Bias vs Variance

Part Of: Machine Learning sequence
Followup To: Regression vs Classification
Content Summary: 800 words, 8 min read

A Taxonomy of Models

Last time, we discussed how to create prediction machines. For example, given an animal’s height and weight, we might build a prediction machine to guess what kind of animal it is. While this sounds complicated, in this case prediction machines are simple region-color maps, like these:

Partitioning- Comparing Classification Outputs

These two classification models are both fairly accurate, but differ in their complexity. 

But it’s important to acknowledge the possibility of erroneous-simple and erroneous-complex models. I like to think of models in terms of an accuracy-complexity quadrant.

BiasVariance_ Classification Quadrant (1)

This quadrant is not limited to classification. Regression models can also vary in their accuracy, and their complexity.

BiasVariance_ Both Quadrants (1)

A couple brief caveats before we proceed.

  • This quadrant concept is best understood as a two-dimensional continuum, rather than a four-category space. More on this later.
  • Here “accuracy” tries to capture lay intuitions about prediction quality & performance. I’m not using it in the metric sense of “alternative to F1 score”.

Formalizing Complexity

Neural networks are often used as classification models against large numbers of images. The complexity of the models tends to correlate with the number of layers. For some models then, complexity is captured in the number of parameters.

While not used much in the industry, polynomial models are pedagogically useful examples of regression models. Here, the degree of the polynomial expresses the complexity of the model: a degree-eight polynomial has more “bumps” than a degree-two polynomial.

Consider, however, the difference between the following regression models

y_A = 4x^4 + 0.0001x^3 + 0.0007x^2 + 2.1x + 7
y_B = 4x^4 + 2.1x + 7

Model A uses five parameters; Model B uses three. But their predictions are, for all practical purposes, identical. Thus, the size of each parameter is also relevant to the question of complexity.

The above approaches rely on the model’s parameters (its “visceral organs”) to define complexity. But it is also possible to rely on the model’s outputs (its “behaviors”) to achieve the same task. Consider again the classification decision boundaries above. We can simply measure the spatial frequency (the “squiggliness” of the boundary) as another proxy towards complexity.

Here, then, are three possible criteria for complexity:

  1. Number of parameters
  2. Size of parameters
  3. Spatial frequency of decision manifold

Thus, operationalizing the definition of “complexity” is surprisingly challenging. But there is another way to detect whether a model is too complex…

Simplicity as Generalizability

Recall our distinction between training and prediction:


We compute model performance on historical data. We can contrast this with model performance again future data. 

BiasVariance_ Operationalizing the Quadrant (2)

Take a moment to digest this image. What is it telling you?

Model complexity is not merely aesthetically ugly. Rather, complexity is the enemy of generalization. Want to future-proof your model? Simplicity might help!

Underfitting vs Overfitting

There is another way of interpreting this tradeoff, that emphasizes the continuity of model complexity. Starting from a very simple model, increases in model complexity will improve both historical and future error. The best response to underfitting is increasing the expressivity of your model.

But at a certain point, your model will become too complex, and begin to overfit the data. At that point, your historical error will continue to decrease, but your future error will increase.

BiasVariance_ Complexity vs Accuracy Graph

Data Partitioning: creating a Holdout Set

So you now appreciate the importance of striking a balance between accuracy and simplicity. That’s all very nice conceptually, but how might you go about building a well-balanced prediction machine?

The bias trade-off is only apparent when the machine is given new data!  “If only I had practiced against unseen test data earlier”, the statistician might say, “then I could have discovered how complex to make my model before it was too late”.

Read the above regret again. It is the germinating seed of a truly enormous idea.

Many decades ago, some creative mind took the above regret and sought to reform it: “What stops me from treating some of my old, pre-processed data as if it were new? Can I not hide data from myself?”


This approach, known as data partitioning, is now ubiquitous in the machine learning community.  Historical-Known data is the training set, Historical-Novel data is the test set, aka the holdout set.

How much data should we put in the holdout set? While the correct answer ultimately derives from the particular application domain, a typical rule of thumb:

  • On small data (~100 thousand records), data are typically split to 80% train, 20% test
  • On large data (~10 billion records), data are typically split to 95% train, 5% test

Next time, we will explore cross-validation (CV). Cross-validation is sometimes used instead of, and other times in addition to, data partitioning.

See you then!


Why are humans ecologically dominant?

Part Of: Demystifying Culture sequence
Content Summary: 1100 words, 11 min read

Ecological Dominance

Compared to the erects, sapiens are uniquely ecologically dominant. The emergence of hunter-gatherers out of Africa 70,000 years ago caused:

  • The extermination of hundreds of megafauna species (more than 90%)
  • Dwarfing of the surviving species.
  • A huge increase in the frequency and impact of fire (we used fire to reshape ecosystems to our liking)

12,000 years ago, we began domesticating animals and plants. The subsequent agricultural revolution unlocked powerful new ways to acquire energy, which in turn increased our species’ population density.

  • 9000 BCE:   5 million people
  •          1 CE:   300 million people
  •   2100 CE:   11,000 million people

200 years ago, the industrial revolution was heralded by the discovery of energy transduction: that electricity can be used to run a vacuum, or freeze meat products.

These population explosion correlates with a hefty ecological footprint:

  • We have altered more than one-third of the earth’s land surface.
  • We have changed the flow of two-thirds of the earth’s rivers.
  • We use 100 times more biomass than any large species that has ever lived.
  • If you include our vast herds of domesticated animals, we account for more than 98% of terrestrial vertebrate biomass.

Ecological Dominance_ Vertebrate Biomass

Three Kinds of Theories

As with any other species, the scientist must explain how ours has affected the ecosystem. We can do this by examining how our anatomies and psychologies differ from other animals, and then consider which of these human universals explain our ecological dominance.

Pound for pound, other primates are approximately twice as strong. We also lack the anatomical weaponry of our cousins; for example, our canines are much less dangerous.

So, strength cannot explain our dominance. Three other candidate theories tend to recur:

  1. We are more intelligent and creative. Theories of this sort focus on e.g., the invention of Mode 3 stone tools.
  2. We are more cooperative and prosocial. Theories of this sort focus on e.g., massively cooperative hunting expeditions.
  3. We accumulate powerful cultural adaptations. Theories of this sort focus on e.g., how Inuit technology became uniquely adaptive for their environment.

Let’s take a closer look!

Intelligence-Based Theories

Is intellect the secret for our success? Consider the following theories:

First, generative linguists like Noam Chomsky argue that language is not about communication: recursion is an entirely different means of cognition; the root of our species’ creativity. To him, the language instinct (as a genetic package) appeared abruptly at 70 kya, and transformed the mind from a kluge of instincts to a mathematical, general-purpose processor. Language evolution is said to coincide with the explosion of technology called behavioral modernity.

Second, evolutionary psychologists like Leda Cosmides & John Tooby advocate the massive modularity hypothesis: the mind isn’t general purpose processor; it is instead more like a swiss army knife. We are not more intelligent because we have fewer instincts, but more. Specifically, we accrued hundreds of hunter-gatherer instincts in the intervening millenia and these instincts give us our characteristically human flexibility.

Third, social anthropologists like David Lewis-Williams argues that a change in consciousness made us more intelligent. We are the only species that has animistic spirituality, these are caused by numinous experiences. These altered states of consciousness were the byproducts of our consciousness machinery rearranging itself. Specifically, he invokes Dehaene’s theory that while all mammals experience primary consciousness, only sapiens have second-order consciousness (awareness of their own awareness). This was allegedly the event that caused fully modern language.

Sociality-Based Theories

Is sociality the secret for our success? Consider the following theories:

First, sociobiologists like Edward O Wilson thinks that the secret of our success is because of group selection: that vigorous between-group warfare created selective pressure for within-group cooperation. As our ethnic psychology (and specifically, ethnocentrism) became more pronounced, sapien tribes began behaving much like superorganisms. A useful analogy is eusocial insects like ants, who became are arguably even more ecologically dominant than humans.

Second, historians like Yuval Harari thinks that mythology (fictional orders) is the key ingredient enabling humans to act cooperatively. Political and economic phenomena don’t happen in a vacuum: they are caused by certain ideological commitments e.g., nationalism and the value of a currency. To change our myths is to refactor the social structure of our society.

Culture-Based Theories

Is culture the secret for our success? Consider the following theory:

Anthropologists like Richerson, Boyd and Henrich argue that cumulative cultural knowledge comprises a dual-inheritance system, and propose a theory of gene-culture coevolution. They are that an expanding collective mind gave individuals access to unparalleled know-how. This is turn emboldened our niche stealing proclivities: “like the spiders, hominins could trap, snare, or jet their prey; but the latter could also ambush, excavate, expose, entice, corral, hook, spear, preserve, or contain a steadily enlarging range of food types.” Socially-learned norms induce our cooperation, and socially-learned thinking tools explain our intelligence.

My Take

Contra Chomsky,

Contra Cosmides & Tooby:

  • I agree wholeheartedly with the massive modularity hypothesis. It accords well with modern cognitive neuroscience.
  • While selection endowed us with hunter-gatherer instincts (e.g., folk biology), I don’t think such instincts provide sufficient explanatory power.

Contra David Lewis-WIlliams:

  • I need hard evidence showing that animals never hallucinate, before appropriating numinous experiences as a human universal.
  • Global Workspace Theory (GWT) enjoys better empirical support than integrated information theory.
  • I don’t understand the selective pressure or mechanistic implications for changes to our conscious machinery.

Contra sociality-first theories

  • Group selection is still immersed in controversy, especially the free-rider problem.
  • Why must myths be the causal first movers? Surely other factors matter more..

My own thinking most closely aligns with culture-based explanations of our ecological dominance. This sequence will try to explicate this culture-first view.

But at present, culture-first theories leaves several questions unanswered:

  • What, specifically, is the behavioral and biological signature of a social norm? For now, appeals to norm psychology risk explaining too much.
  • How did our species (and our species alone) become psychologically equipped to generate cumulative culture?
  • If erectus was a cultural creature, why did the rate of technological innovation so dramatically change between erectus and sapiens?

Someday I hope to explore these questions too. Until then.


  1. Tim Flannery. The Future Eaters
  2. David Lewis-Williams. The Mind in The Cave.
  3. Yuval Harari. Sapiens.
  4. Henrich, The Secret of Our Success

The Evolution of Faith

Part Of: Demystifying Culture sequence
Content Summary: 1200 words, 12 min read


Recall that human beings have two different vehicles for learning:

  • Individual Learning: using personal experiences to refine behavioral techniques, and build causal models of how the world works.
  • Social Learning: using social interactions to learn what other people have learned.

Today, we will try to explain the following observations:

  • Most cultural traditions have adaptive value.
  • This value typically cannot be articulated by practitioners.

Why should this be the case?

Example 1: Manioc Detoxification

Consider an example of food preparation, provided by Joseph Henrich:

In the Colombian Amazon, a starchy tuber called manioc has lots of nutritional value, but also releases hydrogen cyanide when consumed. If eaten unprocessed, manioc can cause chronic cyanide poisoning. Because it emerges only gradually after years of consuming manioc that tastes fine, chronic poisoning is particularly insidious, and has been linked to neurological problems, paralysis of the legs, thyroid problems, and immune suppression.

Indigenous Tukanoans use a multistep, multiday processing technique that involves scraping, grating, and finally washing the roots in order to separate the fiber, starch, and liquid. Once separated, the liquid is boiled into a beverage, but the fiber and starch must then sit for two more days, when they can then be baked and eaten. Chemical analyses confirm that each major step in the processing is necessary to remove cyanogenic content from the root. [5]

Yet consider the point of view of a woman learning such techniques. She may never have seen anyone get cyanide poisoning, because the techniques work. And she would be required to spend about four hours per day detoxifying manioc. [4]

Consider what might result if a self-reliant Tukanoan mother decided to drop seemingly unnecessary steps from the processing of her bitter manioc. She might critically examine the procedure handed down to her from earlier generations and conclude that the goal of the procedure is to remove the bitter taste. She would quickly find that with the much less labor-intensive process of boiling, she could remove the bitter taste. Only decades later her family would begin to develop the symptoms of chronic cyanide poisoning.

Here, the willingness of the mother to take on faith received cultural practices is the only thing preventing the early death of her family. Individual learning does not pay here; after all, it can take decades for the effects of the poison to manifest. Manioc processing is causally opaque.

The detoxification of dozens of other food products (corn, nardoo, etc) are similarly inscrutable. In fact, history is littered with examples of European explorers imperfectly copying indigenous food processing techniques, and meeting gruesome ends.

Example 2: Pregnancy Taboos

Another example, again from Henrich:

During pregnancy and breastfeeding, women on Fiji adhere to a series of food taboos that selectively excise the most toxic marine species from their diet. These large marine species, which include moray eels, barracuda, sharks, rock cod, and several large species of grouper, contribute substantially to the diet in these communities; but all are known in the medical literature to be associated with ciguatera poisoning.

This set of taboos represents a cultural adaptation that selectively targets the most toxic species in women’s usual diets, just when mothers and their offspring are most susceptible. [2] To explore how this cultural adaptation emerged, we studied both how women acquire these taboos and what kind of causal understandings they possess. Fijian women use cues of age, knowledge, and prestige to figure out from whom to learn their taboos. [3] Such selectivity alone is capable of generating an adaptive repertoire over generations, without anyone understanding anything.

We also looked for a shared underlying mental model of why one would not eat these marine species during pregnancy or breastfeeding: a causal model or set of reasoned principles. Unlike the highly consistent answers on what not to eat and when, women’s responses to our why questions were all over the map. Many women simply said they did not know and clearly thought it was an odd question. Others said it was “custom.” Some did suggest that the consumption of some of the species might result in harmful effects to the fetus, but what precisely would happen to the fetus varied greatly: many women explained that babies would be born with rough skin if sharks were eaten and smelly joints if morrays were eaten.  

These answers are blatant rationalizations: “since I’m being asked for a reason, let me try to think one up now”.  The rationale for a taboo is not perceived by its adherents. This is yet another example of competence without comprehension.

A Theory of Overimitation

Human beings exhibit overimitation: a willingness to adopt complex practices even if many individual steps are inscrutable. Overimitation requires faith, defined here as a willingness to accept information in the absence of (or even contrasting with) your personal causal model.

We have replicated this phenomenon in the laboratory. First, present a puzzle box to a child, equipped with several switches, levers, and pulleys. Then have an adult teach the child how to open the box and get the treat inside. If the “solution” involves several useless procedures e.g., tapping the box with a stick three times, humans will imitate the entire procedure. In contrast, chimpanzees ignore the noise, and zoom in on the causally efficacious steps.

Why should chimpanzees outperform humans in this experiment? Chimpanzees don’t share our penchant for mimicry. Chimpanzees are not gullible by default. They must try to parse the relevant factors using the gray matter between their ears.

Humans fare poorly in such tests, because these opaque practices are in fact useless. But more often in our prehistory, inscrutable practices are nevertheless valuable. We are born to go with the flow.

In a species with cumulative culture, and only in such a species, faith in one’s cultural inheritance often yields greater survival and reproduction.

Is Culture Adaptive? Mostly.

We humans do not spend much time inspecting the content of our cultural inheritance. We blindly copy it. How then can cultural practices be adaptive?

For the same reason that natural selection produces increasingly sophisticated body plans. Communities with effective cultural practices outcompete their neighbors.

Overimitation serves to bind cultural practices together into holistic traditions. This makes another analogy to natural selection apt:

  • Genes don’t die, genomes die. Natural selection transmits an error signal for an entire genetic package.
  • Memes don’t die, traditions die. Cultural selection transmits an error signal for an entire cultural package.

Just as genomes can host individual parasitic elements (e.g., transposons), so too cultural traditions can contain maladaptive practices (e.g., dangerous bodily modifications). As long as the entire cultural tradition is adaptive, dangerous ideas can persist undetected in a particular culture.

Does Reason Matter? Yes.

So far, this post has been descriptive. It tries to explain why sapiens are prone to overimitation, and why faith is an adaptation.

Yet individual learning matters. Without it, culture would replicate but not improve. Reason is the fuel of innovation. We pay attention to intelligent, innovative people because of another cultural adaptation: prestige.

Perhaps the powers of the lone intellect are less stupendous than you were brought up to believe.

But we need not be slaves to neither our cultural nor our genetic inheritance. We can do better.

Related Resources

  1. Henrich (2016). The Secret Of Our Success.
  2. Henrich & Henrich (2010). The evolution of cultural adaptations: Fijian food taboos protect against dangerous marine toxins
  3. Henrich & Broesch (2011). On the nature of cultural transmission networks: evidence from Fijian villages for adaptive learning biases
  4. Dufour (1984). The time and energy expenditure of indigenous women horticulturalists in the northwest Amazon. 
  5. Dufour (1994). Cassave in Amazonia: Lessons in utilization and safety from native peoples. 

[Excerpt] Jesus as Apocalyptic Prophet

Excerpt From: Blog Post
Content Summary: 1800 words, 9 min read

I agree with mainstream scholarship on the historical Jesus (e.g., E.P. Sanders, Geza Vermes, Bart Ehrman, Dale Allison, Paula Fredriksen, et al.) that Jesus was a failed apocalyptic prophet. Such a hypothesis, if true, would be a simple one that would make sense of a wide range of data, including the following twenty:

  1. John the Baptist preached a message of repentance to escape the imminent judgment of the eschaton. Jesus was his baptized disciple, and thus accepted his message — and in fact preached basically the same message.
  2. Jesus’ Son of Man passages are allusions to the son of man figure in Daniel 7:13-14 and Enoch ch 37-71 (both texts were widely discussed in first century Palestine). This figure was an end of the world arbiter of God’s justice, and Jesus kept preaching that he was on his way (e.g., “From now on, you will see the Son of Man sitting at the right hand of Power, and coming on the clouds of heaven.” Matt. 26:64).
  3. The earliest canonical writing: Paul taught of an imminent eschaton, and it mirrors in wording the end-time passages in the synoptics (especially the so-called “Little Apocalypse” in Mark, and the subsequently-written parallels in Matthew and Luke).
  4. Many passages depict Jesus predicting the end within his generation.
    • “The time is fulfilled, and the kingdom of heaven is at hand. Repent and believe the good news” (Mark 1:15)
    • “This generation will not pass away until all these things take place” (Mark 13:30)
    • “You will not finish going through the cities of Israel until the Son of Man comes” (Matthew 10:23)
    • “There are some of those who are standing here who will not taste death until they see the kingdom of God after it has come with power.” (Mark 9:1)
    • “From now on, you shall see the Son of Man coming in the clouds” (Matt 26:64)
  5. A sense of urgency permeates the gospels and the other NT writings. For example:
    • The disciples must hurry to send the message to the cities of Israel before Daniel’s “Son of Man” comes
    • Jesus’ statement that even burying one’s parents has a lower priority
    • Paul telling the Corinthians not to change their current state, since it’s all about to end (e.g., don’t seek marriage, or to leave one’s slave condition, etc., since the end of all things is at hand)
  6. Relatedly, Jesus and Paul taught a radical “interim ethic” (e.g., don’t divorce, radical forgiveness, don’t judge others, love one’s enemies, etc.). This makes sense if they believed that the eschaton would occur within their generation, and that all needed to repent and prepare for its arrival.
  7. Jesus had his disciples leave everything and follow him around. This makes sense if Jesus believed that he and they were to be God’s final messengers before the eschaton.
  8. Jesus gathered twelve disciples, which is the number of the twelve tribes of Israel. He also said they were to sit on twelve thrones and serve as judges of the twelve tribes of Israel. This reflects the common expectation that at the end of days, all twelve tribes would return to the land. The twelve are a symbolic representation of restored Israel.
  9. There is a clear pattern of a successive watering down of Jesus’ prediction of the eschaton within the generation of his disciples, starting with Mark (widely believed among NT scholars to be the first gospel written), and continuing through the rest of the synoptic gospels. By the time we get to John, the last gospel written, the eschatological “kingdom of God” talk is dropped (except for one passage, and it no longer has clear eschatological connotations), along with the end-time predictions, and is replaced with “eternal life” talk. Further, the epistles presuppose that the early church thought Jesus really predicted the end within their lifetimes. Finally, this successive backpedaling continues beyond the NT writings and into those of the apocrypha and the early church leaders, even to the point where some writings attribute an anti-apocalyptic message to Jesus. All of these things make perfect sense if Jesus really did make such a prediction, and the church needed to reinterpret his message in light of the fact that his generation passed away, yet the eschaton never came.
  10. Jesus’ base followers were all considered to represent the “bottom” of society in his day: the poor, sinners, prostitutes, outcasts, tax collectors, lepers, and the demon-possessed. This is perfectly in line with the standard apocalyptic doctrine of the reversal of fortunes when the kingdom of God comes: “the first shall be last, and the last shall be first”.
  11. Jesus performed many exorcisms, which he claimed marked the inbreaking of the kingdom of God on Earth. They were thus signs of the imminent apocalypse. Satan and his minions were being cast out of power, and God’s power was taking its place.
  12. Jesus’ trip to Jerusalem for the Passover Celebration, and his subsequent activities there, are best explained in terms of his apocalyptic message and his perceived role in proclaiming it. Jesus went to the temple during the Passover Festival, and spent many days teaching about his apocalyptic message of the imminent coming kingdom of God. The apocalyptic message included the idea that the temple in Jerusalem would also be destroyed.
  13. Jesus caused a disturbance in the temple itself, which appears to have been a symbolic enactment of his apocalyptic teaching about the temple’s destruction.
  14. Jesus’ betrayal by Judas Iscariot, and Jesus’ subsequent arrest, is best explained in terms of Judas’ betraying to the religious authorities (the Sadducees and the chief priests) Jesus’ teaching (to his inner circle of disciples) that he would be the King of the Jews in the coming Kingdom of God.
  15. Jesus was executed on the charge of political sedition, due to his claim that he was the King of the Jews. His execution was therefore directly related to his apocalyptic message of the imminent coming of the kingdom of God.
  16. The fact that not just all New Testament authors, but the early church as a whole, believed the end would occur in their generation makes perfect sense if Jesus really did make such claims.
  17. The passages that attribute these predictions to Jesus and Paul satisfy the historical criteria of multiple attestation (and forms), embarrassment, earliest strata (Mark, Q, M, L, Paul’s earliest letters, the ancient “Maranatha” creed/hymn) etc., thus strongly indicating that these words go back to the lips of Jesus.
  18. Jesus’ parables: virtually all explicitly or implicitly teach a message about an imminent eschaton.
  19. Jesus’ “inversion” teachings (e.g., “The first shall be last, and the last shall be first”): a common theme among Jewish apocalypticists generally. The general message of apocalypticists is that those who are evil and defy God will not get away with it forever. The just are trampled, and the unjust prosper; thus, this situation needs to be inverted – as it will be when the “Son of Man” from the book of Daniel comes to exact God’s judgment at any moment.
  20. The earliest Christians believed that Jesus’ putative resurrection was (to use Paul’s terminology) the “first fruits” of the general resurrection of the dead at the end of time. This is an agricultural metaphor. When farmers reaped and ate the first fruits of the harvest, they would then reap the full harvest the very next day — the “general” harvest was “imminent”, as it was “inaugurated” with the reaping of the first-fruits. Similarly, the earliest Christians believed that the final judgement and the general resurrection were imminent, given their belief that Jesus’ resurrection was itself the inaugurating event of the general resurrection and the end of all things. Thus, there is a continuity between the beliefs of the early Christians and the beliefs of many Jews of his time: Jesus’ resurrection was fundamentally construed in these eschatological terms

And so, no matter which way you slice it, the “statute of limitations” has run out on Jesus and his apostle’s claim for an imminent end, within a single generation.

It needs to be emphasized that this line of reasoning isn’t controversial among mainstream, middle-of-the-road NT critics. I’m not talking about a view held by the Jesus Seminar, or earlier “radical” form and redaction critics like Norman Perrin. Rather, I’m talking about the kinds of considerations that are largely accepted by moderates who are also committed Christians, such as Dale Allison and John P. Meier. Indeed, conservative scholars of the likes of none other than Ben Witherington and N.T. Wright largely admit this line of reasoning. Why are they still Christians, you ask? I’ll tell you: by giving unnatural, ad hoc explanations of the data. For example,

  1. Meier gets around the problem by arguing that the false prediction passages are inauthentic (i.e., Jesus never said those things; the early church just put those words on the lips of Jesus, and they ended up in the gospels).
  2. Witherington gets around the problem by saying that what Jesus really meant was that the imminent arrival of the eschatological kingdom might be at hand(!)
  3. Wright gets around the problem by adopting the partial preterist line that the imminent end that Jesus predicted really did occur — it’s just that it was all fulfilled with the destruction of Jerusalem.
    1. Oh, really? So are we also to think that since he’s already come again, he’s not coming back? Or perhaps there will be a third coming?
    2. And why does Paul tell various communities very far outside of Israel about the same sorts of predictions of an imminent end that would affect them — one that, like the one Jesus talked about, involved judgement, destruction, and the gathering of all the elect?

Are you convinced by these responses? Me neither. And now you know why nobody outside of orthodox circles buys them, either.

To all of this, I say what should be obvious: you know, deep in your gut (don’t you?) that such responses are unnatural, ad hoc dodges of what we know to be the truth here: Jesus really did predict the end within the lifetime of his disciples, but he was simply wrong.

This isn’t about some remark Jesus said in passing.  It was his central message: “Repent, for the kingdom of heaven is at hand!”

Putting it all together, we get the following argument for Jesus as a failed apocalyptic prophet:

  • Let H1 be the hypothesis that Jesus was a failed apocalyptic prophet of an imminent eschaton.
  • Let H2 be the hypothesis that Jesus is the Son of God of orthodox Christianity.
  • Let D1-D23 be the data sketched above.

Then the argument can be expressed as follows:

  1. H1 is a better explanation of D1-D23 than H2.
  2. If H1 is a better explanation of D1-D23 than H2, then H1 is more probable than H2.
  3. Therefore, H1 is more probable than H2.


[Excerpt] The Sphex Within You

Excerpt From: Keith Stanovitch, Robot’s Rebellion
Content Summary: 400 words, 2 min read

Consider the behavior of the digger wasp, Sphex ichneumoneus.  The female Sphex does a host of amazing things in preparation for her eggs.  

  1. After digging a burrow, she flies off looking for a cricket.
  2. When she finds one, she stings it in a way that paralyzes it but does not kill it.  
  3. She brings it back to the burrow and sets it just outside at the threshold
  4. Then she goes inside to make sure things are safe inside the burrow.  
  5. If they are, she then goes back outside and drags in the paralyzed cricket.  
  6. She then lays her eggs inside the burrow, seals it up, and flies away.  When the eggs hatch, the wasp grubs feed off the paralyzed cricket which has not decayed because it was paralyzed rather than killed.

All of this seems to be a rather complex and impressive performance put on by the Sphex – a real exercise of animal intelligence.  It seems so, that is, until we learn that virtually every step of the wasp’s behavior was choreographed by rigid and inflexible preprogrammed responses to specific stimuli in the Sphex environment.

Consider, for example, the wasp’s pattern of putting the paralyzed cricket on the threshold of the burrow, checking the burrow, and then dragging the cricket inside.  Scientists have uncovered the rigidity of these behaviors by moving the cricket a few inches away from the threshold while the wasp is inside checking the burrow.  When she comes out, the wasp will not now drag the cricket in.  Instead, she will take the cricket to the threshold and go in again to check the burrow.  If the cricket is again moved an inch or so away from the threshold, the Sphex will again not drag the cricket inside, but will once more drag it to the threshold and for the third time go in to inspect the burrow.  Indeed, in one experiment where the investigators persisted, the wasp checked the burrow forty times and still not drag the cricket straight in.  These fixed action patterns dictated a certain sequence of behaviors triggered by a particular set of stimuli, and any deviation from this was not tolerated.

Ethologists often feel unnerved while observing insects and other lower animals: all that bustling activity, but there’s nobody home!

Let’s call this unnerving property sphexishness.  These simple, rigid routines that underpin the complexity of the surface behavior of simple creatures spawns in us a worrying thought:

What makes you sure you’re not sphexish – at least a little bit?

Modern theories of cognition all propose, in one way or another, that in fact we all are a little bit sphexish.  In fact, many of these theories, in emphasizing the pervasiveness of unconscious processing and the rarity and difficulty of analytic processing, are in effect proposing that our default mode of processing is sphexish.

The Exodus of the Levites

Part Of: History sequence
Related To: Yahweh, god of metallurgy
Content Summary: 2200 words, 11 min read


Last time, we explored the following:

  • The Israelite origin story is largely a patriotic fiction.
  • The Israelite people were indigenous Canaanites.
  • The first Israelites worshiped the pantheon of El.
  • The original Yahweh cult was a Shasu religion located in southern Edom
  • Yahweh was first worshiped as a god of metallurgy
  • The founder of Judaism, Moses, was said to be a Midianite
  • Yahweh was introduced to Israel as a second tier deity (a member of El’s family)

But how was Yahwism transmitted to Israel? One obvious explanation involves trade; economic transactions often serve as a vehicle for transmission of religious ideas.

But then there’s the matter of the Exodus narrative. The absence of evidence for such a massive event gravitates against a massive exodus. But it is silent on the question of an exodus on a small scale.

There was no mass exodus. But I will argue there was a mini-exodus of a group of Levite priests from Egypt. The Biblical evidence suggests that Moses was a Midianite, and his encounter with Yahweh occurred in Midian.

Textual Evidence for a Levite Mini-Exodus

The Bible was written by four authors: J, E, P and D. Of these, E, P and D are traced to Levite priestly authors. There exist startling differences across Levite and non-Levite texts.

First, the two oldest texts in the Bible are the Song of the Sea, and the Song of Deborah. The Song of the Sea is a Levite text that does not mention Israel. The Song of Deborah, meanwhile, lists all ten tribes of Israel (Judah and Simeon were a separate community at this time and not part of Israel) but doesn’t mention Levi. Similarly, all twelve tribes are mentioned in the Blessings of Moses, but it is the only tribe associated with the exodus.

Second, only the Levite sources tell the entire story of the plagues and exodus from Egypt.  J, the non-Levite source, doesn’t tell it. If you read J, it jumps from Moses’ saying “Let my people go” in Exodus 5:1f to the people’s already having departed Egypt in Exodus 13:21.

Third, if the Levites brought Yahweh into Israel, they should be keen to describe the relationship between Yahweh and El. And only our Levite sources do this: J presumes the name is Yahweh from the beginning of her document.

Fourth, It is likewise the Levite sources that concentrate on the Tabernacle.  E mentions it a little; P treats it a lot. There is more about the Tabernacle than about anything else in the Torah.  But the non-Levite source J never mentions it at all.

Archaelogical Evidence

Egypt was known to host many Semitic peoples over the years. It is not unthinkable to imagine some small group escaping. The Shasu people were allowed by Mernepteh to bring their herds into Egyptian territory. 

  • Names of the Levites. Hophni, Hur, Phinehas, Merari, Pashhur and above all Moses are Egyptian names. No one else, in all the names mentioned in the Bible, has an Egyptian name. If Egyptian names were invented, why only attribute them to the Levites? Further, the story of Moses’ name suggests the Biblical redactors did not know these names were Egyptian).
  • Cultural derivatives. There are strong parallels between the Levite priests’ description of the Ark and Egyptian barks. Likewise, the Seraphim that occupy the First Temple come from Egypt (the uraeus) IG.151. The serpent on Aaron’s staff mirrors Egyptian mythology. Professor Michael Homan showed that the Tabernacle has architectural parallels with the battle tent of Pharaoh Ramses II.
  • Exodus 24:8 features Moses splashing blood on his followers in a ritual ceremony. This kind of blood covenant was unknown to Canaan, but common in pre-Islamic Arabia.
  • Circumcision. Only texts written by Levites (11/11)  give the requirement to practice circumcision — which was a known practice in Egypt.  So Egyptian cultural influences are present, but only in the Levite texts!

The Levites came into contact with the Shasu cult, and brought Yahwism to Israel

We have seen that Yahweh was first worshiped as a god of metallurgy in Edom.

We have seen evidence that a mini-exodus of the Levites may be historical.

As far as I know, neither advocates of the Levite mini-exodus nor advocates of the Midianite-Kenite hypothesis see an obvious synergy between their theories:

The Levites left Egypt and encountered Yahweh in Midian.

We can see the overlap in these theories in Mount Sinai. Religious thinking in that era strongly associated gods with locations. Mount Sinai (aka Mount Horeb) was the house of Yahweh. This mountain was located in southern Edom, and the Levites regularly traveled to that location to worship him.

We can also see overlap in Moses’ home town. Moses was a Midianite:

Moses is described as having settled down with the Midianite people (the Shasu). His wife Zipporah and two sons were Midianite. What’s more: Moses’ father-in-law Jethro is called a priest. A priest of what god? Well, in Exodus 18:12, Jethro (and not Moses) is portrayed initiating a sacrifice to Yahweh. The Biblical editors seem uncomfortable with this tradition, for they later interjected a confession of faith on Jethro’s lips, which very much mirrors other such confessions. All of this suggests that Moses’ Midianite father-in-law was a priest of Yahweh. In fact, he seems to have spiritual authority over Moses in this passage.

The E source is replete with this kind of claim. We first meet Moses in Midian (no claims of him being born in Egypt, in this document). Moses’ response to Yahweh’s call, “Who am I that I should bring the Israelites out of Egypt?” would be a fair question for a man in Midian. E also claims he cannot go to Egypt because he is “heavy of tongue”. Traditionally interpreted as a speech defect, this phrase only occurs in one other place in the Hebrew Bible, where it means cannot speak the language. Finally, E also claims that the Midianites are direct descendents of Abraham.

While two Levite sources admit Moses’ Midianite connection, P actively tried to hide it. In the P source, has absolutely nothing about his ever being in Midian. Nothing about a Midianite wife, a priest father-in-law, nothing about his sons. Two books later, the P source injects a (blood-curdling) story designed to vilify the Midianites. Moses himself gives the order to kill all of the Midianite women. And this source does not include the little fact that Moses has a wife who happens to be a Midianite woman. The fact that the P source tries to deny the Midianite connection suggests the underlying claim is historical.

It is difficult to reverse-engineer the role of Moses

Three hypotheses seem possible:

  1. Levites in Egypt, Moses in Midian. The Levites were enslaved Egyptians, who fled to the East, and fell under the influence of Moses, a Midianite Yahwist.
    • Pro: Moses not speaking Egyptian language.
    • Con: Hard to explain why Moses has an Egyptian name.
  2. Levites in Egypt, Moses in Egypt. The “people” were enslaved in Egypt, and fled to the East, where their leader Moses converted to Yahwism.
    • Pro: Moses has an Egyptian name
    • Con: Hard to explain why Moses didn’t speak the Egyptian language.
  3. Levites in Egypt, Moses in transit.
    • Pro: explains both Moses’ Egyptian and Midianite stories.
    • Con: Hard to explain why a Midianite would come to Egypt.

Of these hypotheses, the first seems most plausible to me. By the criterion of embarrassment, the evidence of Moses’ Midianite heritage strikes me as more persuasive than his alleged exploits in Egypt.

However, there seems to be inadequate evidence to fully resolve this question. Fortunately, the Levite-Kenite connection can survive this ambiguity. The key point is, once the Levites left Egypt, came into contact with the Shasu cult, and brought Yahwism to Israel.

The Levites “attached” themselves as priestly class

The Levites claim responsibility for the massacres in Genesis 34, Exodus 32:26-29, and Numbers 25:6-15 and Jacob’s blessing “Levi’s knives are vicious weapons. May I never enter their council. For in their anger they kill men, and on a whim they hamstring oxen. Their anger is cursed, for it is strong,and their fury, for it is cruel!” While the bloody purges specified in the conquest narrative are non-historical, they too speak towards the bloody zeal of the Levite people. All of this is to say: when they did arrive in Israel asking for refuge, they were not a people the Israelites could easily say no to.

In the book of Exodus, there are myriad references to “the people” and very few (retro-fitted) references to the Israelites. It is very plausible that “the people” referred exclusively to militant Levites. Deut 33:2-5 seems to support this distinction: “his people assembled with the tribes of Israel”.

On arrival, the Levites are not given territory. Instead, they are given a 10% tithe as priests. This fits into William Propp’s commentary on Exodus, which makes a strong case on the etymology of the very word “Levi” that its most probable meaning is an “attached person” in the sense of resident alien.

Over and over, the Levite sources command that one must not mistreat an alien. Why? “Because we were aliens in Egypt”. In the three Levite sources, the command to treat aliens fairly comes up 52 time! And how many times in the non-Levite source, J? None. Compared to legal texts of surrounding nations, this aspect is unique to the Israelite law code.

The Levites wrote the national history.

Those who accept that a mass exodus is non-historical still need to explain how the story of the Exodus made it into the Bible. But we are not being asked to explain how it was invented whole-cloth. Rather, we must explain why and how memory of the mini-exodus became stretched and aggrandized over time.

Why did the Levites invent the mass-exodus narrative?

  1. Promoting worship of Yahweh. The Levites were convinced that Yahweh had saved them from Egypt. What better way to have Israel worship Yahweh, than create a new history?
  2. Simple power politics. Political influence is easier to hold & retain if your group is the only “outsider”.
  3. Political unification. Iron age Israel was theocratic. The priests and kings shared (and sometimes competed for) power. A common origin story is a powerful tool for unification and shared identity. Similarly, the demonization on lowland city states (cultural & ethic siblings) as “Canaanite” served to support campaigns against them.

How did they accomplish this? By the production and dissemination of an origin story.  

While we are investigating the historicity of the Biblical narrative, we should also consider: why do these texts exist at all? The Hebrew Bible is humanity’s first attempt at prose, and of history. This intermingling of religion and history was unique to the ancient world. Instead of cyclic episodes of mythological combat, the Israelite religious imagination was fixated on events of their material past. Its structure is entirely unique, and cries out for an explanation. The Bible was written to create a written tradition (much more stable than oral traditions) of national identity.

In addition to violence, the Levites also had a reputation for teaching. We can see this in verses like Deuteronomy 6:20-23:

When your children ask you later on, “What are these laws that Yahweh commanded you?” you must say to them, “We were Pharaoh’s slaves in Egypt, but the Lord brought us out of Egypt in a powerful way. And he brought signs and great, devastating wonders on Egypt, on Pharaoh, and on his whole family before our very eyes. He delivered us from there so that he could give us the land he had promised our ancestors.

What specifically did the Levites fabricate?

They started with their own experience (an actual event), and added the following:

First, to make a mini-exodus massive, you need large numbers. You can actually “watch” the estimates grow as we move from earlier to later sources. J doesn’t mention numbers at all. E estimates a total of around 600,000, and P estimates of total of 600,000 fighting-age males (for a total of two million).

Second, the Exodus, without the conquest, would never have survived as a story. You need to explain how a nomadic nation came to reside in someone else’s territory. The conquest does this (and also stokes political sentiment of a later time period).

Why did the Israelites believe this story?

Don’t we all evaluate our personal origin stories with a bit too much credulity? Many Romans literally believed a wolf raised their patriarchs. Even in American culture, many people I’ve spoken with conceive of the Founding Fathers in mythic, rather than human, terms.

But why didn’t the first recipients of the mass exodus story reject it? Imagine the Levites waited ten or twenty generations before telling the story, and the mini-exodus narrative expansion happened only gradually. Israelites would only have distant inklings of the remembered past to go on. It is true that, for the exodus story to take root in early Israel it was necessary for it to pertain to the remembered past of settlers who did not emigrate from Egypt. And this is in fact the case. Egypt did control and oppress Canaan, during the mini-Exodus.