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- Format:Cambridge Elevate
- Subject(s):Computer Science
- Qualification:AQA
- Author(s):David Waller
- Available from: June 2016
- Notes: Not available for credit card purchase. Please contact Customer Services.
A new series of bespoke, full-coverage resources developed for the 2016 GCSE Computer Science qualifications.
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Written for the AQA GCSE Computer Science specification for first teaching from 2016, this enhanced digital resource uses an exciting and engaging approach to help students master underlying computing principles and concepts, and develop their computational thinking, programming and problem-solving skills. Interactive worksheets consolidate students' learning and rich digital content including animations demonstrate how computer science relates to everyday life. This resource allows students to annotate text and add audio notes, and enables teachers to assess, track and report on students' progress. Accessible online and on tablet devices through the Cambridge Elevate app (iOS and Android).
- Contents
Tailored to the new AQA GCSE Computer Science specification for first teaching from 2016.
The Cambridge Elevate Assess to Progress tool provides support for assessing, tracking and reporting on students' progress
Rich digital content including images and animations that help students relate Computer Science to everyday life.
Allows teachers and students to annotate text, add audio notes and link to external resources.
Contains a wide variety of practice problems, interactive worksheets and exam-style questions to help with exam preparation.
Accessible online and on tablet devices through the Cambridge Elevate app (iOS and Android). For information on how to use Cambridge Elevate editions and on supported devices please visit elevate.cambridge.org/support.
A print Student Book and a free digital Teacher's Resource are also available.
- Author(s)
- Introduction
- 1. Algorithms
- 2. Iteration
- 3. Data types and structures
- 4. Sorting and searching
- 5. Input and output
- 6. Software development
- 7. Representing numbers
- 8. Representing text, graphics and sound
- 9. Computer systems
- 10. Boolean logic
- 11. Programming languages
- 12. Computer networks
- 13. Cyber security
- 14. Impact of digital technologies
- Non-exam assessment preparation
David Waller
David Waller is an experienced Computing Teacher and Author. A former ICT Director, David has taught at KS3, GCSE, A Level and vocational qualifications such as GNVQ and DiDA. He has authored 14 published computing titles including textbooks, teacher resources, revision materials, online publications and interactive activities. David has always believed computational thinking and programming are vital as they allow students to develop problem-solving skills and an ability to express solutions clearly and creatively – similar to writing a story, a poem or composing music.
Ann Weidmann
Ann Weidmann has extensive experience of assessment and qualification design. Ann has taught computing in a variety of settings and held various positions at Edexcel including Assessment Leader, Qualifications Leader and Head of IT and Computer Science. She has co-authored a wide range of computing resources and teaching materials, regularly delivers teacher training both F2F and online, and is an Ofqual subject expert for computer science.
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This is an excerpt from Sport Finance, Third Edition, by Gil Fried, Timothy DeSchriver, and Michael Mondello.
Paying Student-Athletes
Although certainly not a new concept, over the last several years advocates for paying student-athletes have collectively voiced support for such action. Although current NCAA president Mark Emmert publicly acknowledged that paying stipends to student-athletes would not happen under his leadership, he also strongly opined that something needs to be done sooner rather than later. Specifically, Emmert agreed that discussions should occur about how the NCAA's revenues could be distributed to the actual workforce, but his reservation about creating an employee–employer relationship should be carefully considered (Weiberg, 2011).
In an attempt to provide several perspectives regarding the compensation levels for those directly involved with the production of revenue in major collegiate sports, essentially the student-athletes and coaches, Huma and Staurowsky (2011) analyzed financial metrics including room and board, coaching salaries, and revenues produced by each team. Following four analyses, they released a report titled "The Price of Poverty in Big Time College Sport." Among their findings were the following:
Based on these findings, Huma and Staurowsky (2011) proposed several recommendations:
Brown (2011) estimated that the rents generated by the top college football players significantly exceeded the costs associated with athletic scholarships. A top college football player, defined as one drafted into the National Football League (NFL), produced marginal revenues exceeding $1 million in 2005, representing a 30% increase from estimates 16 years earlier.
Broadcasting Deals
In 2011 the University of Texas (UT) reached an agreement with ESPN to launch the Longhorn Network, a channel devoted exclusively to broadcasting and promoting both the university's athletic department and the university. As part of the agreement, UT will receive payments totaling over $300 million dollars distributed over 20 years. This money is in addition to the share of Big 12 revenues that the university already receives as a conference member. Although the University of Texas will certainly reap the financial benefit of having their own dedicated network, the biggest advantage for Texas may not be the financial payoff, because half of the money will initially go to academics, but rather the constant presence on television and other platforms. Potential high school recruits will see the Longhorn Network in their homes and on their iPads and smart phones. Potentially, the Longhorn Network could become the nation's first regional college sports network focusing on one school with a limited high-profile inventory.
Despite the increased media attention brought to a host institution, televising collegiate sporting events are not always profitable for everyone. For example, in 2010 the University of Pittsburgh hosted a four-team subregional in the NCAA women's basketball tournament. But Pittsburgh failed to qualify and was not among the participants. Four teams without a local draw were selected, and only 2,000 tickets were sold after the participating teams were announced. Although the amount of money that Pittsburgh lost was not made public, an Associated Press report in 2009 stated that 11 of the 16 first- and second-round host sites lost money (Zeise, 2010).
Conference Realignment
Although the start of the 2010 college football season was overshadowed by off-field controversies involving high-profile coaches and player-related incidents, the 2011 season was equally compelling away from the gridiron in the form of conference realignment. Several marquee universities including the University of Nebraska (Big Ten) and Colorado (Pac-12) competed in new conferences, and the number of institutions changing conferences or contemplating a change in membership snowballed as the season began. Just a month into the 2011 football season, the Atlantic Coast Conference welcomed Syracuse University and the University of Pittsburgh to their conference, bringing their membership to 14 institutions. Other schools were also being considered, potentially creating a 16-team league (Dinch, 2011). Although stakeholders of college athletics continue to talk about conference membership being influenced by geography and academic reputations, realistically these changes are driven by financial opportunities, specifically the revenue-sharing models of each conference. Furthermore, if conferences all shared revenues equally, the number of schools seeking new conference membership would likely diminish significantly. For example, after the Big 12 conference lost members Colorado and Nebraska respectively to other conferences in 2011, the conference was criticized for its disproportionate television revenue distribution. Only after losing teams and seeing the potential exodus of several other institutions did the Big 12 conference administration agree to modify their existing revenue-sharing policy to distribute money equally among conference members.
Before this change, the Big 12 operated differently. For example, although half of the television revenue was equally shared, the remaining half was distributed proportionately to the number of television appearances for football and men's basketball. Consequently, high-profile institutions with a consistent television presence received more money than other conference members did. This revenue distribution disparity was closely aligned with the model used by several professional sport leagues. Specifically, although Major League Baseball (MLB) teams equally share revenue from national broadcast deals, local television revenues are negotiated independently and vary significantly across teams. The bidding wars among conferences to secure the most lucrative television deals will undoubtedly be an important criteria as universities become engaged in conference realignment discussions. When the Pac-12 conference negotiated a $3 billion, 12-year broadcast deal in 2011 with ESPN and Fox Sports respectively, the deal became the top financial deal in college sports (Miller, 2011). Given the dynamic state of college sports, particularly football conference affiliation, this deal will undoubtedly be surpassed in the
Read more from Sport Finance, Third Edition by Gil Fried, Timothy DeSchriver, and Michael Mondello.
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Habitat is the best clue for identifying this wren; rarely strays from cattail marshes and rushes for breeding. Migrants occasionally move into wet fields. Often difficult to see well as it skulks through grasses. Its plumage is rather bright rufous with darker brown cap, contrasting whitish eyebrow and throat, and black-and-white stripes on back. Overall darker and more contrasting than similar Sedge Wren.
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User:Bob Jones
- 1 Why am I here?
- 2 A letter to Mark
- 3 Exodus 4
- 4 Text Transformation
- 5 Commentary
- 6 Orthodox Wiki
Why am I here?
I have found articles and messages from these sources are from people who know the same Christ I do.
- "A Biblical Christian is the one who, wherever he looks, on every page of Scripture, finds everywhere Christ." [1]
- Ancient Faith Radio [2]
I see Christ everywhere in the scriptures and am looking for a place to share what I see.
I am hoping that the Orthodox position on typology will welcome the sharing since I believe the images are consistent with Orthodoxy.
A very simple example
The shadows I see are hidden in double entendre, shadow and riddle. A single verse demonstrates all three:
In Genesis 2:21 the Hebrew words have multiple meanings. Sleep also means death, rib means limping and side, flesh means mankind, took means married, etc, I call these the double entendre. For a single example it is impossible to demonstrate intent, and the example can easily be ignored as a novelty. If you hang in there with me, you will see sufficient examples to know that I am not clever, but that God intended to speak to us in this fashion.
What I call shadows are words similar to 'rock' as Christ. There are rules concerning them and although they look like allegory, the rules constrain them even more so than the meaning of the double entendre is constrained. In this verse substituting Christ for Adam is a shadow substitution.
We now get: Gen 2:21 And God caused Christ to die and he died, and he married a certain limping side and redeemed mankind.
This is a riddle. The annoying thing about riddles is that you cannot discern the answer from the content of the riddle. You must first know the answer then apply it back to the riddle. The answer is always found in Christ. He is the light of the New Testament that reveals what is in the shadows of the Old. The "limping side" of Christ is the side with the bruised heel, it is his flesh that he married to the church.
We now see the shadow of Christ and the cross in Gen 2:21... and this isn't even the first mention of the cross.
Some of the early church fathers went down to the jot and tittle layer to see shadows of Christ, and reserved sharing them for only the most devout. The shadows are a reward for those who believe God is and is a rewarder of those who seek Him. They give great delight when discovered by meditating upon his law.
The shadows do not elevate the expositor, but instead humble Him as mysteries are unfolded in the light of Christ. They also humble him since is it through the childish silliness of riddles that he speaks. As adults we forget that he said he would speak in riddles:
- Prov 1:5 A wise man will hear, and will increase learning; and a man of understanding shall attain unto wise counsels:
- 6 To understand a proverb, and the interpretation; the words of the wise, and their dark sayings <02420> (riddles).
- Ps 49:3 My mouth shall speak of wisdom; and the meditation of my heart shall be of understanding.
- 4 I will incline mine ear to a parable: I will open my dark saying <02420> upon the harp.
I hope you will examine these closely to see if they are true. And I hope to find a place where I might submit many more for discussion.
Here are the rules for shadows:
They are discerned from the scriptures using the same hermeneutic:
- 1. Since God has said that not a jot or tittle will pass away, until one knows why each jot and tittle is there, a complete understanding has not been derived. (This keeps us humble)
- 2. Since man shall live "..by every word", a doctrine is not sound until it sums up and includes all that God has said about it. (This keeps us searching)
- 3. Since every word must be established by two or three witnesses, every shadow must have at least two supporting scripture witnesses. (This keeps us rigorous in methodology)
- 4. Since God's word is established forever, a shadow means the same thing everywhere is it used. So, since a donkey is a shadow of a prophet, everywhere there is a donkey, it is a shadow of a prophet. This rule alone makes the shadows humanly impossible to fabricate. (This keeps us an awe)
- 5. The riddle of Samson tells us Christ is the answer to all the riddles. If the shadow doesn't look like Christ, it isn't a good shadow. (This keeps us focussed)
- 6. And since we are to "let everyman be a liar and God be true", outside references are not required to solve the riddles and see the shadows. (This keeps us devoted)
A letter to Mark
This is a note I wrote to a friend to explain how I came to be able to see the shadows.
Dear Mark,
Twenty-six years ago I taught hermeneutics in seminars prior to teaching evangelism. Understanding the reasons for one's faith is critical to a rational presentation of the gospel. After showing the methods for literal interpretation and emphasizing a clear and solid understanding of the authors' intentions, I concluded with a statement, based in faith, that all scriptures spoke of Christ, and so we should look for him everywhere.
This simple assertion was based upon "And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself." (Lu 24:27 AV)
I believe that God has blessed that simple faith, and has blessed me richly by permitting me to see the outline, and perhaps some of the details of that sermon on the road to Emmaus.
I studied briefly with a rabbi, which experience I found most unsatisfactory. His methods were strange and his conclusions always wrong, since they missed the salvific message of Christ.
When I returned to my own studies, pictures of Christ popped out everywhere. I have since realized that I am using his methods, but applying them to the Old and New Testaments together, whereas he was blind to Christ since he would not look at the New Testament.
The first clear picture of Christ that I saw was in the story of Tamar in Gen 38. It is difficult to find meaning in the literal interpretation and the best interpreters are relegated to concluding that the narrative shows that Jesus was descended from some colorfully sinful people, or that "What goes around comes around".
However, there are hints to a deeper meaning:
The name Timnath means "appointment" and Tamar met Judah before Timanth. It is appointed unto man, once to die, and Mary met God before Christ's appointed time.
Tamar was promised a goat, Mary was promised a scape goat, for he will save his people from their sin.
Both Tamar and Mary wanted an assurance of the promise.
Tamar was given the rod, and Mary was told "The power of God..." Tamar was given a signet ring, and Mary was told "He will be called the Son ..." In Numbers we find out that an empty vessel without bracelets is unclean. Tamar was given bracelets (was clean) and Mary was told "The Holy Ghost will come upon you (not unclean)
When they were discovered to be pregnant both were threatened. When the father was discovered, they both were honored.
Judah was told "There was no prostitute here" Joseph was told not to be afraid to take Mary.
Tamar had twins… Mary had the God-man.
The names of the twins means "Breaking forth" "rising sun" and Jesus was called "Dayspring"
Pharez was a usurping second son (in a long line) and Jesus was the second man who obtained the promise. (Adam being the first man, and he did not obtain the promise).
We immediately sense a picture of the birth of Christ.
Now what just happened?
Hearing, Seeing, Walking
The Jewish word 'Torah' is most commonly used to speak of the first five books of the Bible, however, the meaning is deeper than this. "Torah' includes the full revelation of God. This is expressed in the ideas of hearing, seeing and walking by Jesus.
When God met Israel at the mountain he first spoke to them, but they could not hear him. He showed them the works of his hand in the written law in the stone tablets, but they could not see him, so he "walked" among them as a pillar of smoke and fire.
Paul, in his letter to the Romans, tells the same story in different words. All men are without excuse because God has spoken to them (He is made manifest). He then has shown them the works of his hand (all creation testifies...). And now he walks among us as the Son.
These three witnesses testify for us or against us. When we are deaf, we cannot hear the voice of the Shepherd. We do not respond to our instinctive knowledge of God. When we are blind, we do not respond when our intellect has been engaged, and reason demands that we acknowledge God. We are lame, when we are unable to live as Christ would have us live because we are shackled with the chains of sin, or burdened with the yoke of the law of sin and death.
By sensing that in the story is a shadow of the birth of Christ, you have just experienced hearing. It is likely that you already hear His voice in many parts of the Bible, but that it is a distant voice that isn't clear.
We sense that the parting waters of the Red Sea and the Jordan River, the cleft rock, the torn veil are all parts of the same picture of Christ, but the picture isn't clear. This is hearing.
We notice that there is a strange pattern of inheritance among the Hebrews where the second son gets the inheritance and we know there is something hiding just beneath the surface that speaks of Christ. We observe that the pattern of the second wife being the loved, but can't connect it to Christ. These are the muffled words of God, indiscernible in content, but recognizable by His voice.
At my age I am beginning to not hear so well. I find that it is helpful to my understanding if I look at the person speaking. This is no different for our spiritual nature. The muffled words of Christ become clear when we look at Him when he speaks.
When we engage our intellect, and examine to see if the word is true, then the words we heard become clear. I believe the methods I learned from the rabbi are intellectual exercises that permit us to see. The rabbi was unable to see Christ simply because he refused to look at Christ. He refuses to read the New Testament scriptures and apply the methods of seeing upon them.
I am writing this to you to share the wonderful gift this rabbi has given me. I know you share the same simple faith expressed above, that all the scriptures speak of Him. I hope I am able to communicate the gift in such a way that you too can experience the joy and delight of seeing our Lord in the shadows of the Old Testament.
As I became more comfortable with the hermeneutic, I discovered that every word helps paint the picture of Christ.
In scriptures the word 'sleep' is used for death. Rib also means 'limping' and 'side', 'took' also means 'married', 'flesh' means 'man', "closed up" also means "deliver".
Knowing that Adam is a shadow of Christ I substitute his name and Gen 2:21 now loosely reads:
- "And the Lord God caused death to fall upon Christ, and he died: and he married his limping side, and delivered mankind."
Anyone can verify the word substitutions from a Hebrew dictionary.
Initially, this seems like a very unlikely way to communicate. As adults, we are accustomed to filtering out the alternate meanings of words automatically, based on the context of the conversation. Children are unable to do this.
When I first started to teach myself Hebrew, I thought I would take a shortcut. I realized that the earliest Hebrew words didn't have vowels. Seeing that there were sometimes three, four or five identical words differing only by the vowels, I would only have to learn one third, fourth or fifth as many words if I simply learned them without the vowels.
This fortunate mistake put me in the same position that a child is in when he is first learning language. When he hears a word, he must consciously try to apply all the meanings of the words, with which he is aware, in order to make sense of what he is hearing.
We take great amusement in the products of childish mistakes in understanding when he has misapplied a meaning to a word. But we also reward those who are able to intentionally build these multiple meanings into phrases that can be understood in multiple ways. Bob Hope was famous for his double entendre.
It is important that we distinguish between what is called allegory, and what I and the author of Hebrews call shadows. The meaning of shadows is firmly attached to the same words used in the literal interpretation. Allegory has no rules and was invented by the Greeks to make their myths say something figuratively that they couldn't say literally. Allegory is used primarily by those who do not wish to believe the literal interpretation.
There is good allegory, though it is invention, it faithfully represents truth, though possibly, not from the passage being allegorized.
The interpreter of shadows has no such freedom. The raw material for meaning must come from the words themselves. A shadow does not exist, unless something real exists first. The Jewish interpreters have a saying: "The pashat never loses it's meaning." This is a good saying. It means that the literal meaning never disappears. There must have been a real Tamar for there to be a shadow of the birth of Christ in the Tamar narrative.
So unlike the Greeks who sought to change the essential message of the myths with allegory, the shadows must build upon what is already known about truth, not alter it.
Not totally foreign
The idea that Hebrew words have multiple meanings is not completely foreign to us. The Bible itself often tells us the meaning of someone's name. Some have found 'hidden' messages in long lists of names. Others are amused to discover that the word for 'wife' also means 'burning ember' and are delighted to embarrass the elderly sisters by announcing from the pulpit that when Adam first saw his wife he proclaimed "Hot stuff!".
All of this suggests that we have been hearing the muffled words of the Lord.
See if you can hear his voice if we remove some sayings from their context:
- "If you do right, won't you be lifted up?" - to Cain
- "Because of you, I will live" - Abram to Sarah
- "God will provide himself, the sacrifice" Abraham to Isaac
- "He was dead, but now he is alive" - Prodigal son
- "His love for the world, and betrayal because of riches, killed him and he became desolate" - parable of the sower paraphrase
- "Take these, and whatever account you have against them I will pay" - Good Samaritan
The reason that you can hear the muffled words in these sayings, is because of the double meaning of the words. The word 'because' in Hebrew and in English can be understood as "causative" or "emotive".
In the case of Abraham to Sarah, in the literal it means "the actions you take will save my life". But in the shadows it is understood as "my love for you motivates me to rise from the dead."
In the case of Abraham to Isaac: We hear in the literal "God will provide a sacrifice for himself." But in the shadows we hear "God will provide himself as the sacrifice."
Even without using the double meanings or words that sound alike, or are spelled alike, we can find multiple meanings in the words used. We must simply trust that we are hearing the voice of God, and then dig to see that it is true.
Gen 2:21 "And the Lord God caused death to fall upon Christ, and he died: and he married his limping side, and redeemed mankind."
Later I realized that there was yet another layer. What was the limping side of Christ? The answer is easy, it is the side with the bruised heel. And of course, he married the church.
But that wasn't really the question. What kind of communication is this "he married his limping side"? Observe that is is written as a riddle. It is child's play.
Would the Almighty God actually do something as silly as communicate with us in riddles? Would He bypass the precise systematic theologies of the learned and wise men and speak in the language of children? Would he expect us to "become as little children" to hear his word?
God speaks in riddles
God says he would. The word "dark sayings" in Hebrew is also the word for 'riddle':
- Nu 12:8 With him will I speak mouth to mouth, even apparently, and not in dark speeches <02420>; and the similitude of the LORD shall he behold: wherefore then were ye not afraid to speak against my servant Moses?
- Ps 49:4 I will incline mine ear to a parable: I will open my dark saying <02420> upon the harp.
- Ps 78:2 I will open my mouth in a parable: I will utter dark sayings <02420> of old:
- Pr 1:6 To understand a proverb, and the interpretation; the words of the wise, and their dark sayings <02420>.
- Eze 17:2 Son of man, put forth a riddle <02420>, and speak a parable unto the house of Israel;
- Da 8:23 And in the latter time of their kingdom, when the transgressors are come to the full, a king of fierce countenance, and understanding dark sentences <02420>, shall stand up.
It is clear that God says He speaks in riddles. Why would we adults not believe it? When we learn to listen like children, we learn to discern the riddles.
Rules for riddles
God says that not one jot nor tittle will pass away from the law, so as a child I hear that every one of them must be important. And as an adult I realize that I don't fully understand scripture until I understand why every jot and tittle is there. This keeps me humble.
God says that man should live by "every word" that proceeds from his mouth. As a child I hear that I must understand every word. As an adult I reason that a doctrine is not sound until it sums up and includes every word God has spoken about it. This keeps me seeking.
God says that "every word shall be established by two or three witnesses". As a child I hear that every shadow must have other scriptures that confirm what they are. As an adult I reason that the shadows cannot be invented, but must be defined by the scriptures themselves. This keep my methods rigorous.
God says His word is established forever. As a child I hear that a shadow doen't change. So if a donkey is a prophet in one place, it must be a prophet in all places. As an adult I discern the impossibility of human invention to comply with this rule in all cases and in all scriptures. This keeps me in awe.
God says that we should "let all men be liars and God be true. As a child I hear that I can only trust God to teach the shadows, As an adult I discern that outside resources should not be used. Histories, cultures, and non-canonical books are off limits for helping to discern the shadows. they are word play and are self-contained and do not depend on the works of men. This keeps me devoted to the word of God. (I use a Hebrew dictionary because I am not fluent in Hebrew. I suspect this is OK)
Solving riddles
The annoying thing about children's riddles is that there is insufficient information in the riddle to solve it. You must know the answer first. Then apply the answer back into the riddle.
The solution to all the riddles is given to us by Samson:
Samson came across a lion and killed it. When he returned to the carcass, bees had made a hive and produced honey in it. Samson created a riddle in order to confound his enemies. Now remember what we said. A riddle can't be solved unless you know something of the answer already.
So his enemies threatened his wife and she found out the riddle from him and told them.
Judges 14:12 14 And he said unto them, Out of the eater came forth meat, and out of the strong came forth sweetness. 18 And the men of the city said unto him on the seventh day before the sun went down, What is sweeter than honey? and what is stronger than a lion? And he said unto them, If ye had not plowed with my heifer, ye had not found out my riddle.
You can find all kinds of bizarre interpretations for this from the literal-historical school, including that the Philistines must have slept with Delilah.
- Hint 1: What do you plow?
- Hint 2: What is a heifer used for?
You plow the earth, and a heifer is used for sacrifice.
So you turn over or plow the earthly with a sacrifice. Hmm, but the earthly is the literal and Christ is the sacrifice. Let's try again: You turn over the literal using the Christ. There we go.
Christ is the key to unlocking the riddles. We must apply what we know of Christ to the literal, in order to uncover and solve the riddles. It is the birth of Christ that unlocked the riddle of Tamar.
This gives us the simplest rule of all concerning shadows: If the shadow doesn't look like Christ, it is not a shadow of Christ.
An orthodox Christian site says:
"A Biblical Christian is the one who, wherever he looks, on every page of Scripture, finds everywhere Christ."
So let's look at difficult passages:
The story of Uzziah is said to be a problem because he is called Azariah in the second telling of the story. Leprosy is always a picture of sin. Incense is reminiscent of the sweet savor of the burnt offering, which itself commemorates that perfect devotion the Son had toward the Father.
So Uzziah who "did everything according to his Father" (knew no sin), through offering incense (perfect devotion) became leprous (made to be sin) and afterwards is known as Azariah, (the name of the high priest who confronted him) which indicates Christ was made to be high priest.
What looks like an error is actually a perfect picture of Christ.
Now take a look at the three women who were by the well. The first, Rebekah, was chosen by the Father. The second, Rachel, was called or wooed by the son (he kissed her). Now if you are hearing, your soul just leapt at the possibility that the third was gathered by the Spirit. And isn't that exactly what happened when the woman came to Christ at Sychar. But it is hidden in riddle. Sychar means "intoxicated" and is associated with the Spirit through the scene at Pentecost. (and seen also when Hannah prays in the temple). Jesus wasn't looking for a wife, but the Spirit gathered her into the bride. And the well is likely the same well for all three. (There is much more imagery around the well)
This shadow crosses thousands of years and languages and couldn't possibly have been known by the human authors without divine inspiration.
When I first saw the shadows, I saw them the way the rabbi would have if he had looked. First I saw the hints, then compared and contrasted, then saw the hidden meaning. But I have reverse engineered the process so that I can flush out the pictures without first seeing the hints.
- Identify possible double meanings for the words.
- Replace the known shadows.
- Identify the riddle.
- Solve the riddle.
This has allowed me to see Christ in places where he was least expected. The story of Japheth, the Levite with the concubine, and even the parables that we think we know so well. The servant who cooks the books, is the same role as the rich man and the brother of the prodigal, and each a picture of Christ as judge. In the shadows the judge dies indicating the end of judgment and the beginning of grace. Yes, and so Lazarus (or Eliezer in Hebrew) is Christ as priest.
The book of Matthew has sequential parallels that suggest an eschatology that is quite different than popular rapture myths. Job is the conversation between the Father and the Son...You must die, you are the son of man... why won't you hear my defense, I am innocent. Just the opposite of Jesus' conversation with Peter... You can't die, you are the Son of God.
I am no where near having unpacked the whole Bible. But I have seen the shadows in sufficient number and density to be confident that there is nearly a whole second Bible hidden in the double entendre. Had I said that at the start, one might think I was nuts. (and perhaps you do anyway)
However I hope by demonstrating the method and obtaining undocumented shadows of Christ from difficult passages, that at least I have persuaded you to look at the claim and perhaps try the hermeneutic for yourself.
It is a fantastic claim... a marvelously fantastic claim. It should not just be accepted (nor dismissed) but examined closely.
The bigger picture
I first saw isolated pictures of Christ, then narratives, then themes and finally I think I see which persons of the Godhead wrote which parts of the scriptures, and am beginning to see "personality" difference like one might observe between human authors.
So I am most anxious that others can see them for themselves and verify my hypotheses.
Here is my observation. Each person speaks with four voices :
I. Adam and all the Patriarchs tell of Christ (Father's Testimony) The Father speaks primarily of the son. The father chooses a bride for his son.
- a. Noah - Judge (the flood)
- b. Adam to Methuselah - Priest (the sacrifices are central to Adam, Cain and Abel)
- c. Abraham, Isaac, Jacob, Joseph - King (the land is central)
- d. Creation - Prophet (The Son having dominion is central)
II. Israel is called out to be a witness to all men. (Son's testimony, Israel is called God's son) The son speaks primarily of his bride and his suffering. The Son calls his bride and woos her. Israel has four voices as the son:
- a. Priests (heavenly testimony of the heavenly)
- b. Judges (heavenly testimony of the earthly)
- c. Kings (earthly testimony of the earthly)
- d. Prophets. (earthly testimony of the heavenly)
III. The life of Christ (The Spirit's testimony) The Son had emptied himself and was filled with the Spirit. The Son did not testify of himself. The Holy Spirit speak primarily of the Son and his bride becoming one and being fruitful. The Spirit gathers the bride to proclaim "Behold the Lamb of God!" He also speaks with four voices.
- a. Matthew (heavenly testimony of the heavenly)
- b. Mark-Peter (heavenly testimony of the earthly)
- c. Luke (earthly testimony of the earthly)
- d. John (earthly testimony of the heavenly)
IV. The epistles following the cross (Perhaps the testimony of the church)
Christ and his bride are fruitful and multiply. I am sure that the four voices must be here as well, I have not yet unpacked them. Although, the imagery all has the judge and the prophet dying at the cross, so there is a possibility that only the voices of Kings and Priests will be heard in the epistles.
I have tried to show you brief examples of what I am seeing.
I have been called a heretic for seeing Christ in the scriptures. This makes no sense to me.
I have been told that my salvation is in jeopardy. Yet I have drawn closer to God in seeing them, and have more confidence in His word than ever I had.
I have been told that it is dangerous, yet what is more dangerous than not reading the Bible and finding Christ there?
I hope you will take the time to examine my notes carefully and see if the shadows are really there for yourself. If they are invention, my notes are garbage. If they are real, I would think every Christian would want to see the shadows for themselves.
Your friend, Bob
The four voices of God
Each person (Father, Son, and Holy Ghost) speaks with four voices. Not only can we distinguish the person who wrote a passage, but we should be able to hear all four voices.
The basis of this comes from the nature of the number four. It is two two's. Since two is a heavenly and earthly something, two two's doubles this. (We will also see this in the "wheels in wheels" and the two Cherubim each holding a two edged sword.)
- Earthly language with an earthly message - King
- Earthly language with a divine message - Judge
- Heavenly language with an earthly message - Prophet
- Heavenly language with a divine message - Priest
Earthly language with an earthly message
The king uses "horses" or earthly strength as the language. Show of force and the use of force communicate earthly messages. The message of the king relates to possession of the land or the earthly. The Jewish Pashat, or literal interpretation is the story of what happened "on earth" and is the voice of the king.
Moses and the serpent: When Moses backed away from the rod which had become the serpent, he was literally afraid of the serpent.
Earthly language with a divine message
The judge uses force or earthly things to declare God's will concerning a matter. This view exposes the spiritual reality behind the physical happenings. This view may be used to ascertain the reasons people did what they did.
Moses and the serpent: The serpent represent sin, the earth represents earthly, and the rod represents the power of God in discipline. When Moses disciplined the Egyption in an earthly manner (and killed him), he sinned.
Heavenly language with an earthly message
The prophet speaks in a strange language, sometimes living 'dinner theater' to make his point, sometimes using parables to confront sin. Though the language is strange, the content of the message is earthly, concerning earthly happenings.
Moses and the serpent: Now Moses represents Christ on earth. Christ will be disciplined with the power of God and face the temptation in the wilderness. When Moses backs away it shows that the earthly Jesus had a moment of temptation when facing Satan in the desert.
Heavenly language with a divine message
The priest speaks in a strange language using symbols in dress, sacrifices, utensils, temple architecture, etc. The salvific gospel of Christ is always the heart of the priest's message.
Moses and the serpent: Before Christ became incarnate, He had to decide to do so; to empty himself, face temptation, be made to be sin, and to be separated from the Father by death. The voice of the priest tells us that in heaven, Christ initially said "no I won't do it, it is too much to ask." And at this time in Rev 5
- 3 And no man in heaven, nor in earth, neither under the earth, was able to open the book, neither to look thereon.
4 And I wept much, because no man was found worthy to open and to read the book, neither to look thereon. 5 And one of the elders saith unto me, Weep not: behold, the Lion of the tribe of Juda, the Root of David, hath prevailed to open the book, and to loose the seven seals thereof.
He is the worthy son in the parable who first said he wouldn't do it, and then did.
Christ had to face Gethsemane twice. once in heaven and once on earth. The earthly Gethsemane was man-sized. The heavenly Gethsemane was God-sized. He sweat great drops of blood at Gethsemane in the flesh. I cannot imagine his agony, in omniscience and omnipotence when making the choice in heaven.
Hearing God's voices
An individual in history may have served multiple roles. David was a king, a judge (when he slew Goliath), a priest (when he offered sacrifice), and a prophet (when he wrote the Psalms).
Through the voice of the king we can see that Adam and Eve sinned, and their excuses for doing so.
Through the voice of the judge we see the heart conditions of Adam and Eve as they sinned. Adam played lawyer as he reasoned that by eating the fruit "from" Eve, he was not violating the command to not eat "from" the tree. Eve was giving in to the temptation to live instinctively, like animals, rather than by the word of God.
Through the voice of the prophet we see that men will try to justify themselves by the law, and that the temptation to live instinctively, will be what separates man from God throughout history.
Through the voice of the priest we see that mankind will be deceived to follow the flesh, and that Christ will willingly die for his bride, taking her sin upon himself.
God speaks four times in one breath.
Exodus 4
I mentioned Moses and the serpent above. This is not an isolated picture but is part of a continuous narrative in the double entendre. Based on the symbols defined in
Ex 7:1 And the LORD said unto Moses, See, I have made thee a god to Pharaoh: and Aaron thy brother shall be thy prophet.
Moses is God and Aaron is Jesus.
So I took Exodus 4 and replaced Moses with MYLORD just so you can track when it was originally God vs a changed name.
Then I replaced Aaron with Jesus.
I filled in other symbols along the way. Each symbol replacement can be verified by at least two or three 'witnesses' scriptures.
The verses now seem to suggest a conversation between "the Lord and MYLORD" as David hinted and Jesus confirmed (Psalm 2, Matthew 22:41-45).
Text Transformation
(some verses link to commentaries below)
|Original text
|Transformed text
|(Exod 4:1) And Moses answered and said, But, behold, they will not believe me, nor hearken unto my voice: for they will say, The LORD hath not appeared unto thee.
|Exod 4:1 And MYLORD answered and said, But, behold, they will not believe me, nor hearken unto my voice: for they will say, The LORD hath not appeared unto thee.
|(Exod 4:2) And the LORD said unto him, What is that in thine hand? And he said, A rod.
|Exod 4:2 And the LORD said unto him, What is that work? And he said, [the power of God in discipline].
Shadow:Rod::Power of God in discipline
|(Exod 4:3) And he said, Cast it on the ground. And he cast it on the ground, and it became a serpent; and Moses fled from before it.
|Exod 4:3 And he said, [Be incarnate]. And he cast [the power of God] on the [earth], and it became [sin incarnate]; and MYLORD fled from before it.
Shadow:Rod::Power of God in discipline
|(Exod 4:4) And the LORD said unto Moses, Put forth thine hand, and take it by the tail. And he put forth his hand, and caught it, and it became a rod in his hand:
|Exod 4:4 And the LORD said unto MYLORD, do the work, conquer the lying prophet. And he put forth his hand, and [conquered it], and it became [power of God in discipline] in his hand:
Shadow:Tail::Lying prophet
Shadow:Rod::Power of God in discipline
|(Exod 4:5) That they may believe that the LORD God of their fathers, the God of Abraham, the God of Isaac, and the God of Jacob, hath appeared unto thee.
|Exod 4:5 That they may believe that the LORD God of their fathers, the God of Abraham, the God of Isaac, and the God of Jacob, hath appeared unto thee.
|(Exod 4:6) And the LORD said furthermore unto him, Put now thine hand into thy bosom. And he put his hand into his bosom: and when he took it out, behold, his hand was leprous as snow.
|Exod 4:6 And the LORD said furthermore unto him, Put now thine works into thy bosom. And he put his works into his bosom: and when he took it out, behold, his works were made sin.
|(Exod 4:7) And he said, Put thine hand into thy bosom again. And he put his hand into his bosom again; and plucked it out of his bosom, and, behold, it was turned again as his other flesh.
|Exod 4:7 And he said, Put thine works into thy bosom again. And he put his works into his bosom again; and plucked it out of his bosom, and, behold, it was sinless as his other flesh.
|(Exod 4:8) And it shall come to pass, if they will not believe thee, neither hearken to the voice of the first sign, that they will believe the voice of the latter sign.
|Exod 4:8 And it shall come to pass, if they will not believe thee, neither hearken to [Jesus] of the first sign [he who knew no sin became sin], that they will believe [Jesus] of the latter sign [that he conquered sin].
|(Exod 4:9) And it shall come to pass, if they will not believe also these two signs, neither hearken unto thy voice, that thou shalt take of the water of the river, and pour it upon the dry land: and the water which thou takest out of the river shall become blood upon the dry land.
|Exod 4:9 And it shall come to pass, if they will not believe also these two signs, neither hearken [Jesus], that thou shalt take of the [Word], and shed it on the dry land: and the [Word] which thou takest out of the river shall become [life] upon the dry land.
|(Exod 4:10) And Moses said unto the LORD, O my Lord, I am not eloquent, neither heretofore, nor since thou hast spoken unto thy servant: but I am slow of speech, and of a slow tongue.
|Exod 4:10 And MYLORD said unto the LORD, O my Lord, I am not eloquent, neither heretofore, nor since thou hast spoken unto thy servant: but my Torah:word, and my Torah:works have been ineffective.
|(Exod 4:11) And the LORD said unto him, Who hath made man's mouth? or who maketh the dumb, or deaf, or the seeing, or the blind? have not I the LORD?
|Exod 4:11 And the LORD said unto him, Who hath made man's mouth? or who maketh the dumb, or deaf, or the seeing, or the blind? have not I the LORD?
|(Exod 4:12) Now therefore go, and I will be with thy mouth, and teach thee what thou shalt say.
|Exod 4:12 Now therefore go, and I will be with [Jesus], and teach thee what thou shalt say.
|(Exod 4:13) And he said, O my Lord, send, I pray thee, by the hand of him whom thou wilt send.
|Exod 4:13 And he said, O my Lord, send, I pray thee, by the hand of him whom thou wilt send.
|(Exod 4:14) And the anger of the LORD was kindled against Moses, and he said, Is not Aaron the Levite thy brother? I know that he can speak well. And also, behold, he cometh forth to meet thee: and when he seeth thee, he will be glad in his heart.
|Exod 4:14 And the anger of the LORD was kindled against MYLORD, and he said, Is not -Jesus- the [priest] thy brother? I know that he [is the Word]. And also, behold, he cometh forth to meet thee: and when he seeth thee, he will be glad in his heart."
|(Exod 4:15) And thou shalt speak unto him, and put words in his mouth: and I will be with thy mouth, and with his mouth, and will teach you what ye shall do.
|Exod 4:15 And thou shalt speak unto him, and put words in his mouth: and I will be with [Jesus], and with his mouth, and will teach you what ye shall do. Mouth is reminiscent of Word:Jesus
|(Exod 4:16) And he shall be thy spokesman unto the people: and he shall be, even he shall be to thee instead of a mouth, and thou shalt be to him instead of God.
|Exod 4:16 And he shall be thy spokesman unto the people: and he[Jesus] shall be, even he shall be to thee [Living Word], and thou shalt be to him instead of God.
|Mouth is reminiscent of Word:Jesus
|(Exod 4:17) And thou shalt take this rod in thine hand, wherewith thou shalt do signs.
|Exod 4:17 And thou shalt take this [the power of God in discipline] in thine hand, wherewith thou shalt do signs.
Shadow:Rod::Power of God in discipline
|(Exod 4:18) And Moses went and returned to Jethro his father in law, and said unto him, Let me go, I pray thee, and return unto my brethren which are in Egypt, and see whether they be yet alive. And Jethro said to Moses, Go in peace.
|Exod 4:18 And MYLORD went and returned to [the Father], and said unto him, Let me go, I pray thee, and return unto my brethren which are in [the world], and see whether they be yet alive. And [the Father] said to MYLORD, Go in peace.
|(Exod 4:19) And the LORD said unto Moses in Midian, Go, return into Egypt: for all the men are dead which sought thy life.
|Exod 4:19 And the LORD said unto MYLORD in Midian, Go, return into [the world]: for all the men are [dead in sin] which sought thy [new] life [zoe].
|(Exod 4:20) And Moses took his wife and his sons, and set them upon an ass, and he returned to the land of Egypt: and Moses took the rod of God in his hand.
|Exod 4:20 And MYLORD took [Israel and his church], and [entrusted them to his prophets], and he returned to the [earth]: and MYLORD took the [power] of God in his works.
Shadow:First wife::Israel
Shadow:Rod::Power of God in discipline
|(Exod 4:21) And the LORD said unto Moses, When thou goest to return into Egypt, see that thou do all those wonders before Pharaoh, which I have put in thine hand: but I will harden his heart, that he shall not let the people go.
|Exod 4:21 And the LORD said unto MYLORD, When thou goest to return into [the world], see that thou do all those wonders before [Lucifer], which I have put in thine hand: but I will harden his heart, that he shall not let the people go.
|(Exod 4:22) And thou shalt say unto Pharaoh, Thus saith the LORD, Israel is my son, even my firstborn:
|Exod 4:22 And thou shalt say unto [Lucifer], Thus saith the LORD, Israel is my son, even my firstborn:
|(Exod 4:23) And I say unto thee, Let my son go, that he may serve me: and if thou refuse to let him go, behold, I will slay thy son, even thy firstborn.
|Exod 4:23 And I say unto thee, Let my son go, that he may serve me: and if thou refuse to let him go, behold, I will slay thy son, even [all of your followers].
|(Exod 4:24) And it came to pass by the way in the inn, that the LORD met him, and sought to kill him.
|Exod 4:24 And it came to pass by the way in the inn, that the LORD met him [Jesus], and [killed] him.
|(Exod 4:25) Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast it at his feet, and said, Surely a bloody husband art thou to me.
|Exod 4:25 Then [Israel] took [the word of God], and [remembered the promise made to Abraham], and [prayed], and said, Surely a husband [of life] art thou to me.
Shadow:First wife::Israel
|(Exod 4:26) So he let him go: then she said, A bloody husband thou art, because of the circumcision.
|Exod 4:26 So he [rose from the dead]: then she said, A husband [of life] thou art, because of the [remembered promise].
|(Exod 4:27) And the LORD said to Aaron, Go into the wilderness to meet Moses. And he went, and met him in the mount of God, and kissed him.
|Exod 4:27 And the LORD said to -Jesus-, Go into the wilderness to meet MYLORD. And he went, and met him in the mount of God, and –burned or sacrificed-.
|(Exod 4:28) And Moses told Aaron all the words of the LORD who had sent him, and all the signs which he had commanded him.
|Exod 4:28 And MYLORD told -Jesus- all the words of the LORD who had sent him, and all the signs which he had commanded him.
|(Exod 4:29) And Moses and Aaron went and gathered together all the elders of the children of Israel:
|Exod 4:29 And MYLORD and -Jesus- went and gathered together all the elders of the children of Israel:
|(Exod 4:30) And Aaron spake all the words which the LORD had spoken unto Moses, and did the signs in the sight of the people.
|Exod 4:30 And -Jesus- spake all the words which the LORD had spoken unto MYLORD, and did the signs in the sight of the people.
|(Exod 4:31) And the people believed: and when they heard that the LORD had visited the children of Israel, and that he had looked upon their affliction, then they bowed their heads and worshipped.
|Exod 4:31] And the people believed: and when they heard that the LORD had visited the children of Israel, and that he had looked upon their affliction, then they bowed their heads and worshipped.
Exod 4:1
David suggested that God has conversations "within himself":
- Ps 110:1 A Psalm of David. The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.
- Mt 22:44 The LORD said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool?
- Lu 20:42 And David himself saith in the book of Psalms, The LORD said unto my Lord, Sit thou on my right hand,
- Ac 2:34 For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand,
Exod 4:2
"The power of God in discipline" is speaking about the cross. Judgment has been given to Christ.
- Joh 5:27 And hath given him authority to execute judgment also, because he is the Son of man.
Exod 4:3
cast it on the ground
The 'power of God in discipline' might be said to be the power to execute judgement. Christ was given all authority to judge. This is a shadow of Christ becoming incarnate.
he fled
- Rev 5:3 And no man in heaven, nor in earth, neither under the earth, was able to open the book, neither to look thereon.
Christ in heaven faced a deity-sized temptation to avoid the cross. The idea of being made sin was so repulsive that initially he said he would not do it. For some interval in eternity, all creation holds it's breath as Rev 5:3 records that there is no one worthy. Jesus also tells the parable of the two brothers:
- Matt 21:28 ¶ But what think ye? A certain man had two sons; and he came to the first, and said, Son, go work to day in my vineyard.
- 29 He answered and said, I will not: but afterward he repented, and went.
- 30 And he came to the second, and said likewise. And he answered and said, I go, sir: and went not.
- 31 Whether of them twain did the will of his father? They say unto him, The first. Jesus saith unto them, Verily I say unto you, That the publicans and the harlots go into the kingdom of God before you.
Jesus can relate to the harlots and the publicans because he himself did not wish to do the Father's will. He faced Gethsemane experiences both in heaven and on earth where he put aside his own will in order to obey the Father.
The book of Hebrews makes the point repeatedly that Israel did not receive grace through the law or through the temple sacrifices. They received a promise of grace only.
Had the days of Christ's tribulation not been shortened, and he had been beaten to death in prison, no flesh would have been saved (Mark 13:20).
So until Christ said "It is finished" there was but a promise of grace.
The cross was not just a symbol of grace having been bestowed from the beginning, it is what made grace effectual. He really suffered to make it effectual, he was really tempted to not face the cross. He really had to put his own will away to do the will of the Father. These were not play acting, but real trials for Christ.
So although God planned for it from the beginning, there was a time, as recorded in Rev 5, when no one was found in heaven, on earth or under the earth to open the seal, until Jesus in the flesh, died to self at Gethsemane, then the Lion overcame and was found to be worthy.
He was made perfect and learned obedience through the things he suffered (Hebrews 5:8, 13:12; 1 Peter 5:10).
Exod 4:9
Christ's life blood poured out upon the dry earth from the cross (water and blood from the spear wound). And His body was buried in the land, from which it was raised with new life (zoe life) which could never die again. This is the life that His children inherit abundantly (John 10:10).
Exod 4:10
God speaks to all men, not just Israel, through His Word (Torah:word) and brought all creation into existence (Torah:works), but this is speech not clearly seen and personally identifying God (Psalm 19; Romans 1:18-32; Hebrews 1:1-3), when compared to the revelation of Jesus Christ (Torah:life).
All revelation of God, short of Christ's incarnation are the stutterings and slow speech compared to Christ, the Word.
see Pattern:Torah
Exod 4:12
Jesus is the living Word of God (John 1:1-3, 14) and the exact character of His divine substance (hypostasis; see Hebrews 1:3).
Exod 4:14
See Matt 21:28-31 In this parable, is it possible that Jesus is speaking of his own, very real, temptation to avoid the cross? At first he said, No.", then did it?
Exod 4:17
This rod split the rock.
Exod 4:19
Death is physical and death is spiritual, which accounts for the double entendre of "men are dead." In the Greek NT life is of two types, which are carefully separated. One type of life is bios and is merely physical and temporary. The other type of life is zoe and is transcendent and eternal, the type of life God has and wants to give through Christ.
Exod 4:25
Zipporah is the first wife of Moses; hence she is the earthly wife. But the Church is the second wife, the heavenly wife.
Zipporah "prayed" is derived from the picture of her cutting the flesh from her son and literally "touching Moses feet" with it. With Moses as MYLORD, the picture can be viewed as a position of submission and prayer. The first wife is asking that her sons (Israelites) be included in God's covenant with humankind, in remebrance of God's covenant with Abraham.
See Dwg:Bunch of women.jpg and remember the story of Leah and Rachel. The first wife was chosen for the son by the workings of the father, the second wife was called by the son himself. The first wife is in a 'threatened' position and is imploring him for security based upon the covenant.
Exod 4:26
In the shadows, when someone is threatened with death and then does not die, it is a death and resurrection image.
Exod 4:27
Jesus gives the best sacrifice (burning::kissing by Hebrew root word association) which is obedience. Aaron's kissing Moses is a picture of Jesus' obedient sacrifice to His Father.
There are three narratives that are related: Israel wanted to go to the wilderness to sacrifice, Aaron kissed Moses, ans Jesus was tempted by Satan. Each of these happened in the wilderness and are related stories. Since 'kiss' means 'burn' which is related to sacrificing, with the simple shadow substitution is is easy to see that Aaron::Jesus sacrificed to Moses::God with the kiss::burn. Furthermore, the burnt offering is a symbol of Christ's total devotion to the father. The priest have no part of the sacrifice and can only observe in awe. There is also no hint of sin in the burnt offering and as such represents his devoted life.
The first two instances we now see as people going to the wilderness to sacrifice to God. But in the third, Jesus met Satan. How can this possibly be the same picture? When we realize that "to obey is better than sacrifice" we see that Jesus' obedience in the face of temptation by Satan was a "better sacrifice" as mentioned in Hebrews.
When we seek holiness by putting off the flesh, even Satan becomes our friend since he gives us opportunity to practice it, and we can face his temptations and persecutions with joy as though we were receiving the very blessings of God.
Orthodox Wiki
I hope there is a place I can share here and submit these observations for discussion. Interpretation must come from the larger body. I will only post on the personal page until I have some sort of approval and guidance to start articles concerning these. Thanks.


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Natural log transformation in growth ...
Mplus Discussion
Growth Modeling of Longitudinal Data
posted on Friday, February 24, 2006 - 12:42 pm
I am interested in accounting for variance in the growth of two variables usnig Mplus. These variables are modeled using a simultaneous growth model. The model fits poorly using the raw data (properly investigating different types of growth). That data is positively skewed, and a natural log transformed data fit a "linear" growth model (I recognize that this is no longer linear after the transformation).
Could someone share their thoughts about the appropriateness of using natural log transformed data, like Willett and Bub(2004, to account for variance in the latent variables? Thanks in advance!
posted on Saturday, February 25, 2006 - 9:03 am
I would recommend against transforming the data if the only reason is to make the variables more normally distributed. Instead, all you have to do is to use a non-normality robust estimator such as the Mplus estimators MLM and MLR.
I would only transform if that made the modeling more transparent, e.g. making the variable scores easier to understand and making the relationships more linear.
posted on Tuesday, February 28, 2006 - 8:14 am
Thank you very much for your help Dr. Muthen. I was able to complete the analyses. I've found the resources that your team provides for Mplus very helpful while learning to use the program.
The output is very interpretable, but I have one final question that I hope that you can help me with.
I recognize the the means found in the "Intercepts" section of the output differs from the means found in Tech4 output.
How do I test whether the latent variable means are significant in conditional models?
The reason I ask is because the means are significant in the unconditional analyses in the "Means" section. These means are almost identical to the means presented in the Tech4 output for the unconditional model. However, the slope for one of the growth factors is not significant in the "Intercepts" section for the conditional parallel model. I'm pretty sure that doesn't mean that the slope is not significantly different than 0, but I'd like to test whether the slope is significantly different than 0 in the unconditional simultaneous model. Sorry for the basic questions, but I greatly appreciate your help. Please feel free to refer me to the user's guide if necessary (I searched but couldn't find the information). Sorry for the basic questions.
posted on Tuesday, February 28, 2006 - 8:47 am
I made a mistake in the previous message. The third to last sentence should read "I'm pretty sure that (the "Intercepts" information) doesn't mean that the slope is not significantly different than 0, but I'd like to test whether the slope is significantly different than 0 in the *conditional* simultaneous model."
posted on Tuesday, February 28, 2006 - 4:19 pm
Consider for example the slope growth factor s regressed on a covariate cov,
(1) s = a + b* cov,
where a is the intercept and b is the slope in this regression. The mean of s is
(2) mean(s) = a + b*mean(cov).
The Mplus intercept parameter a is therefore not the mean of s unless you have centered cov so that it has zero sample mean, but you can get the mean of s in Tech4 as you said. You can test if the mean of s is significantly different from zero very conveniently in the new Mplus Version 4 by defining a parameter "mean(s)" expressed as in (2) using Model Constraint.
Kurt Beron
posted on Saturday, March 10, 2007 - 4:01 pm
I'm trying to implement your Feb 28 test suggestion of the mean (rather than intercept) of a LCM. I've tried several approaches with no success. A snippet:
tsocint tsocslp |
psocint psocslp |
tsocint on aframer (p1)
higrtin (p2)
married (p3);
[tsocint] (p4);
model constraint:
! The following takes the means after the fact
! meantbint=p4+(p1*.212)+(p2*.355)+(p3*.657);
! Here I refer to the variables directly after defining on Variable Constraints line, with no success
! meantbint=p4+(p1*aframer)+(p2*higrtin)+(p3*married) ;
model test:
! And here are various failed tests
! meantbint=p4+(p1*.212)+(p2*.355)+(p3*.657);
! 0=p4+(p1*aframer)+(p2*higrtin)+(p3*married) ;
The best so far is one extra parameter that puts an actual constraint in rather than testing the mean. Thanks.
Linda K. Muthen
posted on Sunday, March 11, 2007 - 6:56 am
It's difficult to say where you are going wrong without more information. Another way to test the mean is the run the model without covariates. If you just want the value of the model estimated mean, you can ask for TECH4 in the OUTPUT command. Otherwise, please send your input, data, output, and license number to
Anjali Gupta
posted on Saturday, October 17, 2009 - 4:02 pm
Am I correct that a transformation of log(x) in the DEFINE area is that of a natural log?
Thank you.
Linda K. Muthen
posted on Saturday, October 17, 2009 - 4:56 pm
Amber Fahey
posted on Monday, February 19, 2018 - 12:19 pm
is it permissible to log transform covariates so they are normal, then run a conditional analyses including these transformed covariates?
Bengt O. Muthen
posted on Monday, February 19, 2018 - 4:35 pm
I don't think the goal of the transformation of the covariates should be to make them normal - the model has no such assumption. Instead, you may transform them if that makes the assumption of linearity in the regression more realistic. With a log transform you would be saying that increasing x at a high level of x doesn't produce as much change in y and at a low level of x.
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Kevin Durant was playing in L.A.'s Drew League this past weekend, the renowned pro-am summer league that features professional, collegiate, and amateur players from around the country. For us, there's twofold joy to this self-assisted alley-oop Durant threw down on a breakaway for team Go HAM: One component is simply in seeing an NBA player do something remarkable again, since it's been all of two weeks since we last had that privilege. The other is seeing him do it in a tiny, no-name gym where there's no JumboTron for instant replay, and no commercial break for a timeout, and where the fans can slap a player on his back as he turns to get back on defense.
There's a lockout ahead, and no Vegas summer league to pretend to care about, and we are getting through the final bouts of PTSD now that the season's actually over. But this is the kind of play we'd never get to see Durant pull off in the NBA, anyway. This is a dunk for the Drew League, and that's what makes it so great.
H/T Eye on Basketball.


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This week, Louisa Shafia is serving as a Guest Editor at Food52. She chose a Wildcard winner, answered your questions on the Hotline, and is continuing to share recipes from her new book, The New Persian Kitchen -- because your kitchen deserves a taste of the exotic every once in a while.
Discovering Persian ingredients is a bit like lifting the lid off a treasure box: the dazzling sight of pink rose petals and green cardamom is surpassed only by the heady scent and delicate flavor of red saffron and golden turmeric. Here are five key ingredients in Persian cooking that give this cuisine its unmistakable taste. If you don't happen to live near an Iranian grocery store, you can find these ingredients online at different outlets including kalamala.com, sadaf.com, and shahrzad.com.
Dried Limes, limoo omani
These small, dried limes have an intense lime flavor. Like regular limes, they're simultaneously bitter and sweet, yet they are far more intense because of the combination of the juice and the rind. Dried limes are thrown whole into soups and stews. Unlike whole spices like bay leaves or cinnamon sticks that you would discard after cooking, you can cut up the softened limes and eat them—rind and all—along with the dish.
Green Herbs, sabzi
Fresh and dried green herbs play many roles in Persian food, from flavor component to main ingredient. There is even a whole meal devoted entirely to them at Norooz, the Persian New Year, which falls on the spring equinox in March. The herbs most commonly used in Persian cooking are dill, mint, parsley, cilantro, basil, chives, fenugreek, and tarragon, while marjoram and oregano make occasional appearances. There's no stigma against using dried herbs, in fact, dried spearmint and dried dill weed are de rigeur in a Persian kitchen.
More: Just a couple drops of rose water perfumes a pistachio meringue stack.
Rose Water and Rose Petals, golab and barg-e gol
Think of rose water as the Iranian equivalent of vanilla extract. You'll encounter its flavor in baklava, rice pudding, cookies, and ice cream. The taste of rose water can be off-putting at first—we're not used to such flowery flavors in the West—but it can really grow on you. Rose petals lend a surprisingly savory flavor to rice, and they make a graceful garnish for yogurt and salads. In The New Persian Kitchen, I use them in a baked egg frittata and with rice.
Saffron, zafaran
Saffron is used everywhere in Persian cooking, flavoring entrées, desserts, and rice with its unmistakable scent. Saffron is infamous for its high price, but fortunately, a little goes a long way. It takes only a teaspoon or less to flavor a whole dish. To prepare saffron for Persian recipes, grind it in a mortar and pestle or spice grinder, then steep it in a little hot water for about half an hour before adding it to whatever you're cooking.
More: Adding a sprinkling of sumac to an heirloom tomato and mango lassi boosts the mango flavor.
Sumac, somagh
I think of sumac as "Persian MSG." It's salty and lemony, and is a wonderful ingredient for setting off other flavors. It's one of the many ingredients used in Persian cooking to give food a tart flavor, along with pomegranate molasses, rhubarb, barberries, dried limes, and sour cherries. It can be used anywhere you would lemon juice. I use it as a meat tenderizer, as a garnish for my watermelon and cucumber salad, and to jazz up a ho-hum bowl of lentil soup.
Now that you know what ingredients you'll need, try Louisa's favorite recipes:Lamb Kebabs in Pomegrante Walnut MarinadeSweet Rice with Carrots and NutsSweet and Smoky Beet BurgersVinegar Carrots with Toasted Sesame Seeds
See what other Food52 readers are saying.


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