Fun With Stats: Macronutrients vs. Calories (Preliminary)

See the first post in this topic for appropriate background.

After 7 days of painstaking weighing and recording of all my food intake, along with macronutrient breakdown of those foods, I have collected enough data to start building some preliminary models.  Of course, 7 days is not enough to definitively conclude anything, but I thought I’d share what I have found so far.

My starting weight was 213.8 lbs, and my current weight is 206.0 pounds.  That amounts to almost 8 lbs lost the first week – no doubt this is primarily due to glycogen and water weight lost, but presumably a couple/few of those pounds were fat.  Unfortunately, some of that weight loss was probably muscle, although I have been doing daily, light resistance training on my Weider weight machine – I always do this near the end of my fasting window, usually around 15-16 hours without eating.  My rationale is that insulin levels are low and growth hormone is high, which aids in muscle preservation.

This is my dataset so far:

CurrentDataSet_June24

As you can see, the initial quick drawdown of weight has slowed, and I have been at 206lbs for a couple days.  Also note I have taken efforts to vary my macronutrient percentages a great deal – the past few days, I ate high carbohydrate percentages despite being hypocaloric (even the 2152 calorie day was probably hypocaloric, given my weight).

Base Model (Only Macronutrient Percentages)

Below is R-Studio output (the statistics package I’m using) for a linear statistical model I’ve built which compares the daily percentage of weight loss to the percent of fat, carbohydrates, and protein.

Model_MacronutrientPercentages

In this output, there are a few t hings to note:

  1.  Notice the Pr(>|t|) column values under the Coefficients sections.  Fat=.331, Carbohydrate=.331, and Protein=.325.  All of these are quite a lot higher than 0.05, which indicates they are not significant contributors to the model
  2. Adjusted R-squared is 0.6031.  This is higher than expected, but this is explained by the fact that percent of weight lost is usually very low.  A value closer to 1 indicates that the outcome variable (percent of weight lost) is explained by the input variables (percent fat, percent carb, percent protein)
  3. Overall P-Value for the model is 0.1408.  To feel confident in the model, we would be looking for a value less than 0.05.
  4. Overall, this is probably not a very good model

Altered Model (Macronutrient Percentages With Calories)

Next, let us consider the same model, but add caloric intake to the list of explanatory variables:

Model_MacronutrientPercentages_WithCalories

There are a few things to note here:

  1.  The overall p-value and r-squared value for this altered model indicate a better model than macronutrient percentages alone
  2. The p-value is still greater than 0.05, suggesting the model is not statistically significant, with confidence of 95%.
  3. The best variable is the log(totalcal); however it is still 0.117, well above the 0.05 threshhold
    *Note:  I transformed the totalcal variable to take the logarithm of it.  This is a common statistical technique used when one variable has a very wide scale, or when it is quite a lot larger than other variables

Calories-only model

Given that total calories has so far been a better predictor of percentage of weight loss, how good is it by itself?  Here are the results:

Model_OnlyCalories

As you can see from above, the p-value of this model is 0.2729 – the worst performing model of the 3.  Adjusted R-squared is 0.07924 – again, worse than the other two models.  So far, the calories-only model is worse than calories plus macronutrients.

Preliminary Thoughts

So far, the best model to predict percent weight change is total calories AND macronutrient percentages.  I’m still very early into this process, and linear modeling might not be the best solution.  Rather, the best solution might be logistic regression, analyzing whether weight was lost on a given day given food intake.  Even still, a person can eat perfectly for days in a row, and not lose any weight – that’s just the nature of weight loss.  So ultimately, I don’t know what later models will look like, or what variables or techniques will be best for my personal results.

Below is a plot of my weight loss given caloric intake.  As you can see, I can both lose weight and remain the same, despite a wide range of caloric intake.  I have yet to gain weight on a given day.

WeightChange_CaloricIntake

Lessons learned

I’ve noticed that a lot of high carb eating also involves high fat eating.  I suspect this is a problem, both from a biological perspective (the interplay between fat and carbohydrates during the metabolic process), and also from a calorie perspective – it is very easy to overeat when eating some of these things – for example, I ate a piece of toffee-cream pie yesterday, which was nearly 700 calories, half of which was fat.  When eating a low-carb/high fat diet, it is difficult to get 700 calories at once.

I also have not eaten many vegetables during this process.  This would have been helpful, at least from a hunger perspective, during my high carb days.  (Select) Vegetables also are a great tool in low-carb eating.

Next Steps

I just went 3 days on a high carbohydrate diet.  I plan to spend the next 3 days on a low carbohydrate diet.  A few things I have not done yet:

  1. Eaten hypercaloric (overeat)
  2. Skip time restricted feeding
  3. Eaten very high protein

 

Upcoming Statistical Analysis: Macronutrients, Calories, and Weight Loss

I’ve been on-and-off low carbohydrate dieting for a few years now.  My personal problem is lack of discipline.  The trend goes like this:  I realize I’ve put on more weight than I meant to, I get serious about eating better, I cut excess sugar, alcohol, and useless carbohydrates from my diet, I drop some weight, apathy sets in, I get bored following a rigid diet, repeat.

My rationale for following a low carbohydrate diet is quite simple, despite its multi-step formula:

  1.  Eating triggers the pancreas to release insulin in varying amounts depending on the macronutrient (sugar=high, fat=low, protein=sustained medium).
    carbs-fats-protein
  2. Insulin delivers the broken down components of food (glucose, fatty acids, etc) to our cells to use for energy and storage
  3.  Excess eating triggers excess insulin
  4. Over time, muscle cells become resistant to insulin delivery, which leads to higher levels of insulin in the blood, along with higher levels of glucose in the blood.  This eventually leads to metabolic syndrome, and for many, type 2 diabetes
  5. High levels of insulin causes muscle cells to prioritize glucose uptake, rather than fat metabolism.
    • High insulin encourages free fatty acids to be stored in fat cells.
    • High insulin discourages stored fatty acids (triglycerides) from being broken down and released from fat cells
    • This creates an environment where stored fat tends not to be used for energy, which leads to fat accumulation
  6. Limiting the initial secretion of insulin prevents this fat accumulation in fat cells
    • This can be done by caloric restriction
    • Theoretically, it could also be done by eating foods that are less insulinogenic (insulin secreting)

Over the past few months, I have become receptive to the idea of time-restricted feeding (also sometimes referred to as intermittent fasting).  One problem overweight people can face is that their base insulin levels tend to be higher than non-overweight people.  It can literally be the case that an overweight person’s fasting insulin level is higher than a thin person’s post-eating insulin level!

Screenshot_20190621-123500_Drive.jpg
*Source:  Twenty-Four-Hour Profiles and Pulsatile Patterns of Insulin Secretion in Normal and Obese Subjects; Polonsky, Given, and Cauter

One strategy I recently tried was to use time restricted feeding (a daily routine of going 16-20 hours without eating – eating within a 4-8 hour window) without limiting carbohydrates.  This did not work very well, and I found myself stagnating in weight loss while I was doing it.  When I combined low carbohydrate eating with intermittent fasting, weight loss resumed.  One thing I do not know is whether my caloric intake was high when I did this (I suspect it was).

As I mentioned above, I tend to lose momentum in my weight loss efforts, and then gain the weight back.  So, I thought I would add some extra incentive for myself by adding an extra layer of intrigue to the process.

One of the things I have wondered for a long time is how caloric intake relates to this weight loss process, versus macronutrient composition.  For example, if I eat 2500 calories comprised mostly of fat (say, at least 65% fat), will that affect weight loss (or gain) differently than if those 2500 calories came mostly from carbohydrates?

Different camps of researchers have different opinions about this, but the majority of researchers (at least from what I can tell) advocate a calories-in-calories-out model, rather than assuming the above insulin model implies one can increase their fat proportion of their diet to lose wight.

My gut instinct, based on research from Kevin Hall (source 1), is that the differences in weight change will be negligible, regardless of macronutrient composition (given consistent caloric intake/deficit) – one article Hall authored even suggested fat restriction is more effective than carbohydrate restriction; I suspect the reason low carb diets tend to be more successful than other diets has to do with satiety – high fat diets lead people to be less hungry.  It also seems to be the case that it is much easier to overeat high carbohydrate food than it is to eat high fat food.  However, Hall has also stated that protein metabolism is different enough from carbohydrate and fat that people can eat more protein calories than the other macronutrients.

I have to admit, I am drawn to the idea that we can alter macronutrient composition and be able to eat more than we otherwise would in a high carbohydrate diet.

My plan is to build statistical models to answer the following questions:

  1.  Is caloric intake predictive of daily weight change?
  2. Does macronutrient composition data improve the models I create?
  3. Is macronutrient composition a better predictor of weight change than caloric intake? (especially when caloric intake is high)
  4. Is there anything surprising from the (to-be-created) models?

This process will require tedious calorie counting, food weighing, and abstinence from eating foods that I don’t know enough about.  I’ve been collecting data for 5 days, and the data I have is shown below.  Once I have more data, I can begin building statistical models.  The trouble is my current data tells me very little right now, as my low carb+time restricted feeding has led me to lose weight every day so far.  Clearly my basal metabolic rate is more than 1800-2000 calories per day…at least when time restricting and limiting carbohydrates.

Weight_Loss_Data

My goal is to collect many different days with varying caloric intake, time restricted feeding, and macronutrient composition.  As the dataset grows, the model will be more reliable…at least for my own body chemistry.

Fun With Stats: Dwindling Christianity

Religiosity is declining in America. In 1948, the first year Gallup began tracking America’s religiosity, 91% of Americans identified as either Protestant or Catholic. In 2018, the total percentage of Christian Americans, which now tracks denominations beyond Protestant and Catholic,was 67%.

Much of this rapid decline occurred after 2000. In 2000, 80% of Americans identified as Christian. Since then, Christian affiliation has fallen by a whopping 16%. In that same time, Americans who identify as having no religious affiliation have increased from 8% to 20%.

Below is a graph showing this decline. The steepest decline has been among Protestants. Catholic numbers have fallen too, but not as impressively as Protestants. The remaining non-Catholic Christianities have actually increased in numbers since 2000.

AllChristianities_Graph

I built statistical models using Gallup data from 2000-2018. I omitted inclusion of pre-2000 data because it seems intuitively less predictive of future patterns than post-2000 data. Though Christianity’s numbers were falling before the turn of the century, the rate of decline increased after 2000.

I used these models to predict future growth or decline of Christianity.

The fields below show a range, which represents a 95% confidence interval, of anticipated Christian affiliation in the coming decades.

Table_Decreasing_Christianity

My models, which all used Caret-machine learning linear models in the statistics package R, anticipate a roughly 1% decrease in association in all Christianities per year. If these models hold, America will have fewer than 50% Christians between 2040 and 2050. If recent trends hold, American Protestantism may be entirely gone by then. These models also show those Americans with no denominational affiliation will represent about 40% of Americans by 2050, doubling its current number.

Interestingly, these models also predict alternative Christianities will increase during this time, and Catholicism will only trend slightly down.

Of course, there is a chance trajectory slows during this time, rendering these estimates entirely incorrect. But I was unable to find a realistic model which anticipated this, given the steep drop since 2000.

Below are predictions in graphical format from now until 2050.

Predictions_Graph_2050

The New Testament Through The Lens of Proverbs 1-9

Many of the themes found throughout the New Testament can be spotted in the Book of Proverbs, particularly Proverbs 1-9.

For example, consider a passage in Proverbs 2:

My son, if you accept my words and store up my commands within you,turning your ear to wisdom and applying your heart to understanding and if you look for it as for silver and search for it as for hidden treasure, then you will understand the fear of the Lord and find the knowledge of God.

Consider how this passage would have read to someone who had in his mind the story of Judas betraying Jesus for a pocketful of silver.

This correlation between the New Testament and Proverbs is not an accident.

When you read the former part of Proverbs, you’ll notice much attention to knowledge or Wisdom. For example, Proverbs 1:22 poses the questions “How long will mockers delight in mockery and fools hate knowledge?” Proverbs 1 continues its lament “…since they hated knowledge and did not choose to fear the Lord. Since they would not accept my advice and spurned my rebuke,they will eat the fruit of their ways”. This fruit rings like the (absence of) fruit Jesus complained about on his way to the temple in Mark 11, when he cursed the fig tree. A popular theological interpretation of the fig tree cursing is that the fig tree represented the Jewish temple, which no longer produced religious fruit, and therefore needed to be destroyed.

Next consider a passage from Proverbs 2:

Wisdom will save you also from the adulterous woman, from the wayward woman with her seductive words, who has left the partner of her youth…

The adulterous woman is a ringer for the woman who rode in on the dragon in Revelation 17:3, who was “sitting on a scarlet beast that was covered with blasphemous names and had seven heads and ten horns”. Therefore, the partner of this adulterous woman’s youth might either be the dragon or the beast to whom the dragon rendered his power in Revelation 13.

Consider this passage from Proverbs 5, another reminder of the adulterous woman:

For the lips of the adulterous woman drip honey, and her speech is smoother than oil;but in the end she is bitter as gall, sharp as a double-edged sword.

In the end, the lady was bitter as gall, the same gall Jesus refused on the cross the first time. But also recall that Jesus accepts the gall the second time. In my opinion, early Christians would have read this as evidence that the Christ Spirit had left Jesus – the Spirit-less man who was rendered a simple Jew who served his purposes, but was rendered empty like the fig tree; the Spirit would live on (to the early Gnostic group, the Basilideans) in the cross-bearer, Simon of Cyrene. Interestingly, the double edged sword shows up in various Christian literature, notably in Revelation 19, when the heavenly warrior who battled the beast, had a tongue as a double edged sword.

In Revelation, the adulterous woman, the Whore of Babylon, had rode in on the dragon which had earlier displaced the lady from Revelation 12. In the aftermath of the dragon (and beast) assuming power, we see a reference to wisdom in Revelation 13:18: “This calls for wisdom. Let the person who has insight calculate the number of the beast…” In other words, the antidote to the control that the beast had was access to Wisdom. Proverbs 7 gives an instruction:

Say to wisdom, “You are my sister,” and to insight, “You are my relative.” They will keep you from the adulterous woman, from the wayward woman with her seductive words.

Revelation 12:17 gives a familial relation between the woman and the keepers, which would have been Nasar in Hebrew. However, in Revelation, the crowned sun lady was the mother.

Wisdom in Revelation 13:18 becomes a pointer to the woman clothed in the sun from Revelation 12. This happens via Proverbs 4:

She will give you a garland to grace your head and present you with a glorious crown.”

This notion from Proverbs 4 is echoed in the Book of Jesus ben Sirach: “you [the high priest] will wear her like a glorious robe, and put her on like a crown of gladness” (6:31). The her to whom Ben Sirach referred to was Wisdom (6:18).
This woman in Proverbs is a queen, and like the star-crowned lady in Revelation 12, is able to present a crown to the next King.

Proverbs 3 gives us more insight into who this woman, Wisdom, is: “She is a tree of life to those who take hold of her; those who hold her fast will be blessed.” Without delving too deeply into the details here, I remind the reader that the story of the 2 trees in Eden was likely a bastardization of an earlier story, constructed to redefine the tree of life as Mosaic law, rather than its earlier meaning, which I believe was a reference to the fashioned poles, known as Asherah poles, which legend has it were present during 1st temple times, prior to Josiah’s Deuteronomic reforms; this is found notably in 2 Kings 23:4: “The king ordered Hilkiah the high priest, the priests next in rank and the doorkeepers to remove from the temple of the Lord all the articles made for Baal and Asherah and all the starry hosts. He burned them outside Jerusalem”.

ea392-asherahpole

The Gnostics seemed to remember the earlier tree story in On the Origin of the World, when Eve escapes the clutches of the creators of the material world (the archons), and goes to live in the tree of knowledge.

Then Eve, being a force, laughed at their decision. She put mist into their eyes and secretly left her likeness with Adam. She entered the tree of knowledge and remained there. And they pursued her, and she revealed to them that she had gone into the tree and become a tree. Then, entering a great state of fear, the blind creatures fled.

In this theory, the dual nature of the lady, who simultaneously represented the tree of life and Wisdom of God, was split and repurposed in the Orthodox Eden-Tree story. Eve is simply a reworking of an earlier Wisdom Queen.

The Proverbs’ writer’s memory had this lady present from the very beginning:

By wisdom the Lord laid the earth’s foundations,by understanding he set the heavens in place; by his knowledge the watery depths were divided, and the clouds let drop the dew.

This is reminiscent of the rethinking of the creation story in the Gospel of John, which injects the Word into the creation (In the beginning was the Word, and the Word was with God and the Word was God). The flip side of this coin in the Gnostic story is in various Gnostic creation stories, which had Sophia (Wisdom) acting as the proxy between God, the archons, and the creation of the material realm. Proverbs 8 continues on this creation theme, recalling something significantly different than what is in Genesis: “The Lord brought me forth as the first of his works, before his deeds of old; I was formed long ages ago, at the very beginning, when the world came to be.”

The last example I present is from Proverbs 9: “Wisdom has built her house; she has set up its seven pillars.She has prepared her meat and mixed her wine; she has also set her table.” But what is Wisdom’s house? We need only consider the context through which Wisdom was cast out of the holy land: it was when Josiah purged her from the 1st temple. Text in the so-called Apocalypse of Weeks in 1 Enoch 93 remembers this purge:

…in the sixth week, all who live in the temple shall be blinded. And the hearts of all of them shalll godlessly forsake Wisdom…in the seventh week, shall an apostate generation arise…

Therefore, the adulterous woman which Proverbs and Revelation remembers is simply a reference to the 2nd temple, which housed this “apostate generation”.  Revelation 21 makes reference to the Christian end-game, which would usher in a new Holy land (something which would have been absent after Jews and Christians were expelled from Jerusalem in the 130s):

I saw the Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband. And I heard a loud voice from the throne saying, “Look! God’s dwelling place is now among the people, and he will dwell with them.

This impulse to call Jerusalem a woman is found throughout Jewish literature. One interesting story is in 2 Esdras 9-10, where Ezra encounters a grieving woman with ashes on her head, lamenting the death of her son in the bridal chamber. Ezra becomes upset with the grieving woman, who planned not to return to the city: “Zion the mother of us all is afflicted in sadness and utterly dejected.” The lady responded “I will not, and I will not go into the city, but I will die here.” The interaction ends with the lady converting the field she was in into the holy city: “Suddenly her face shone brightly…Without warning she let out a noise, a great voice full of fear, so that the earth itself shook…she no longer appeared to me as a woman, but there was a city built, and a place with great foundations appeared”.

The angel Uriel interpreted this interaction for the protagonist Ezra:

This woman whom you saw is Zion, whom you now see built as a city…As for what she said to you, that she was infertile for thirty years, it is because there were three thousand years in the world when offerings weren’t yet made in her. After three thousand years, Solomon built the city and made offerings. That is when the infertile woman bore a son…her son came into his wedding chamber and died and that misfortune happened to her, this is the destruction that happened to Jerusalem.

The decoder key provided by 2 Esdras is quite useful in deciphering Revelation, and other early Christian keywords. The field is the place where the New Jerusalem shall be. The lady is the mother of the temple, and by extension, the people who worship there. The son is the temple. The bridal chamber is where the death of the son occurs. One consideration is that the bridal chamber is the heart of the temple, otherwise known as the Holy of Holies; indeed, the Holy of Holies was where the high priest would go once per year, and become a conduit between Earth and God. The Holy of Holies was separated by a veil – that same veil which tore while Jesus died on the cross.

The lady, the New Jerusalem, mixed wine in her house. Jeremiah (44:19) provides a potential reference to this, via Egyptian refugees who had been forced forced from Jerusalem following the Babylonian invasion:

“Moreover,” said the women, “when we burned incense to the queen of heaven and poured out drink offerings to her, was it without our husbands’ knowledge that we made sacrificial cakes in her image and poured out drink offerings to her?”

The Gospel of John remembers a tradition that made reference to the mother and the son, which featured wine. In this story (John 2), the servants were out of wine. The mother told Jesus they were out of wine, and Jesus wondered why she shared this with him. At that point, Jesus’s mother renders authority to her son, which prompts Jesus to convert water to wine and subsequently begins his messianic career.

The Nasarene Delivery

A curious aspects of the Mandaeans, a small Mesopotamian religious sect which reveres John the Baptist, who it juxtaposes against Jesus the Nazarene, is that they call themselves Nasurai.

Found within their religious texts are pointers to Christian traditions. For example, the Mandaean Book of John re-tells the story of Jesus’s baptism by John. The Mandaean version remembers what is presumably the earliest version of the story, where the Dove descends on Jesus during the baptism ritual, implanting him with the Holy Spirit.

Although this adoptionistic formula is preserved in the modern canon, the Christology of it deviates from Orthodoxy. Jesus’s real claim to fame, according to modern dogma, is not that he was Joe Nobody before baptism, special enough to receive this mysterious Spirit. Rather, Jesus was predetermined to be the messiah, implanted in Mary by God.

We can track the evolution from Holy Spirit adoptionism to virgin birth via the various beliefs of scattered Valentinian sects, particularly in Italy, who believed Jesus was born from Mary as through a pipe, never physically touching her. This rings as a subsequent evolution from the Eastern Valentinian traditions, who believed that the Christ entered Jesus’ psychic body at the time of baptism.

For the Mandaeans, this Holy Spirit was the Earthly malevolent Spirit Ruha. Thus we have a rethinking, but significant relevance for what adoptionism means in the Mandaean system. The general idea, which given its popularity and dispersion must have been the original one, is that Spirits live in people, animals, buildings, and land. This idea originated in Judaism, particularly as Apocalyptic literature became more popular.

In the Gospels, Jesus suceeds John. We can infer that Jesus attracted John’s followers after he was delivered up to Herod. We see evidence of some contention between the John and Jesus sects in Mark 2:18-20. In particular, the contention seems to surround who is the bridegroom – John or Jesus.

Now John’s disciples and the Pharisees were fasting. Some people came and asked Jesus, “How is it that John’s disciples and the disciples of the Pharisees are fasting, but yours are not?”
Jesus answered, “How can the guests of the bridegroom fast while he is with them? They cannot, so long as they have him with them. 20 But the time will come when the bridegroom will be taken from them, and on that day they will fast.

The term delivered (παρεδόθη) caught my eye this morning. Paul uses a version of it in 1 Cor 11:23 (παρεδίδετο). The term Paul uses is usually mistranslated as betrayed (“on the night he was betrayed, Jesus took bread…”). The term is often translated to handed over or delivered, rather than betrayed.

Versions of the term are used throughout the New Testament, but one place I recently noticed its use was in Matthew 4:12. Interestingly enough, this term is not used in the earlier Gospel, Mark, with regard to John. Given Matthew’s closer proximity to Judaism than Mark, I wonder if Matthew remembers something Mark omits by making reference to this term with regards to John.

If that is the case, we might consider reasons why Matthew’s Gospel diverges from Mark, and the motivation behind it. Matthew, even the prototype versions we might presume existed before embellishments about the virgin birth, family lineage, ministry, and resurrection, has a very different idea about Jesus than Mark does. As I have stated in previous posts, and various scholars have detailed from time to time, Mark is a Gospel which canonized Paul.

When we factor in the Mandaean parallels, specifically that they are an extension of the Nasarenes, as well as espousing a similar adoptionism which mirrors the earlier Christian theology, it seems the Christian canon is a bastardization of earlier Nasarene traditions which placed emphasis on this delivery. In other words, the true prophet is handed over to the authorities.

In previous posts, I have argued that John and Jesus are fictional representations of real history described by Josephus. John is Theudas and Jesus is the Egyptian.

In Josephus’s history, the Egyptian causes a riot after claiming he could knock down the temple walls; he escapes, and was never heard from again. A Roman commander mistakes Paul for the Egyptian in Acts 21:38.

Theudas was not so lucky. The Judean procurator sent a band of soldiers to collect his head after he ministered around the Jordan River and performed water rituals of some sort. These events occurred 15 to 25 years after the Gospel timeline.

We are told by Clement of Alexandria that Paul and Theudas had a student/teacher relationship. This is of course problematic for the timeline we get from Josephus; however, if we invert the relationship, we find that Theudas being a teacher of Paul is much more plausible. Clement goes on to write that Theudas was a teacher of Valentinus, who held a high position in the 2nd century Christian “church.”

Given the contention between subsequent Mandaean and Christian traditions, I wonder if this relationship between Paul, Theudas, and Valentinus represents the rift within the Nasarene religion which gave rise to the subsequent divergences within Christianity. If we follow these speculations, we have one tradition where the prophet is handed over, and another where he escapes – tricking the rulers who are pursuing him. Both tropes spring up in subsequent flavors of Christianity, particularly in Gnosticism.