Jesus calls the Law, "your Law," suggesting that the Jewish Law is not "his" Law in some way. This is probably a paraphrase of sorts, but it shows the degree to which John separates Jesus from Judaism.

i. The symbolism of Jesus turning water for purification into wine in John 2 may symbolize that Jesus' blood replaces the Levitical purification system. We might say fulfills. Leviticus probably wouldn't see it that way.

j. Jesus suggests to the woman at the well in John 4 that it is not necessary to worship God in Jerusalem. We might say gets at the true reality. Deuteronomy probably wouldn't see it that way.

k. John 8 probably wasn't in the initial manuscript of John, but in the story of the woman caught in adultery, Jesus works against enacting the punishment in the Law for a person caught in adultery.

5. My personal sense is that Jesus was not a scrupulous Law-observer. I'm not suggesting that he was a flagrant Jewish-Law breaker. I'm saying that the trajectory we pick up in the Gospels is of someone who was repeatedly criticized for not being careful in his attention to the Law. Such a trajectory would help explain both Paul's initial resistance to the Jesus movement and the character his Christianity took once he became a Jesus-follower.

2.1b Rule of Faith cont.

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

4. This is the view of God that Christians have developed in dialog with Scripture, various Christian traditions, their experiences, and their reason. Although various Christians and Christian traditions quibble over the fine points here and there, the vast majority of Christians believe that God is holy, self-sufficient, triune, loving and just, sovereign, eternal, immutable in his nature, creator, spiritual, omnipotent, omniscient, and omnipresent.

We might say that these features of God are a kind of "rule of faith." Most Christians would say that these attributes of God are biblical and are derived from Scripture. In reality, the process of their development has been more of a dialog between Christians and Scripture. Philosophical reasoning was a clear feature of early Christian reflection on God in the first few centuries of Christendom. Further, when we encounter passages in the Bible that seem in tension with an attribute like "omniscience," most Christians deploy intellectual coping strategies to try to explain the passages in some other way.

For example, Genesis 6:6 says that God regretted that he had made humanity. Upon reflection, we realize that this statement conflicts with the notion that God is omniscient and knows everything. If God knew humanity was going to sin, then he cannot truly regret making us. He knew we were going to sin when he made us.

Nor will it work to deploy the fact that humans sometimes know something with their heads and then feel differently when they know it experientially. This dynamic is a function of human finitude. If God knows all things, then he knows what it is like to experience his universe too. Indeed, if God truly created the world out of nothing, then he created the very possible shape of human experience.

So we are faced with only a few options. Perhaps Genesis 6 was originally anthropomorphic, knowingly picturing God in human terms. Or perhaps we think of this passage as anthropomorphic while concluding that the author of Genesis would not yet have realized it. Of course some Christians take the passage literally and no longer believe in God's omniscience.

Our sense is that 1) the author of this passage in Genesis probably did originally understand this statement in 6:6 literally, meaning that this author did not yet have a full understanding of God's omniscience. Yet also, 2) as Christians we take the statement metaphorically, because as Christians we have come to believe that God does in fact know all things, including the future. We take Genesis 6:6 as a step along God's journey with Israel toward an understanding of full omniscience within later Jewish and Christian belief.

5. The absolute, monotheistic sense of God has developed as Christian thinkers throughout the centuries have reflected on the basic truths mentioned above. Most experts would suggest that some details were not yet fully in place at the time of the New Testament. The Trinity would perhaps be the most obvious example of a belief that may not yet have been fully conceptualized in the first century.

The sense of creation out of nothing is another example of a doctrine that may not have been fully crystallized until the end of the second century. If so, then the Christian sense of God as creator could not yet have been fully mature within the time frame of the Bible itself. As Christians, we read the Bible with this understanding of God as creator, but experts of the original meanings may not think that this understanding was fully present in the minds of the original authors.

As modern science expands and refines our general sense of the creation, our sense of God as creator expands and develops too. For example, what are the implications of modern physics for our sense of God? As relativity has shaped our sense of time, we are bound to look at the question of God and time a little differently.

It is not so much that such thoughts contradict Scripture as that they push us to aspects of God that would have been incomprehensible in ancient times. The principle that Scripture was, first, God revealing Godself to the original authors and audiences of the Bible to speak to their context implies that the understanding of God in the Bible has a great deal to do with ancient worldviews. God met them where they were just as God meets us where we are.

6. The pages that follow will make clearer exactly what we are saying here in concrete form. We have begun with the end in view. We have set out in this section the general aspects of a Christian view of God. This section is titled the "rule of faith" because these are the views that generally reflect the consensus of Christians everywhere throughout the centuries.

So we can listen to Old Testament theologies of God in context as well as New Testament theologies of God. We need not feel pressured to twist these texts to make them say exactly what the consensus came to be. We can be honest in our historical and biblical scholarship. We can see these individual texts as points along God's journey with his people on earth, meeting them where they were within their understandings of the world.

But we do not stop there, with how God revealed Godself to ancient Israel or to individual New Testament authors. We take a "canonical" perspective on how God was shaping these texts toward a goal, namely, the understanding of God we have presented in this section. We believe we know where God was leading his people, and we can read the biblical texts in this canonical light.

3. Concentrated Hebrews (2:1-18)

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)
     1. exhortation interruption 1 (2:1-4)

• 2:1-4 is an interruption of the flow of teaching (the exposition) with a warning to the audience (exhortation). Hebrews regularly alternates between teaching and preaching. This helps keep the attention of the audience.
• 2:2-3. The argument is a "lesser to greater" argument (also known as a qal wahomer argument in Hebrew or an a minore ad minore argument in Latin, also an a fortiori argument). The sense is that if you were punished for disobeying the old covenant, you will really be punished for ignoring the new one. 
• This goes against the Protestant sensibilities of many. This is not "in the new covenant we get away with things we didn't get away with in the old." Rather, the sense is that we should be much more careful in the new than the old, because the stakes are higher. The punishment for disobeying the new covenant--for the people of God--is even greater than the punishment was for Israel in the old covenant.
• 2:2. The idea that angels mediated the Law to Moses is mentioned three times in the New Testament (here, Acts 7:53; Gal. 3:19).
• 2:3. This verse does not sound like Paul. Paul typically argued that he received his revelation directly from the Lord and that he was a first tier apostle. This verse seems to put the author in a second tier.
• 2:4. We remember that miracles, signs, and wonders were a regular feature of the early church.

     2. the story of salvation

• 2:5-18 gives us the logic of salvation, the background to the subsequent argument, a general sense of why atonement was necessary.
• 2:5-9 seems to have the following train of thought: 1) God created humanity to have glory and honor in the creation but 2) humanity does not have this status--all things are not under its feet. The reason for this fact may be found in Romans 3:23--"All have sinned and are lacking the glory of God." 3) Therefore Jesus became human to fulfill this destiny. 4) Having suffered death for everyone, he can finally lead humanity to glory.
• The logic of these verses seems to match the inner logic of Paul, perhaps suggesting that the author of Hebrews had some connection to the Pauline circle. The mention of Timothy in 13:23 may support this sense. 
• 2:5. Some take these verses purely Christologically--solely in reference to Jesus. However, the inner logic, not to mention the original meaning of Psalm 8, suggests that humanity in general is first in view. This fact implies that humans will rule in the coming age alongside Jesus and that they will be superior to angels like Christ.
• 2:9. Jesus tasted death potentially for everyone. This seems to connect with the fact that Jesus has defeated the Devil, the one with the power of death (2:14).
• 2:10-13. These verses indicate the solidarity of Jesus with humanity, another indication that humanity has been in view with the quoting of Psalm 8.
• 2:10. The perfection of Jesus in Hebrews has to do with him being made complete in relation to his ability to function as a priest and sacrifice. He is "locked and loaded" to bring atonement through his suffering.
• God is the one for whom and through whom all things exist.
• 2:11. Jesus sanctifies. He sanctifies, which has a sense here of purifying and cleansing, through his blood.
• 2:12. This verse quotes Psalm 22, which was a highly generative psalm for the earliest Christians, likely having been quoted by Jesus from the cross. We are not surprised then that the author of Hebrews heard verse 22 on the lips of Jesus.
• 2:13. A key take-away here is that Jesus had faith in God just as we are to put faith in him.
• 2:14. This is Hebrews' incarnation verse. Jesus took on blood and flesh. 
• This is the Christus Victor angle on atonement. Jesus defeated the Devil with his death.
• There may be a "last Adam" logic in the background here like Romans 5. Death entered the world through Adam. Jesus frees us from death.
• 2:16 is a curious verse that makes us think back to Hebrews 1. Were some in the audience suggesting that Jesus had come as an angel? Are there hints of early Gnosticism here or the precedents of Gnosticism? Were some of the audience worshiping angels as in one interpretation of Colossians 2:18 (not mine, actually)? At the very least, Hebrews associates angels with the administration of the old covenant. I am open to the possibility that the church was experiencing some rumblings of an angel Christology.
• "Seed of Abraham" probably includes Gentiles here. Otherwise Hebrews would seem to exclude Gentiles from salvation. This suggests a time after Paul when this question was no longer much in play--at least not for the author and audience. Earlier, Paul has to argue that Gentiles are part of the seed of Abraham (Rom. 4:16). Hebrews assumes it. So once again, we have a connection to Paul but seemingly an extension of Paul, post-Pauline situation. I think it is a minor data point toward a Gentile audience--that Gentiles can be included and assumed to be in the seed of Abraham without comment or argument.
• 2:17-18. These may very well be the key verses of Hebrews. It is also the first mention of Jesus as high priest in the sermon. 
• These verses imply that Jesus was fully human. He identifies with human suffering and temptation. We therefore have a priest who sympathizes with us.

1. Concentrated Hebrews (1:1-4)

A couple months back I blogged my study notes on Romans. Who knows? I may self-publish them as a study Bible someday. These notes relate to the content I teach in relation to the book.

This semester I'm teaching Hebrews and General Epistles. So here is the beginning of concentrated notes on Hebrews.
________________________
1. Hebrews 1:1-4

• Hebrews does not begin like a letter. It does not tell us its author or audience. In fact, Hebrews has numerous uncertainties: 1) unknown author, 2) uncertain destination, 3) uncertain ethnicity of recipients, 4) unknown point of origin, 4) uncertain date, 5) debated reasons for writing.
• A majority of Hebrews experts are comfortable with a sense that this document is a "sent sermon," that is, a sermon that was sent to its destination as a letter. 
• These verses are the introduction to the sermon, sometimes called the "exordium" or the "proemium" of Hebrews.
• They are one sentence in Greek, one of the most beautiful Greek sentences in the New Testament. The style is generally called a "periodic" style for its balance and beauty.
• 1:1-2. The first few words use the same letter in Greek five times (p sound), a literary feature known as "assonance."
• The first two verses divide up all of history into two ages. "Formerly" and "these last days." Formerly, God spoke to the fathers through the prophets. In these last days, God has spoken to us through a Son. In the former age, God spoke in many and various ways. In these last days, God spoke in one way--through his Son.
• "The last days" is a category of the prophets, especially Jeremiah. We are meant to connect this phrase to the age of the new covenant as in Jeremiah 31, which is quoted in Hebrews 8.
• The term, "Son" is a royal term in addition to being a familial term. The primary sense of Jesus' sonship in Hebrews 1 is that of king, "Son of God," as well as heir. 
• Jesus stands at the beginning and end of history. He is the heir of all things at the end of history, but he is also the one "through whom God made the worlds." Given that Hebrews more typically speaks of God as creator (2:10; 3:4; 11:3). This suggests that 1:2 is speaking somewhat metaphorically of Jesus as creator, probably likening him to God's wisdom (see verse 3).
• 1:3. Some might suggest this material as hymnic or brought in from somewhere else because of the formulaic "who" followed by poetic statements about Jesus. However, it is also possible that the author himself composed it.
• It seems certain that the author was male because of the masculine singular participle in 11:32.
• Jesus is the "reflection of glory" and "stamp of substance." The second item is passive (stamp) suggesting the first is "reflection" rather than "radiance." The first statement is likely an allusion to Wisdom 7:26, where it also arguably has a sense of reflection. The fact that Wisdom 7:26 is talking about God's wisdom supports the sense that 1:2 has God's wisdom as the agent of creation in view.
• "bringing all things by the word of his power" may be an allusion to the logos, also an agent of creation in Jewish logos speculation. "Bringing" may have a sense of new creation.
• "he sat on the right hand of Majesty" - an allusion to Psalm 110:1 and Jesus' "session" at God's right hand when he had finished his atoning work, "having made a purification for sins."
• 1:4. "having become greater than the angels." Jesus became lower than the angels for a little while (2:9) when he "partook of blood and flesh" (2:14). Now that he has accomplished atonement, he has been exalted above them.
• He as much greater than the angels as his inherited name. This inherited title would seem to be "Son," as we will see in the next verse (1:5). It is the title of a king.

2.1 Biblical Theology of God: The Rule of Faith

Every time I teach biblical theology I think, "I should write my own book." So I might put some fragments here as I have opportunity. I have no book contract and have too many things to do to write extensively, but I want to put some depth probes here.
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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
2.1 Basic Beliefs
1. The Christian understanding of God is relatively uncontroversial in its most fundamental aspects. For example, the idea that "God is one" is fundamental not only to Christianity but to Judaism and even Islam. We will see later in the chapter that the understanding of what monotheism means developed some within the pages of Scripture and in the first couple centuries of the church. [textbox] Modern cosmology may help us refine our understanding even further. Nevertheless, the central doctrine goes back to Deuteronomy 6:4.

God's attributes or characteristics are often divided into two categories. These are his "communicable" attributes (characteristics that humans share to some degree) and his "incommunicable" attributes (characteristics that are unique to God alone). However, we might also divide his attributes into his transcendent and economic attributes. Transcendent means apart from or beyond the creation. "Economic" in this means God in relation to the creation, the way God administrates the universe. [1]

2. We might mention seven attributes as characteristic of God in his being apart from the creation: 1) holiness, 2) self-sufficiency, 3) triunity, 4) love, 5) freedom, 6) eternity, 7) immutability.

...

3. Similarly, we might mention six attributes of God that reflect the way God relates to the creation: 1) creator, 2) spirituality, 3) omnipresence, 4) omnipotence, 5) omniscience, 6) justice.

...

[textbox] Monotheism is the belief that there is only one God who stands alone and distinct from everything else that exists.

[1] As a side note, we might argue that all of our knowledge of God is in relation to his creation. That everything we know about God we know by analogy to the creation.

Friday Science: Susskind's Quantum Mechanics

1. About two years ago, I bought Leonard Susskind's Quantum Mechanics: The Theoretical Minimum. I'll confess that I have found it an incredibly frustrating book. As I've read and reread the first few chapters, I have the repeated feeling that all this book needs is a few more paragraphs in each chapter--and maybe some rearrangement of the order of topics--and it would be incredibly helpful. It seems that he has followed a logical order but not a good pedagogical order.

It's like you're in one part of the forest and he's telling you about a set of trees in another part of the forest. And he's not even talking about trees in his part of the forest that are next to each other, but there's one tree he's seen that relates somehow to another important tree he's seen. But he's none too clear even about how those two trees are connected to each other... in some unspecified part of the forest you're not in.

What you need is directions to get from your part of the forest to the part he's in. Then you need to know how to get from one of the trees he's mentioning to another. This height of unnecessary confusion makes me angry, because it's completely avoidable. I'm convinced I could do much better and probably will.

For the record, I don't think it's intentional. I think Susskind really wants to be clear. He just knows the forest too well to tell someone in words how to get around in it, at least someone who's never taken a course in linear algebra. I've wondered if the jokes at the beginning of the chapters are revealing. They seem to demonstrate an inability to grasp what is funny.

But I want to force myself through the book. Richard Feymann once told his sister to read and reread the math and science she didn't understand. I'm convinced this is the way to go with many difficult subjects and authors. So here I go again with Susskind.

2. Chapter one should not be the first chapter. At least a great deal of what is in here should not be first. Most people need to know why they need to know something for the something to stick and make sense. So I have come to realize that there is some linear algebra in this first chapter. It uses notation that Paul Dirac introduced to quantum mechanics I think in the 1940s.

Wrong place to begin. He's thinking. We learn bras and kets, then we use them in later chapters. But bras and kets make little sense when you have no idea what they're for. I know complex numbers, but for someone who doesn't, it would be better to introduce them when we need to know them. Show us the problem they help solve and introduce them there.

3. So what is helpful to take away from chapter one at the beginning? Here is some stuff from the beginning of the chapter:

• The idea of state is fundamental to quantum physics. For the moment, let's talk about the most fundamental state as being either on or off, +1 or -1. Let's call this "two-state system" a one bit system, a quantum bit or "qubit."
• We could call this "either on or off" the quantum spin. It's not a literal spin.
• Experiments are never gentle. You measure one thing, you mess up everything else. You've lost information from the other place because you've chosen to measure this place. (think Heisenburg's Uncertainty Principle)
• What is predictable on the quantum level is not the individual outcome of some measurement, but the statistical average. Individual outcomes are not predictable, but the averages are.
• The quantum mechanical notation for the statistical average is Dirac's bracket notation: 〈Q〉 .

4. Now he gets into some linear algebra.

• The "space of states," the possible values or states of something is a "vector space" in quantum physics. (linear algebra) Another name for such a "space" is a Hilbert space. There could be an infinite number of elements. This is all very abstract. For the moment, I'm just picturing a box you put stuff in, and different boxes will only take a certain number of things.
• The elements of a vector space are called kets or ket-vectors. The notation Dirac used for these is ∣A〉
• The elements of a ket are often a column of complex numbers. We are being set up for matrix multiplication. 
• The "row" matrix that is pit against the "column" matrix of the ket is the bra. The bra looks like this: 〈B∣ . 
• bra-ket. First in the row multiplied by the first in the column and so forth. The inner product of two of these vectors is the result of this sort of operation.
• A vector is normalized if its product with itself is 1.
• A vector is orthogonal if its product with itself is 0.
• The dimension of a vector space is the maximum number of orthogonal vectors in that space. These vectors are orthonormal bases in relation to each other.
• Finally, there is something called the Kronecker delta. As far as I can see, he never tells us what this is. I know the name from somewhere else. The Kronecker delta is symbolized as δ_ij . This function is 0 if i and j have different values and 1 if i and j have the same value.

Why do we need to know these things? He doesn't tell us. Very frustrating.

Friday Science: First Semester Physics in 20 Equations

I like physics. My son's taking high school physics and faces the AP exam at the end of the year. It occurred to me this morning that first semester high school physics really boils down to understanding the following 20 equations/concepts:

1. Know the basic units (lengths, time, mass) and their decimal forms (kilo-, centi-, milli-).

2. Know how to cancel out labels using multiplication, division, etc.

3. Know soh-cah-toa for vectors
(sin a = opposite/hypotenuse; cos a = adjacent/hypotenuse; tan = opposite/adjacent)
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The Big Five Motion Equations
4. d = vt

5. v₂ = v₁ + at 

6. d = v₁t + 1/2 at²

7. d = (v₁ + v₂)/2 * t

8. v₂² = v₁² + 2ad

(Substitute g for a and you have free fall equations.)
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Newton's Laws
9. First Law - a body in motion wants to stay in motion (so horizontal motion is constant if there is no friction).

10. Second Law - F = ma

11. Third Law - For every action there's an equal and opposite reaction: m₁a₁ = m₂a₂

12. Conservation of momentum, where p = mv (momentum = mass x velocity)

13. Impulse: F x t = mΔv (= change in momentum)

Friction Forces
14. The formula for the force to get something moving is F_static = mu_static * normal force. F = μn (The normal force is simply the reverse of weight, mg).

15. The formula for the frictional force of something moving is F_kinetic = mu_kinetic * normal force.
F = μn

Energy Equations
16. Kinetic Energy: K = 1/2 mv²

17. Potential Energy: U = mgh

18. There is a conservation of energy. If there is no friction, potential energy converts completely to kinetic and vice versa. If some is lost as friction or heat, the total is still the same.

19. Work done equals the difference between the start and end values of kinetic energy (work energy equation: W = K₂ - K₁

20. W = Fd (work = force x distance)

New Year's Resolutions 2018

Another year, resolution time.

Looking Back
1. Books I read and reviewed this year.

• I read some but unfortunately not all of Waking Up White.
• I read Adam and the Genome.
• Reality Is Not What It Seems
• I read most of Der Fuhrer.
• I skim/read The Culture Map.
• I skim/read Cultural Intelligence.
• I skimmed Philip Jenkins' The Next Christendom.
• I read Jane Patterson's Keeping the Feast and had a book review published on it.
• I read some but unfortunately not all of The Lemon Tree: An Arab, A Jew, and the Heart of the Middle East.
• I read and reviewed The Shack.
• I skimmed/read some of Sapiens: A Brief History of Humankind. 

2. Things I wrote

• Finished my first novel last week, 70 pages: Gabriel's Diary: The Incarnation. Maybe more to come.
• Self-published my notes on my time as Dean of Wesley Seminary: Six Years a Dean: The Founding of Wesley Seminary.
• I finished a book that was six years late on Hebrews. Turned it in. We'll see if they will still publish it.
• I did explanatory notes on all of Romans. May self-publish with my own translation of Romans.
• One of my most popular posts had 95 theses for the church today, on the 500th anniversary of the Wittenberg Door.
• I finished a series on world history. Got quite far on science and math.
• I did quite a few posts in my Seminary in a Nutshell series on the contexts of a minister.
• I finished a Seminary in a Nutshell series on leadership.

3. And other things

• I became Dean of the School of Theology and Ministry officially in July. Some thoughts. I think it's a job for either 1) people who are ambitious, 2) people who are servants, or often 3) people who like administration. I'm not feeling particularly much like 1 or 3 these days.
• I preached two or three times this year, spoke at the Festival of Preaching. Got sick and so didn't get to deliver this one. Here's the audio of my chapel sermon.

Looking Forward
1. After 13 years of blogging, I almost stopped blogging in September. It would be hard to express how discouraging I have found this past year on multiple levels. I love sharing ideas. I blog because I love sharing ideas. It is no coincidence that I am a preacher/teacher. God often calls us to what we love or we find that we love what God calls us to.

But this year has knocked the wind out of my sails. And of course I've been extremely busy.

So I don't plan on resuming daily posts. Maybe one or two a week. I'll probably do explanatory notes on Hebrews and the General Epistles as I teach that class. My Monday reading group is doing a book called The Evangelicals. Might post some summaries of it. Who knows?

2. I still have the inductive Bible study book to finish. Must get it finished this year. I might do more installments of the Gabriel series. Plenty of books I'd love to write but who cares. Book writing is for the famous, the scholar, and the big-mouthed.

3. Here are my science and math goals.

4. How about a goal of 6 miles a week of running, at least until it warms up? Then 15 miles a week.

Happy New Year!