Deep Homology: our shared genetic toolkit

Part Of: Biology sequence
Content Summary: 1400 words, 14 min read.

Ernst Mayr once wrote that “the search for homologous genes is quite futile except in very close relatives”. But evolutionary developmental biology (aka evo devo) has turned this common knowledge on its face. All complex animals – flies and flycatchers, dinosaurs and trilobites, flatworms and humans, share a common genetic toolkit of that govern the formation and patterning of their bodies and body parts.

Let’s dive in.

Principles of Development

Bodies are not built at random. They are constrained by two important organizing principles.

  1. Bilateral symmetry. The left and right sides of our bodies tend to mirror one another.
  2. Modularity. Our genomes tend to build recurring segments, and then proceed to customize each segment.

Modularity is one of the most important principles in anatomy. In protostomes like worms and centipedes, modules are expressed in repeating segments. In deuterostomes like penguins and humans, modules are expressed in repeated somites (e.g. vertebrae).

Consider the following facts:

  • Trilobite anatomy features many identical legs. In contrast, its descendants (e.g., crayfish) have fewer, and highly specialized appendages.
  • Early teeth in e.g., sharks were numerous and undifferentiated. Contrast this with the horse, which has incisors, canines, premolars, and molars.

Williston’s Law generalizes such observations. Earlier species have many, unspecialized modular repetitions. Over time, there is a trend towards fewer, increasingly specialized parts.

Hox Genes and Localization

The genome contains coding genes, which directly encode proteins, and also regulatory genes that modify the activation profile of those coding genes. Regulatory genes form a regulatory hierarchy, whereby gene activation is controlled by increasingly specific activation profiles. The process is an abstraction hierarchy, such as feature hierarchies found in convolutional neural networks. This regulatory system learns how to e.g., deploy calcium proteins in areas where bone formation is prescribed.

Recall that every cell in an organism contains the exact same DNA. How then does one cell know to become an eye tissue, and another cell knows to become liver tissue? How is cellular differentiation possible?

In order to learn what kind of cell it is, a cell must learn where it is: differentiation requires localization. Roughly speaking, a cell will manufacture eye-specific proteins once it knows that it is located above the nose, and between the ears.

How do cells learn their position? One bit at a time. Per the intension-extension tradeoff, as cells get more location information, their localization window shrinks.

All this is nice in theory, but how does it work in practice?

Just as brain lesions shed light on neuroscience, birth defects shed light on developmental biology. Biologists have been particularly interested in homeotic mutations: mutations that cause body structure to grow in “the wrong place”. Examples include extra fingers in humans, only one central eye in sheep, and legs in the place of eyes in the fruit fly.

A closer look has revealed that homeotic mutations are caused by damage to a specific set of genes: homeobox (Hox) genes. These genes (near the top of the regulatory hierarchy) encode location information, and are conserved across species – the same genes exist in a mouse and a fruit fly:

Hox genes help explain the phenomenon of Williston’s Law (module customization). In arthropod segments, boundaries in Hox gene formation promote customizations across different segments:  

Bodybuilding & the Genetic Toolkit

In both flies and humans, the very same gene (Pax-6) orchestrates eye development, despite enormous differences in eye phenotypes. Even if you activate this gene in the wing of a fly, that wing will grow eye tissue. When the gene is deactivated, eye formation fails.  And if you transplant the fly’s Pax-6 gene into a eyeless mouse, that mouse will regain the ability to grow its eyes.

The Pax-6 gene is an example of a master bodybuilder gene. Here are two other examples from this category

  1. The DLL “Distal-Less” gene builds appendages. In chickens it builds legs; fins in fish, siphons in sea squirts, and tube feet in sea urchins.
  2. The NK2 “Tinman” gene contributes to the circulatory system. It orchestrates heart development across many different phyla.

There is more to the story than just Hox and bodybuilder genes. Other “master” genes are shared across all animal phyla. These include genes for hormones, those that regulate cell type, those involved in signaling pathways, coloration, receptor mechanisms, and other DNA binding use cases. Together, these genes comprise the genetic toolkit: a set of genes responsible for the development of multicellular organisms.

Explaining the Cambrian Explosion

Often two different species will have a feature in common.  Such facts can be explained in two different ways.

  1. Homology: the feature is shared because it was invented in a common ancestor of both species.
  2. Homoplasy (aka analogy, or convergent evolution): the feature was not derived from a common ancestor; it was invented separately and independently

One example of homology is having four limbs: our tetrapod ancestors were the first to try this new body plan. In contrast, the evolution of wings in birds and bats is an example of homoplasy – the common ancestor of these species was terrestrial. This example is nicely illustrated in a phylogeny:

Protostomes and deuterostomes use the very same Hox and bodybuilder genes. It is very unlikely that the exact same genetic toolkit was constructed twice. The most parsimonious explanation is homology. Their common ancestor, a bilateral symmetric population Urbilateria, also possessed this genetic toolkit. Specifically, we can safely conclude that Urbilateria had a toolkit if at least six or seven Hox genes, Pax-6, Distal-Less, Tinman, and a few hundred more bodybuilding genes.

Urbilaterians have not yet been found in the fossil record. However, we can do better than envisioning some featureless worm. We can use our knowledge of their genome to infer their body plans.

Because Pax-6 resides in both branches of bilaterians, Urbilateria probably had some kind of light-sensing organ. Similar inferences from homologous genes adds more detail to this portrait. The first bilateral population probably had some form of appendage, a primitive heart, a through-gut with mouth and anus, and a diverse set of cell types (including photoreceptive, nerve, muscle, digestive, secretory, phagocytic, and contractile).

One of the great mysteries of evolutionary biology is the Cambrian Explosion, an adaptive radiation where dozens of new phyla appear in the fossil record in the span of about 40 million years. The genetic toolkit was fully in place by the time of the Cambrian Explosion. It seems likely that the compilation of the toolkit was a important prerequisite for such a radiation (although ecological factors surely also played a role).

Deep Homology

Consider the evolution of the eye. Evolutionary biologists once thought eyes had evolved independently dozens or even hundreds of times. This remarkable feat of evolution was attributed to strong selective pressure: having a light-sensitive organ just pays off, and the selective pressure is overwhelming enough to induce many species towards the same end product.

But modern genomics has revealed that these “independent inventions” actually derive from the redeployment of the conserved Pax-6 gene.  The diversity of modern eyes is the result of specializations built on top of this basic genetic framework.

More generally, the deep homology hypothesis suggests that the body organization of all bilaterians derives from a substantial swathe of genes that comprise our genetic toolkit. Bilaterians do not invent novel developmental regimens whole-cloth. Rather, once the full toolkit assembled, changes in phyla occurred via alterations of regulatory circuits.

This principle sharpens how scientists explore new hypotheses. For example, humans are unique among primates for our penchant for vocal mimicry (we can learn how to produce novel sounds). But our more distant relatives (parrots, even seals) practice vocal mimicry. Because so much of our genetic material is conserved, we cannot afford to ignore similarities with even our distant relatives.

Until next time.


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.

Polytheistic Roots of Israelite Religion

Part Of: Demystifying Religion sequence
Followup To: Yahweh and the Levites
Content Summary: 2000 words, 10min read.


Is the Hebrew Bible monotheistic?  

We might be tempted to say yes after reading Isaiah 44:6 “I am the first and I am the last; besides me there is no God”.

But the situation is more complicated. The Hebrew Bible is also replete with polytheism. A few examples:

  • “Do you not possess that which Chemosh, your god, has given you? So shall we possess what Yahweh has given us.” Judges 11:24
  • “Who is like Yahweh among the gods?” Exodus 15:11
  • “The people of Judah have as many gods as they have towns.” Jeremiah 11:13

We also see middle ground staked out between these two positions. For example, the original audience of the book of Deuteronomy is often exhorted not to follow after other gods, without it ever being asserted that these gods did not exist or were not real. This is known as monolatrism (“single worship”).

Which belief came first?

Last time, we showed how Yahweh was originally a god of metallurgy in northwest Saudi Arabia. Today, we will work with the framework that Yahweh was introduced to Israel in a five-stage process:

  1. Traditional Polytheism. The earliest Israelites worshipped creator god El, his wife Asherah, and his sons e.g., Baal.
  2. Incorporation. Yahweh was incorporated as a 2nd tier god in El’s pantheon.
  3. Elevation. Yahweh and El are identified as the same deity.
  4. Monolatrism. A new Yahweh-only movement emerges, and the gods of the second tier are denied.
  5. Monotheism. Gods of other nations are denied, Yahweh’s power is deemed universal in scope.

Why did Yahweh worship progress along this trajectory? As we shall explore next time, as with the theocracies of surrounding nations, changes in the religious landscape have strong, robust correlates in the sociopolitical life.

Today I’d like to focus on a different, simpler topic. We shall turn to archaeology and cultural anthropology to explore expressions of polytheism within the Hebrew Bible. Many of my readers already know that the text acknowledges (polemicizes against) polytheistic practices. Less well-known are examples of celebration (bald assertions of polytheistic beliefs) and assimilation (Yahweh “adopts” the roles and characteristics of rival deities). 

Monotheism_ Five Stages (2)


Let’s review the deities in El’s pantheon, and their appearance in the Hebrew Bible.

A Disclaimer

For many modern readers, polytheism is a term loaded with negative connotation. Partisans use it as a weapon. Attackers point to continuities between Israelite religion & polytheism, and defenders point to instances where Israelite rhetoric polemicizes against polytheism. But all ideological innovations have both features.

More to the point, those who spend time interacting with polytheism understands how earnestly it grapples with the same aspects of the human condition as other strands of religious expression. Polytheism must be encountered on its own terms. To weaponize is to misunderstand.

The important thing to bear in mind in the following, is that underneath the images and icons of religious expression lie a particular group of people, responding to social and political pressures in thoroughly understandable ways. My experience has been, the more time you spend in someone else’s culture, the easier it becomes to empathize with their plight.


Israelite Polytheism_ El

At some point in its history, El was identified with Yahweh as the same god.

This equation is expressed clearly in Exodus 6:2-3. “And God said to Moses, “I am Yahweh. I appeared to the patriarchs as El, but by my name Yahweh I did not make myself known to them.” Other Biblical material asserts this equation. Joshua 22:22 states “the god of gods is Yahweh”. Judges 9:46 refers to “El of the covenant”.

The Yahweh-alone movement vigorously condemn prominent Canaanite gods… except El. There are zero condemnations of El in the Hebrew Bible. This makes sense if Yahweh was ultimately identified with this Canaanite creator-god. What’s more, archaeological evidence suggests that the Yahweh religious centers in Shiloh and Bethel were originally a place of El worship.

El and Yahweh are attributed same characteristics. El is depicted as a wise old man with a beard eg “You are great, O El, and your hoary beard instructs you”. Yahweh is described in the same terms (Daniel 7:9, Job 36:26, Habakkuk 3:6). Like “Kind El, the Compassionate”, Yahweh is a “merciful and gracious god”. The description of Yahweh’s dwelling place as a tent (Psalms 15:1, 27:6, 91:10) recalls the tent of El in the Canaanite narrative of Elkunirsa. Finally, both Yahweh and El are said to dwell amidst cosmic waters (Isaiah 33:20-22, Ezekiel 47:1-12, Zechariah 14:8).

Just as Zeus had a council, or assembly, of other gods, so too does Yahweh. The Hebrew Bible is overflowing with references to Yahweh’s (El’s) assembly. See for example Psalm 89:6-8, Zechariah 14:5, 1 Kings 22:19, Isaiah 6:1-8, and Jeremiah 23:18,22.


Israelite Polytheism_ Baal

Worship of Baal can be dated back to the foundation of Israelite societies. This can be seen in onamatology, the study of proper names. Names in the Ancient Near East tend to have a theophoric component: usually a suffix that honors a deity. Yahwistic names include Josiah, Jehu (note the “J” sound); Baal-oriented names include e.g., “Zerubabbel”. In addition to hundreds of icons devoted to Baal worship, we also see Ba’al theophoric names as common in the Levant in this time period.

Yahwistic prophets of this period reserve the most vitriol for Baal worship. Why? Because the Omride dynasty (including King Ahab & Jezebel) erected a temple to Ba’al. While the cult of Yahweh continued in the northern kingdom, Baal was perhaps elevated as the patron god of the northern monarchy, thus creating some sort of theopolitical unity between the kingdom of the north and the city of Tyre.

Indeed, there is some evidence that the cult of Baal and Yahweh got conflated in the north. Hosea 2:16-24 suggest that some northern Israelites did not distinguish between Yahweh and Baal. The religious sanctuaries in the Israelite cities of Dan and Bethel centered around golden calves; this iconography strongly parallels that of Baal. Finally, the redundancy in 1 Kings 16:32 was almost certainly a scribe glossing over the original text, “altar for Baal in temple of Yahweh”.

To induce the Israelites to stop worshipping Baal, the imagery of Baal was adopted by the Yahweh cult. The Baal Cycle, ancient mythology on the scale of the Epic of Gilgameth, has four literary themes for the storm god. Here are those themes, along with the Biblical text which mirrors them.

  1. The march of the divine warrior (Psalm 104:3 “He makes the clouds his chariot, and travels along on the wings of the wind”)
  2. The convulsions of nature as the divine warrior manifests his power (Judges 5:5, Hab 3:10)
  3. The return of the divine warrior to his holy mountain to assume divine kingship (Isaiah 31:4)
  4. The utterance of the divine warrior’s voice from his palace provides rains that fertilize the earth (Jeremiah 10:13)

Yahweh is also depicted as defeating Baal’s classic enemies:

  • Baal/Yahweh defeats a seven headed dragon, Leviathan, and River (CAT 5.1, Psalm 74:13-15).
  • Baal/Yahweh defeats Sea (KTU 1.14, Psalm 89:10).
  • Baal/Yahweh defeats Death/Mot (KTU 1.4 VIII-1.6, Isaiah 25:8).


Israelite Polytheism_ Asherah

El’s wife was named Asherah. When Yahweh was identified with El, did he also inherit his wife? In the blessings of Joseph, Genesis 49:25 contains language specific to the Asherah cult “blessings from Breast-and-Womb”. The Bible further admits that the Israelites frequently worshipped a “Queen of Heaven” (Jeremiah 7:18, 44:17-25). Indeed, 2 Kings 21:7 tells us that worship of Asherah happened within the Temple itself. Finally, archaeology has uncovered several icons with the inscription “Yahweh and his Asherah”. This evidence cumulatively suggests that, in early forms of Israelite religion Yahweh was believed to have a wife.

Israelite polytheism_ Yahweh and his Asherah

The push towards monolatrism led to the eviction of the Asherah cult, whose memory may be preserved in Zechariah 5:5-11. But this eviction created a deficit of femininity to Israelite religious expression. To compensate, the Biblical writers began attributing feminine attributes to Yahweh (Isaiah 49:15, 46:3, 44:2,24, 42:14). Asherah-like characteristics also appear in the goddess of Wisdom in Proverbs 8.


There is extensive evidence for worship of an astral deity (sun god) in Jerusalem.  And Jerusalem is presumably the site that Yahweh was identifed with El. Since the Ugaritic texts hint that El’s family was astral in character, it is not unthinkable that Yahweh was viewed similarly.

  • Proper names. A certain number of proper names are constructed from the root ‘-w-r (“shine, gleam, light”). These include Uriyyah (“Yhwh is my light”) the name of one of David’s generals, Neriyahu “Yhwh is my lamp”, Yizrayah “Yhwh gleams”, minister of Hezekiah, and dozens more.
  • Archaeology. Many pieces of material evidence, including many seals found in Jerusalem with image of the sun, or the sun god in the form of a wing bed scarab.
  • Biblical affirmations. Job 38:6-7 may attest to Israelite recognition of astral deities “Who sets its cornerstone when the morning stars sang together, and all the divine beings shouted for joy?” Similarly Judges 5:20 features conflict in the astral plane “the stars fought in the heavens”.
  • Biblical acknowledgements. Ezekiel 8:16 has Israelites worshipping sun gods. So does 2 Kings 23:5,10-11 and Zephaniah 1:4-5.
  • Biblical Incorporation. The story of Sodom and Gomorrah reflects astral themes, where the divine punishment is meted out at the moment when the sun rises. It is even possible that the two messengers and the deity in the story represent the sun god and his two acolytes. Psalm 19:4-6 and Psalm 84:11 also shows Yahweh taking on astral qualities.

Other Deities

The Ugaritic texts mention hundreds of Canaanite gods. The Bible only criticizes two of them: Ba’al and Asherah. What gives?

The Biblical authors conflates Asherah and Astarte, and conflates multiple male god as “the Baals”.  Despite this, there is only evidence of ~10 gods worshipped in early Israel. This is also true amongst Israel’s neighbors. It appears that the religious landscape of Iron Age Canaan was simply less diverse than Bronze Age Ugarit.

Do we see evidence for these gods in the Bible, despite their not being named in that text?

Anat. Known for her savagery, Anat worship involves a celebration of gore. “Knee-deep she gleans in warrior blood, neck-deep in the gore of soldiers, until she [Anat] is sated with fighting.”  While no evidence of Anat-worship exists in ancient Israel, these divine themes have strong parallels in the Biblical text. The Bible describes heaps of copses, drinking blood, devouring flesh, and swords dripping with viscera.

Astarte. In the Bible, the Name of Yahweh is described in personal terms. The divine name acts as a warrior (Isaiah 30:27) and possesses martial qualities such as radiance and strength (Psalm 29:1-2). The warrior goddess Astarte bears the title “name of Baal”. This designation of Astarte and her martial character and special relationship to the god Baal approximate the martial character of the name, and its special relationship to Yahweh as warrior god. Further evidence for this hypothesis has been adduced from the Elephantine papyri

Similar lines of argument can be made for entities like Light and Truth of Psalm 43:3.

Angels. The lowest tier of the Israelite pantheon also went through alterations. As the Ugaritic texts show, the lowest tier involved a number of deities who served in menial capacities. A common task for such gods was to act as messenger, the literal meaning of the English word “angel”. Certainly angels are not regarded in later traditions as gods. But they were in early traditions.


This post provides evidence for a simple point. Polytheistic expression (not just condemnation!) occurs in the Hebrew Bible.

These expressions are best explained by the Yahweh cult shifting away from its traditional pagan roots, and towards a monolatrist (worship one god) and later monotheist (acknowledge one god) understandings.

As we will see next time, the reasons why Yahweh worship proceeded in this interesting (but not original) trajectory, are fairly easy to understand.

Yahweh, god of metallurgy

Part Of: History sequence
Content Summary: 2200 words, 11 min read.

Where, and how, was the god of Judaism first worshiped?

Yahweh was originally a god of metallurgy in northwest Saudi Arabia. 

Rethinking the Israelite origin story

First, a mass exodus of two million people (six hundred thousand fighting-age men) is vanishingly unlikely. If it was historical, we would expect:

  1. physical debris from the pilgrimage, at any of the thirty locations they are said to have stopped.
  2. archaeological evidence of a dramatic demographic shift in the highlands of Israel.
  3. inclusion in the (otherwise quite voluminous) records of the Egyptian border guards
  4. Egyptian texts discussing the new political situation (since the Egyptians had control over, and military outposts throughout Canaan)

How much of the above evidence do we have? Zero! Recall that absence of evidence can (and in this case does) mean evidence of absence. The very first piece of evidence aligns with the Biblical text is from 1000 BCE, where the Tel Dan stele affirms the existence of the “house of David”.

Second, the conquest narrative is non-historical. Most cities listed as razed in the Joshua narrative show evidence of uninterrupted prosperity in the archaeological record. And the three (out of thirty-one!) cities that do show interruption have not been localized to Israelite violence.

Third, until 700 BCE Judah is a much smaller political force than it makes itself to be. One demonstration of the small scale of this society is the request in one of the Armarna letter sent by the king of Jerusalem to the pharaoh that he supply fifty men “to protect the land.” Another letter asks the pharoah for one hundred soldiers to guard Megiddo from an attack by his aggressive neighbor, the king of Shechem. (Finkelstein, pp78). These letters date to the 14th century BCE. But the population in the intervening time period does not change much. Until 700 BCE, Judah’s population totaled no more than twenty settlements with a population of roughly 30,000. Only after the fall of Israel did Judah experience a population boom and full statehood.   

The Israelite people were indigenous Canaanites.

So where did the Israelite people come from? The Israelite people were originally Canaanite pastoralists who, in 1300 BCE. changed their economic strategy in response to worsening conditions. There is substantial evidence for this hypothesis

  • Ecological: we now know that the Late Bronze Age collapse (a dark age from 1200 – 900 BCE) was caused primarily by climate change-driven famine. The pastoralist strategy can only be successful if neighboring agriculturalists have surplus wheat available to trade. When that surplus dried up, former pastoralists are forced to grow their own wheat, and adapt a hybrid lifestyle.
  • Linguistic: Hebrew and Canaanite language are increasingly indistinguishable the further back you go in the Iron Age.
  • Material culture: Israelite and Canaanites shared the same building plans, pottery designs, village layouts, cooking habits …
  • Historic repetition: Canaanite pastoralists had twice before settled the highlands, but the previous two attempts had eventually failed.

We can also see when these highlands settlements began to slowly differentiate themselves from their “parent” lowland cities. First, the highland settlements did not consume pork (pigs were available for food in all regions of Canaan). Second, the highland peoples seemed to go identify themselves by the name “Israelite”, earliest mention of which is in the Merneptah stele (1204 BCE).

Since Israelites were indigenous Canaanites, we know they share the same culture. But did they start out worship the same gods?

The first Israelites worshiped the pantheon of El

In Egyptian mythology, the most powerful god was Ra. In Babylon, it was Marduk. In Greece, it was Chronus.

Monotheism_ Greek Pantheon

In Canaan, the chief god was El. El’s wife was Asherah, and his sons include Ba’al and Anut. The Canaanite pantheon is well-understood from the discovery of the Ugaritic texts.

In most English translations of the Hebrew Bible, you will see frequent use of the words “God” and “Lord”. The Hebrew terms for these phrases are more literally translated “El” and “Yahweh”. They are used so interchangeably in the Hebrew Bible that you would think them synonyms.

  • Names. The very name “Israel” means “house of El”. In contrast, later Israelite names have “Yahweh”-based suffixes e.g., Jehu. Further, most Israelite cities were named after the gods in El’s assembly.  The god Anat was honored in the city of Anathoth, the place of origin of the prophet Jeremiah. The god Dagan in Beth-Dagan. The god El in Beth-El. The god Shamash in Beth-Shamash. The god Shalimu in Jerusalem.
  • Ritual systems. The priestly system laid out in Leviticus is very nearly copy-and-pasted from the Ugaritic sacrificial system.
  • Legal codes. the Covenant, Holiness, and Deuteronomic law codes share strong parallels with surrounding Canaanite legal systems.
  • Iconography. A seal found in Jerusalem in a tomb of the seventh century shows a solar god flanked by two minor gods: “Righteousness” and “Justice”

There are also expressions of polytheism throughout the Hebrew Bible. For example,

  • “Do you not possess that which Chemosh, your god, has given you? So shall we possess what Yahweh has given us.” Judges 11:24
  • “Who is like Yahweh among the gods?” Exodus 15:11
  • “The people of Judah have as many gods as they have towns.” Jeremiah 11:13

In part two of this series, we will see hundreds more data establishing Israel’s traditional religion as polytheism.

The original Yahweh cult was a Shasu religion located in southern Edom

Recognized for their goatees and hair held back in a hairband, the Shasu nomads were well-known to the Egyptian authorities. They conducted copper mining in the wilderness, and also were quite successful camel breeders. The Bible uses the terms Edom, Teman, and Midianite interchangeably. Egyptian descriptions of the Shasu geographically overlap the Biblical land of the Midianites.

Okay. So how do we know that the Yahweh cult originated with the Shashu people?

  • Four of the oldest texts in the Bible tell us so. See Deut 33:2, Judges 5:4-5, Habakkuk 3:3 and Isaiah 63:1.
  • Special treatment of Edom. The Bible repeatedly condemns the gods of the Ammonites, the Moabites, and the Sidionites, but never the god of Edom. Deut 23:7 calls Edomites the “brothers” of the Israelites. Edom’s patriarch Esau is said to be the brother of Israel’s patriarch Jacob. The Bible makes a point of not mentioning Qos, the national god of Edom. We have evidence that Qos was a rather late theological development in Edom. Given this evidence, it is plausible to assume that Yahweh was worshiped in Edom and Qos stepped in only when Yahweh became the national god of Israel/Judah.
  • Archaeology.  Two Egyptian inscriptions, one dated to the period of Amenhotep III (14th century BCE), the other to the age of Ramesses II (13th century BCE), refer to “Yahweh in the land of the Shasu”. We also have one 9th century BCE text at Kuntillet Ajrud which refers to “Yahweh of Teman”.

Yahweh was first worshiped as a god of metallurgy

Gods in the ancient worlds were given a specific set of powers. For reasons we will get into next time, Yahweh in the Bible is attributed the attributes of many kinds of gods: he exhibits power of the storm, of the sun, and even of femininity. But if we limit our search for descriptions of God in Midianite territory, we see the following picture:

For more information, I recommend Amzallag, 2009. Yahweh, the Canaanite God of Metallurgy?

The founder of Judaism, Moses, was said to be 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.

One does not need to take a position on the historicity of Moses, or of a mini-Exodus, to consider the above evidence. Even if he was entirely fictional, the fact that Israelite priests portrayed Moses as a Midianite is significant.

Yahweh was introduced to Israel as a second tier deity (a member of El’s family)

This can be seen in Deuteronomy 32:8-9, where El gives each of his sons a nation to rule over:

When El gave the nations their inheritance, when he divided all mankind, he set up boundaries for the peoples according to the number of the sons of El. For Yahweh’s portion is his people, Jacob his allotted inheritance.

In Psalm 82, we see Yahweh not at the head of the pantheon, but later asked to assume the job of all gods. “Yahweh stands in the divine assembly of El. Among the divinities, he pronounces judgment… Arise O Yahweh, judge the world; for You inherit all the nations.” Genesis 49:24-25 and Numbers 23-24 also view YHWH and El existing as distinct deities.

We have seen how Yahweh was first worshiped in Midian, and not Israel. Concurrently, El was worshiped in the land of Israel.

Then, when Yahwism emigrated to Israel (incorporation), Yahweh was not recognized as a god of gods. Rather, Yahweh was elevated to this position (equated with El) as the nation of Judah transitioned towards statehood.

As we will see next, worship of Yahweh emerged gradually, in five stages:

Monotheism_ Five Stages (2)


Here’s what we covered today:

  • 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)

Until next time.

The Documentary Hypothesis

Part Of: Demystifying Religion sequence
Followup To: A Secret in The Ark
Content Summary: 1900 words, 19min read.

Who Wrote The Hebrew Bible?

A close reading of the Hebrew Bible reveals the existence of doublets: two stories that describe the same event. A few examples:

  • Abraham’s covenant (Genesis 15:1-21 and 17:1-27),
  • Jacob becoming Israel (Genesis 32:25-33 and 35:9-15),
  • Yahweh summons Moses (Exodus 3-4 and 6:2-30)
  • Water in the wilderness (Exodus 15:22b-25a and 17:1-7)

Dozens of these doublets appear throughout the first five books of the Hebrew Bible (also known as the Torah). Traditionally, the Torah is thought to have a single author, and doublets like these were explained as either a) different events, or b) same event but with different emphases.

But what if these doublets exist because the Torah has multiple authors?

Let’s look deeper.

Source Identification as Unsupervised Learning

In principle, how might we discern between a single- and a multi-author book?

The Clustering Method. Let’s conjecture two sources (clusters) and, for each sentence, assign it either Cluster 1 or Cluster 2. We have complete freedom in our assignments. We want to chose clusters that maximize the coherence within each source, and also maximize the difference between the sources.

  • If the clusters are not very different, there is probably only one author.
  • If they are very different, we can safely conclude two authors.

For readers familiar with machine learning: this is unsupervised learning – searching for latent variables that best explain our data.

A Tale of Two Books

Suppose you encounter a book you have never read before, originally written in English by a single author. Call this Book A.

But you don’t know if Book A has one or two authors! To find out, you might use the Clustering Method.

What happens if you look at every sentence in Book A, and try to make each source-cluster as different as possible. Even for books written by a single author, the resultant source-clusters could be contrived to be truly different. For example, you could put all optimistic sentences in one bucket, and all pessimistic sentences in the other. But even though the texts feel a little different, they don’t differ that much (after all, a single person wrote both!)

In contrast, imagine you come across another book, Book B, replete with doublets. You break those doublets into clusters, and discover the following facts:

  1. Dialect. One cluster uses an antiquated dialect of English (e.g., Shakespearean), the other a modern dialect (e.g., African-American Vernacular English).
  2. Terminology. One cluster consistently uses the word “soda”, the other consistently uses the alternative, “pop”. 
  3. Consistent Content. One cluster is very interested in economic issues. The other is more interested in rehashing political debates.
  4. Narrative Flow.  Reading each cluster as a standalone book tends to smooth out non-sequiturs, and generally improve the sense of narrative flow.
  5. Inter-Source Relationships.  Imagine Book B is situated in an anthology with other books (B2 and B3) of unknown authorship. These other books are kinda dissimilar  from B. But B2 has lots in common with Cluster 1, and B3 sounds like it shares an author with Cluster 2. 
  6. Historical Grounding. Given the above information, we can make a pretty good guess as to identify of both authors, and why they got merged into a single anonymous volume.

On this evidence, it seems very unlikely that there is a single author of Book B. Instead, most people would indeed accept that this document has two different authors.

The Hypothesis: Five Sources

The Hebrew Bible is like Book B. Only, instead of two distinct authors, we have identified five. These are the Jahwist source (J), the Elohim source (E), the  Priestly source (P), the Deuteronomist source (D), and the Redactor (R). This is the Documentary Hypothesis.

We will explore the different personalities of these authors in more detail next section; for now, I want to briefly describe their contributions to the Torah from a textual perspective:

Documentary Hypothesis_ Source Distribution

And here is the timeline on which our source documents were authored, where the final redactor R (Ezra) compiled the final JEPD product.

Documentary Hypothesis_ Composition Timeline (2)

Evidence For The Hypothesis

How do we know all of this? On the following grounds:

  1. Dialect. Sources J and E are written in the Hebrew of the 10th BCE. In contrast, P and D are written in 8th century BCE.
  2. Terminology. A couple examples. Source D alone use of the phrase “with all your heart and with all your soul”. Source P uses all 100 instances of the word “congregation”, and 67 out of 69 examples of the work “chieftain”. Here are more examples:

Documentary Hypothesis_ Terminology (1)

  1. Consistent Content.
    • The Revelation of God’s Name.  According to J, the name YHWH was known since the earliest generations of humans. But in E and P it is stated just as explicitly that YHWH does not reveal this name until the generation of Moses.
    • Sacred Objects.
      • Tabernacle: P discusses the Tabernacle 200 times, it receives more attention than any other subject. It is never mentioned in J or D. E mentions it three times.
      • The Ark: J identifies the ark is identified as crucial to Israel’s travels and military successes; it is never mentioned in E.
      • Urim and Thummim: P mentions Urim and Thummim. J, E, and D never do.
      • Cherubs: P and J invoke cherubs. E and D never do.
      • Miracles: E has miracles performed by Moses’ staff. P uses Aaron’s staff.
    • Priestly Leadership. In P, access to the divine is limited to Aaronid priests. There is no talk of dreams, angels, talking animals, judges, and very few mentions to prophets. These themes are developed almost exclusively in J, E, and D.
  2. Narrative Flow.  Reading J, E, D, and P as standalone narratives tends to remove non-sequiturs and contradictions, and generally improve the sense of narrative flow. Want to see this for yourself? Go compare the original composite story of Noah, and contrast it with the original two stories (the original stories were weaved together by a later redactor).
  3. Inter-Source Relationships. Source D shares the same tone, emphases, and worldview as the book of Jeremiah. Source P resonates strongly with the book of Ezekiel. Finally, Sources J and E mirrors the book of Hosea.
  4. Historical Grounding. This is the most exciting piece of evidence, for reasons I will more fully explore next time. Suffice to say that we can localize each source to the historical context in which it was written. We have evidence suggesting that J and E were composed during the divided monarchy, before Israel fell in 722 BCE. J is written from a Southern perspective (in Judah), E is written from a Norther perspective (in Israel). After the fall of the northern kingdom, many Israelites fled to Judah. Because the old tribal disputes had faded in importance, J and E were combined into a JE narrative. The Priestly source P was an alternative telling of JE written in 8th century Judah. Finally, the first iteration of Deuteronomy was composed during the reign of King Josiah (641 BCE), just 20 years before the Babylonian exile (622 BCE).

I’ll let Richard Elliott Friedman wrap up this section.

Above all, the strongest evidence establishing the Documentary Hypothesis is that several different lines of evidence converge. There are more than thirty cases of doublets: stories or laws that are repeated in the Torah. The existence of so many overlapping texts is noteworthy itself. But their mere existence is not the strongest argument. One could respond, after all, that this is just a matter of style of narrative strategy. Similarly, there are hundreds of apparent contradictions in the text, but one could respond that we can taken them one by one and find some explanation for each contradiction. And, similarly, there is a matter of the texts that consistently call the deity God while other texts consistently call God by the name YHWH, to which one could respond that this is simply like calling someone sometimes by his name and sometimes by his title.

The powerful argument is not any one of these matters. It is that all these matters converge. When we separate the doublets, this also results in the resolution of nearly all the contradictions. And when we separate the doublets, the name of God divides consistently in all but three out of more than two thousand occurrences. And when we separate the doublets, the terminology of each source remains consistent within the source. And when we separate the sources, this produces continuous narratives that flow with only a rare break. And when we separate the sources, this fits with the linguistic evidence, where the Hebrew of each source fits consistently with what we know of the Hebrew in each period. And so on for each of the categories that precede this section.

The name of God and doublets were the were the starting-points of the investigation into the formation of the Bible. But they are not major arguments or evidence in themselves. The most compelling argument is that all this evidence of so many kinds comes together so consistently. To this day, no one known to me who challenged the hypothesis has ever addressed this fact.

Open Questions

Most scholars agree with the broad picture of four sources (J, E, P, D) and two redactions (JE and JEPD). There does exist considerable controversy at finer levels of detail. The four most contentious mini-debates I know of are as follows:

  • While there is consensus on the dating of J, E, and D, the dating of P is somewhat controversial (700 vs 500 BCE).
  • The exact relationship of J and E is at times hard to work out, particularly because E has less material than J. Were parts of E ejected during the redaction process of JE? Or was E composed as a supplement to J, and not a standalone work?
  • It is hard to make out how the two redaction processes actually worked. The Hebrew Bible is the very first example of prose writing in the entire world (earlier writing was entirely poetic).
  • There is consensus that J, E, P, and D were authored long after the events that they describe. They were undoubtedly influenced by early oral traditions. However, the extent of continuity and historical memory transferred from these oral traditions is in some doubt.


I was raised in an evangelical household, which means that growing up, I have read the Hebrew Bible (known to Christians as the Old Testament) cover-to-cover several times. I found such reading difficult. Some of this was mere cultural distance: a kid in the 20th century CE is three millenia removed from Canaanite culture in which the Bible was written.

But for me, the Hebrew Bible feels much easier to understand in light of the Documentary Hypothesis.

  • Contradictions are explained.
  • The within-source stories flow much better.
  • It is easier to understand the narrative discontinuities in the composite.
  • The diverse perspectives can be situated within their originating cultural milieu.

I wish more people knew about the Documentary Hypothesis for these reasons. Or better yet, could look at the labelled sources of the Hebrew Bible online. But for now, if you’d like to read the Hebrew Bible yourself, with labelled sources, the best way to do this is simply to purchase a book like, The Bible With Sources Revealed for a copy of the complete Torah, color coded by authorship.

Until next time.

The Structure of Ethical Theories

Part Of: Demystifying Ethics sequence
Followup ToAn Introduction To Ethical Theories
See Also: Shelly Kagan (1994). The Structure of Normative Ethics
Content Summary: 700 words, 7 min read

Are Ethical Theories Incompatible?

Last time, we introduced five major ethical theories:

Ethical Theories- Summary

At first glance, we might consider these theories as rivals competing for the status of a ground for morality. However, when discussing these theories, one has a distinct sense that they are simple addressing different concerns.

Perhaps these theories are compatible with one another. But it is hard to see how, because we lack a map of the major conceptual regions of normative ethics, and how they relate to one another.

Let’s try to construct such a map.

Identifying Morally Relevant Factors

There are two major activities in the philosophical discourse about normative ethics: factorial analysis, and foundational theories.

Factorial analysis involves getting clear on which variables affect in our moral judgments. This is the goal of moral thought experiments. By constructing maps from situations to moral judgment, we seek to understand situational factors that contribute to (and compete for control over) our final moral appraisals.

We can discern four categories of factors which bear on moral judgments: Goodness of Outcome, General Constraints, Special Obligations, and Options. We might call these categories factorial genres. Here are some example factors from each genre.

Ethics Taxonomy- Morally Relevant Factors (1)

While conducting factorial analysis, we typically ask questions about:

  1. Relative Strength. Does Don’t Harm always outweigh factors related to outcome?
  2. Explanatory Parsimony. Is Keep Your Promises redundant with Don’t Be Unfair?
  3. Subfactor Elaboration. What does Maximize Overall Happiness mean, exactly?

Constructing Foundational Theories

A foundational mechanism is a conceptual apparatus designed to generate the right set of morally relevant factors. An example of such a theory is contractarianism, which roughly states that:

Morally relevant factors are those which would be agreed to by a social community, if they were placed in an Original Position (imagine you are designing a social community from scratch), and subject to the Veil of Ignorance (you don’t know the details of what your particular role will be).

Thus, our two philosophic activities relate as follows:

Ethical Structure- Factors vs Foundations (2)

These two activities are fueled by different sets of intuitions.

  • Factorial intuitions are identified by appeal to concrete ethical dilemmas.
  • Foundational intuitions are often related to one’s metaethical dispositions.

Let us examine other accounts of foundational mechanisms. These claim that we should accept only morally relevant factors that…

  • …if everyone followed such rules, total well-being would be maximized (rule utilitarianism).
  •  … if the factor was universalized, became like a law of nature, no contradictions would emerge (Kantian universalization).
  • … can be attributed to a being acting purely in self-interest (egoism).

Localizing Ethical Theories in our Map

We can now use this scheme to better understand the space of ethical theories.

Proposition 1. Ethical theories can be decomposed into their foundational and factorial components.

Three of our five ethical theories have the following decomposition:

Ethical Structure- Deconstructing Ethical Theories (1)

Proposition 2. Factorial pluralism is compatible with foundational monism.

Certain flavors of consequentialists, deontologists, consequentialists insist on factorial monism, that only one kind of moral factor really matters.

But as a descriptive matter, it seems that human morality is sensitive to many different kinds of factors. Outcome valence, action constraint, role-based obligations all seem to play in real moral decisions.

Factorial monism has the unpleasant implication of demonstrating some of these factors as misguided. But philosophers are perfectly free to affirm factorial pluralism: that each intuition “genre” are prescriptively justified.

Some examples of one foundational device generating a plurality of genres:

  1. Rule Utilitarianism (rules that maximize societal well-being) could easily generate rules to keep one’s promises.
  2. Kantian Universalization might generate outcome-sensitive moral factors that are immune to contradiction.
  3. People in the Original Position might enter into a contract of general constraints (e.g., human rights).


Are ethical theories truly competitors? One might suspect that the answer is no. Ethical theories seem to address different concerns.

We can give flesh to this intuition by analyzing the structure of ethical theories. They can be decomposed into two parts: factorial analysis, and foundational mechanisms.

  • Factorial analysis provide the list of factors relevant to moral judgments.
  • Foundational mechanisms are hypothesized to generate these moral factors.

Ethical Structure- Factors vs Foundations (2)

Most defenses of foundational mechanisms have them generating a single factorial genre. However, it is possible to endorse factorial pluralism. There is nothing incoherent in the view that e.g., both event outcome and general constraints bear on morality.

This taxonomy allows us to contrast ethical theories in a new way. Utilitarianism can be seen as a theory about the normative factors, contractarianism is a foundational mechanism. Far from being rival views, one could in fact endorse both!

An Introduction To Energy

Part Of: Demystifying Physics sequence
Content Summary: 700 words, 7min reading time.

Energy As Universal Currency

Why does burning gasoline allow a car to move? Chemical reactions and kinetic propulsion seem quite distinct.

How does a magnet pull a nail from the ground? What relation exists between magnetism and gravitational pull?

What must occur for a nuclear reactor to illuminate a light bulb? What connection is there between nuclear physics and light waves?

Energy is the hypothesis of a hidden commonality among the above phenomena. There are many forms of energy: kinetic, electric, chemical, gravitational, magnetic, radiant. But these forms are expressions of a single underlying phenomena.

A single object may possess many different energy forms simultaneously:

A block of wood thrown into the air will possess kinetic energy because of its motion, gravitational potential energy because of its height above the ground, chemical energy in the wood (which can be burned), heat energy depending on its temperature, and nuclear energy in its atoms (this form is not readily available from our block of wood, but the other forms may be).

Non-physicists worry that physics involves memorizing a giant catalogue of phenomena, each discovered by some guy who got an equation named after him. Energy is the reason why physics is not “stamp collecting”. It allows us to seamlessly switch between different phenomena.

Change As Energy Transformation

The only thing that is constant is change.

Certain Greek philosophers were obsessed with change. Physics gives us a language that formalizes these intuitions. Consider the following.

  • Energy is the capacity to do work; that is, initiate processes.
  • Processes (i.e., work) involve continuous and controlled actions, or changes.

A confusing diversity of phenomena can produce force (the ability to accelerate things), but they all share the same blood. Change is energy transformation.

We can play “where does the energy come from” game on literally any event in the physical universe:


A Worked Example

Let’s get concrete, and go through a simple illustration of work as energy transformation. 

Our example involves a ball sliding down an incline.


To get our bearings, let’s calculate the acceleration experienced by the ball


To demonstrate conservation of energy, we first need to solve for the ball’s final velocity (v) at the bottom of the ramp. Recall the lesson of kinematic calculus, that displacement, velocity, and acceleration are intimately related:

x(t) = \int v(t) = \int \int a(t)

a(t) = v'(t) = x''(t)

We can use these formulae to calculate final velocity (for a tutorial see here).


So the ball’s final velocity will be 6.26 meters per second \sqrt{4g} m/s). However, recall the classical definitions of kinetic and potential (gravitational) energy, which are KE = \frac{1}{2}mv^2 and PE = mgh.

If conservation of energy is true, then we should expect the following to hold:

(KE + PE)_{final} - (KE + PE)_{initial} = 0

Is this in fact the case? Yes!

m[(0 + 2g) - (\frac{ \sqrt{(4g)^2} }{2})] + 0 = m[2g - 2g] = 0

Total energy of the ball stays the same across these two points. Conservation of energy can also be demonstrated at any other time in the ball’s journey. In fact, we can show that potential energy is smoothly converted to kinetic energy (image credit Physics Classroom).


Why is the ball transforming its energy KE \rightarrow PE? Because it is experiencing a force.

Cosmological Interpretation

Just as space and time are expressions of a single spacetime fabric, Einstein also demonstrated mass-energy equivalence. Mass is simply a condensed form of energy, capable of being released in e.g., nuclear explosions. Do not confuse mass and matter. Mass and energy are (interchangeable) properties of matter.

So there are two components of reality: energymass and spacetime. Spacetime bends for energymass. Energy is conserved, but has many faces. The laws of physics (quantum field theory and general relativity) describe the interactions between energymass and spacetime. And since we know that energy is conserved, all there is today was all there was at the beginning of time.

If the amount of energy contained in our universe doesn’t change, what is this quantity? How much energy is there? One strong candidate theory is zero. The flat universe hypothesis rests on the realization that gravitational energy is negative, and claims that it counterbalances all other mediums.


Next time, we will explore the distinction between usable vs inaccessible energy. Until then.

The Birth of the Universe

Part Of: Demystifying Physics sequence
Content Summary: 1200 words, 12 min reading time.

Our lifespan is 80 years. Our consciousness refreshes every 300 milliseconds. Timespans beyond these, human brains are not well-equipped to conceive. Nevertheless, to learn the origin story of the universe, we must stare into the abyss of deep time.

Where do we come from?   

Poets, philosophers and theologians have explored this question for millennia, in part seeking to ascribe meaning to the cosmos. Only recently have we discovered a literal answer, which constrains and complements our narratives.

Here are the facts.

Particle Physics

The universe is built from fermions and bosons.

Fermions are the bedrock of matter, the “meat” in our particle soup. They come in two flavors: quarks and leptons. You’ve heard of antimatter, yes? This term refers to antiquarks and antileptons.

In contrast, bosons are force carriers; the “broth” of the soup. They mediate the four fundamental forces: gravity, the strong force (which holds atoms together), the weak force (radioactivity), and electromagnetism (literally everything else).

Here are the most significant species of particles:

Deep Time- Particle Physics (1)

Protons & neutrons are not elementary particles. They are coalitions! Gluons combine quarks into groups called hadrons. When hadrons contain three quarks, they are called baryons

Deep Time- Hadrons (2)

Hydrogen is one electron orbiting one proton; that is, one lepton orbiting three quarks!

The Primordial Era

13.8 billion years ago, the Big Bang happened. At that moment, a gravitational singularity (the primeval atom) exploded, and became the basis of all matter, energy, space and time.

  • What happened before the Big Bang? This question is incoherent: it reduces to “what happened before time existed”?
  • What happened after the Big Bang? To answer this, let us divide time into eight segments.

1. Planck Epoch (0 → 10-43 sec). The climate of this period of history is so intense, known laws of physics break down. We suspect that gravity merges with the other forces, but we do not yet possess a theory of quantum gravity. Only with such a Theory of Everything can we hope to better understand what caused the Big Bang.

2. Grand Unification Epoch (10-43 → 10-36 sec). Science recovers its ability to describe nature during this epoch. The Strong, Weak, and Electromagnetic Forces exist as a single entity: the electronuclear force. The universe is expanding, but it is still a small, hot ball of plasma. Physical characteristics like mass, charge, etc are completely meaningless.

3. Inflationary Epoch (10-36 → 10-32 sec). Next, the mysterious phenomenon of cosmic inflation obtained. The fabric of spacetime explodes at a rate that far, far exceeds the speed of light. The volume of the universe expands at least seventy-eight orders of magnitude (1078 times bigger).

Few people realize the implications of such an overpowered process. Have you heard the phrase observable universe? Buried within this phrase is the implication of unobservable universes. You don’t need to wander into QM interpretations to encounter Many Worlds. We already know that there are myriad universes that we can never access: inflation simply pushed them beyond any distance our radio signals could traverse.

Deep TIme- Observable Universe (1)

4. Electroweak Epoch (10-32 → 10-12 sec). At the end of this epoch, the universe has cooled enough for the Strong force to dissociate from the Electroweak force. Quarks, antiquarks, and gluons dominate the cosmos.

5. Quark Epoch (10-12 → 10-6 sec). Despite the newly independent Strong force, quarks are unable to combine. Ambient temperature is too hot, preventing nuclear fusion.

6, 7. Hadron Epoch, and Lepton Epoch (10-6 → 10 sec) . Things have finally cooled enough for quarks and antiquarks to combine! The universe fills with hadrons (e.g., protons) and anti-hadrons (e.g., anti-protons).

In this era, matter slightly outnumbered antimatter, for reasons we don’t yet understand.

Deep Time- Matter Asymmetry

Antimatter was suppressed during these epochs. At the end of the Hadron Epoch, most hadrons and anti-hadrons experience annihilation reactions. The few survivors were matter: this is baryogenesis (baryons are a species of hadron).

In the subsequent Lepton Epoch, leptons and anti-leptons (e.g., electrons and anti-electrons) also annihilate one another en masse. Antimatter was again underrepresented in the survivors: this is leptogenesis.

8. Photon Epoch (10 sec → 380,000 years). 10 seconds after the big bang, and photons dominate the universe. Protons and electrons (hadrons and leptons) exist, but are unable to come together due to high temperatures. The free electrons scatter light: photon travel is randomized by collisions with free electrons, in a process known as Compton scattering.

As the fabric of spacetime continues to expand, two other things happen:

  • Recombination: Temperatures drop to a point where electrons and protons could come together to form hydrogen atoms!
  • Rise of the Fermions: The expansion of space stretches photon wavelength, decreasing its total energy content.  Fermions, whose populations had been decimated in the destruction of antimatter (c.f. baryogenesis and leptogenesis), reclaim the title as the most energetic substance in the universe.

The eventual result was photon decoupling. Temperature finally permits light could travel freely. The universe becomes transparent.

You’ve probably heard that it takes light from the Sun eight minutes to reach Earth. If the Sun suddenly disappeared, we would only learn that fact eight minutes later. Similarly, if a star 40,000 light-years away suddenly explodes in a supernova, we must wait until 42,016 AD to learn about that. Starlight is a form of time-travel. 

What are the oldest photons we can see? How far back into our past can we peer?

Well, we can see galaxies being formed 200 million years after the Big Bang. And we can peer back farther still. We can directly see light emitted the moment the universe became transparent; this is the Cosmic Microwave Background (CMB).

Why is the CMB not smooth? The ripples are microscopic phenomena writ large: inflation exploded quantum fluctuations on a cosmic scale…

Deep Time- Cosmic Background Radiation (1)

Some of the static in TV antenna is caused by the CMB. You can literally see evidence of the Big Bang with your own eyes. 

Structure Formation

Photon decoupling has ensured that light can travel freely in a sea of hydrogen. However, there were no stars at this point: the CMB is the only light source. This is the Dark Age of the universe, a time before stars.  

Deep Time- Cosmogenesis Timeline (1)

Why is so much of space a vacuum?

In the Inflationary Epoch, inflation etched ripples into the energy distribution of the cosmos. Gravity accentuates this heterogeneity by pulling matter together. Space is mostly empty because particles like to spend time together. 

Gravity appears to operate at three different spatial frequencies.

  1. Very large clumps of hydrogen become superclusters.
  2. Within every supercluster, there are billions of smaller clumps called galaxies.
  3. Galaxies in turn comprise billions of smaller assemblies: stars and solar systems

The origin of all things is the hydrogen cloud, and gravitational attraction.  


  • There are two kinds of particles in the universe: fermions (“matter particles”) and bosons (“force particles”)
  • The Big Bang happened 13.8 billion years ago. The early universe was hot, and expanded quickly.
  • Three important events in occur in the first second of the universe
    • Cosmic Inflation: the fabric of the universe stretched much faster than the speed of light, creating unobservable universes.
    • Force Differentiation: the four forces (gravity, strong, weak, electromagnetic) separated from one another
    • Fermion Asymmetry: antimatter was preferentially annihilated
Deep Time- Primordial Era (4)
  • Afterwards, the universe was replete with clouds of hydrogen. Gravity pulled these together to form stars, galaxies, and superclusters.

An Introduction To Natural Selection

Part OfDemystifying Life sequence
Followup To: Population Genetics
Content Summary: 1400 words, 14 min read

How Natural Selection Works

Consider the following process:

  1. Organisms pass along traits to their offspring.
  2. Organisms vary. These random but small variations trickle through the generations.
  3. Occasionally, the offspring of some individual will vary in a way that gives them an advantage.
  4. On average, such individuals will survive and reproduce more successfully.

This is how favorable variations come to accumulate in populations.

Let’s plug in a concrete example. Consider a population of grizzly bears that has recently migrated to the Arctic.

  1. Occasionally, the offspring of some grizzly bear will have a fur color mutation that renders their fur white.
  2. This descendent will on average survive and reproduce more successfully.

Over time, we would expect increasing numbers of such bears to possess white fur.

Biological Fitness Is Height

The above process is straightforward enough, but it lacks a rigorous mathematical basis. In the 1940s, the Modern Evolutionary Synthesis enriched natural selection by connecting it to population genetics, and its metaphor of Gene-Space. Recall what we mean by such a landscape:

  • A Genotype Is A Location.
  • Organisms Are Unmoving Points
  • Birth Is Point Creation, Death Is Point Erasure
  • Genome Differences Are Distances

Onto this topography, we identified the following features:

  • A Species Is A Cluster Of Points
  • Species Are Vehicles
  • Genetic Drift is Random Travel.

In order to understand how natural selection enriches this metaphor, we must define “advantage”. Let biological fitness refer to how how many fertile offspring an individual organism leaves behind. An elephant with eight grandchildren is more fit than her neighbor with two grandchildren.

Every organism achieves one particular level of biological fitness. Fitness denotes how well-suited an organism is to its environment. Being a measure of organism-environment harmony, we can view fitness as defined for every genotype. Since we can define some number for every point in gene-space, we have license to introduce the following identification:

  • Biological Fitness Is Height

Here is one possible fitness landscape (image credit Bjørn Østman).

Natural Selection- Fitness Landscape (1)

We can imagine millions of alien worlds, each with its own fitness landscape. What is the contours of Earth’s?

Let me gesture at three facts of our fitness landscape, to be elaborated next time:

  • The total volume of fitness is constrained by the sun. This is hinted at by the ecological notion of carrying capacity.
  • Fitness volume can be forcibly taken from one area of the landscape to another. This is the meaning of predation.
  • Since most mutations are harmless, the landscape is flat in most directions. Most non-neutral mutations are negative, but some are positive (example).

Natural Selection As Mountain Climbing

A species is a cluster of points. Biological fitness is height. What happens when a species resides on a slope?

The organisms uphill will produce comparatively more copies of themselves than those downhill. Child points that would have been evenly distributed now move preferentially uphill. Child points continue appearing more frequently uphill. This is locomotion: a slithering, amoeba-like process of genotype improvement.


We have thus arrived at a new identification:

  • Natural Selection Is Uphill Locomotion

As you can see, natural selection explains how species gradually become better suited to their environment. It is a non-random process: genetic movement is in a single direction.

Consider: ancestral species of the camel family originated in the American Southwest millions of years ago, where they evolved a number of adaptations to wind-blown deserts and other unfavorable environments, including a  long neck and long legs. Numerous other special designs emerged in the course of time: double rows of protective eyelashes, hairy ear openings, the ability to close the nostrils, a keen sense of sight and smell, humps for storing fat, a protective coat of long and coarse hair (different from the soft undercoat known as “camel hair”), and remarkable abilities to take in water (up to 100 liters at a time) and do without it (up to 17 days).

Moles, on the other hand, evolved for burrowing in the earth in search of earthworms and other food sources inaccessible to most animals. A number of specialized adaptations evolved, but often in directions opposite to those of the camel: round bodies, short legs, a flat pointed head, broad claws on the forefeet for digging. In addition, most moles are blind and hard of hearing.

The mechanism behind these adaptations is selection, because each results in an increase in fitness, with one exception. Loss of sight and hearing in moles is not an example of natural selection, but of genetic drift: blindness wouldn’t confer any advantages underground, but arguably neither would eyesight.

Microbiologists in my audience might recognize a strong analogy with bacterial locomotion. Most bacteria have two modes of movement: directed movement (chemotaxis) when its chemical sensors detect food, and a random walk when no such signal is present. This corresponds with natural selection and genetic drift, respectively.

Consequences Of Optimization Algorithms

Computer scientists in my audience might note a strong analogy to gradient descent, a kind of algorithm. In fact, there is a precise sense in which natural selection is an optimization algorithm. In fact, computer scientists have used this insight to design powerful evolutionary algorithms that spawn not one program, but thousands of programs, rewarding those with a comparative advantage. Evolutionary algorithms have proven an extremely fertile discipline in problem spaces with high dimensionality. Consider, for example, recent advances in evolvable hardware:

As predicted, the principle of natural selection could successfully produce specialized circuits using a fraction of the resources a human would have required. And no one had the foggiest notion how it worked. Dr. Thompson peered inside his perfect offspring to gain insight into its methods, but what he found inside was baffling. The plucky chip was utilizing only thirty-seven of its one hundred logic gates, and most of them were arranged in a curious collection of feedback loops. Five individual logic cells were functionally disconnected from the rest— with no pathways that would allow them to influence the output— yet when the researcher disabled any one of them the chip lost its ability to discriminate the tones…

It seems that evolution had not merely selected the best code for the task, it had also advocated those programs which took advantage of the electromagnetic quirks of that specific microchip environment. The five separate logic cells were clearly crucial to the chip’s operation, but they were interacting with the main circuitry through some unorthodox method— most likely via the subtle magnetic fields that are created when electrons flow through circuitry, an effect known as magnetic flux. There was also evidence that the circuit was not relying solely on the transistors’ absolute ON and OFF positions like a typical chip; it was capitalizing upon analogue shades of gray along with the digital black and white.

In gradient descent, there is a distinction between global optima and local optima. Despite the existence of an objectively superior solution, the algorithm cannot get there due to its fixation with local ascent.

Natural Selection- Local vs. Global Optima

This distinction also features strongly in nature. Consider again our example of camels and moles:

Given such a stunning variety of specialized differences between the camel and the mole, it is curious that the structure of their necks remains basically the same. Surely the camel could do with more vertebrae and flex in foraging through the coarse and thorny plants that compose its standard fare, whereas moles could just as surely do with fewer vertebrae and less flex. What is almost as sure, however, is that there is substantial cost in restructuring the neck’s nerve network to conform to a greater or fewer number of vertebrae, particularly in rerouting spinal nerves which innervate different aspects of the body.

Here we see natural selection as a “tinkerer”; unable to completely throw away old solutions, but instead perpetually laboring to improve its current designs.


  • In the landscape of all possible genomes, we can encode comparative advantages as differences in height.
  • Well-adapted organisms are better at replicating their genes (in other words, none of your ancestors were childless).
  • Viewed in the lens of population genetics, natural selection becomes a kind of uphill locomotion.
  • When view computationally, natural selection reveals itself to be an optimization algorithm.
  • Natural solution can outmatch human intelligence, but it is also a “tinkerer”; unable to start from scratch.

An Introduction To Population Genetics

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

Central Thesis Of Molecular Biology

In every cell of your body, there exist molecules called deoxyribonucleic acid. Such cells come in four flavors and (due to their atomic shape) tend to pair up and create long strings. These strings become very long, over two inches when held end-to-end (but of course, they fold up dramatically so each can comfortably inhabit a single cell). Since your cells have about 46 inches worth (six billion molecules), each cell contains twenty-three unique strings. They look like this:

Natural Selection- Chromosomes

Let us refer to these strings as chromosomes, and to all of them collectively as the human genome. Finally, since typing “deoxyribonucleic acid” is fairly onerous, we will use the acronym DNA.

In 1956, Francis Crick presented his Central Thesis Of Molecular Biology, which describes how the causal chain DNA → RNA → amino acids → protein ultimately motivates every trait of every living organism.  A gene is a sequence of DNA that encodes a protein. A genotype (some animal’s unique DNA) explains phenotype (that animal’s unique traits).  Genotype-phenotype maps (GP-maps) turn out to be very important in what follows.

Duplication vs. Mutation

Every time a cell duplicates itself (mitosis), its DNA is copied into the new cell. If every cell contains exactly the same code, how can they be different? The basic explanation of cellular differentiation involves feedback loops in the genetic causal chain (collectively named the Gene Regulatory Network). When a lung cell is duplicated, for example, it inherits not just the entire genome, but also proteins for activating lung genes and deactivating other code.

Germ cells are created by a different process entirely. Instead of genome duplication (mitosis), germ cells inherit what is essentially half a genome, in a process known as meiosis. Here’s how these two processes work:

Natural Selection- Mitosis vs. Meiosis

Recall that deoxyribonucleic acid is a collection of atoms. Replicating such a fragile object is imperfect. There are many kinds of ways the process can go wrong; for example:

  1. Replacement Mutation (e.g., AGTC → AATC)
  2. Duplication Mutation (e.g., AGTC → AGGTC)
  3. Insertion Mutation (e.g., AGTC → AGATC)

How many mutations do you have? While you can always get your DNA sequenced to find out, the answer for most people is about sixty.

The Landscape Of Gene-Space

Consider all animals whose genome is three molecules long. How many genetically unique kinds of these animals are there?  Recall there are four kinds of DNA: cytosine (C), guanine (G), adenine (A), or thymine (T). We can use the following formula:

|Permutations| = |Possibilities|^{|Slots|}

Here we have 3^4 = 81 possible genotypes in this particular gene-space. To visualize this, imagine a 4-sided Rubik’s Cube: each dimension is a slot, each cube a particular genotype in the space.

But humans have approximately three billion base pairs; the size of a realistic gene-space is almost incomprehensibly large (4^3,000,000,000), far exceeding the number of atoms in the universe. Reasoning about 3D cubes is easy, reasoning about 3,000,000,000-D hypercubes is a bit harder. So we employ dimension reduction to aid comprehension. If you laid all 4^3,000,000,000 numbers out on a two dimensional matrix, each cell would be so tiny that the surface would appear continuous. We have arrived at our first metaphor identification:

  • A Genotype Is A Location

We can summarize our discussion of mitosis, meiosis, and mutation as follows:

  • An Organism Is A Stationary Point
  • Birth Is Point Creation, Death Is Point Erasure.

Finally, let us explore the concept of genetic distance. From our toy gene-space, let me take seven nodes and draw lines indicating valid replacement mutations between them.

Population Genetics- Visualizing Genetic Distance

The key observation is that distances vary. Many nodes are connected via one mutation, but the minimum distance from top (ATG) to bottom (CCC) is three mutations. In other words:

  • Varying Genome Differences Are Varying Distances

Our gene-space landscape, then, looks something like this:

Population Genetics- Gene Landscape (1)

Species Are Clusters

What is a species? After all, there is no encoding of the word “jaguar” in the jaguar genome. Rather, members of a species share more genetic similarities to one another than other organisms. In terms of our metaphor:

  • A Species Is A Cluster Of Points

In the above landscape, we might have two species. But there are many ways to cluster data. Consider these competing definitions:

Population Genetics- Species Granularity (1)

Which clustering approach is correct? It depends on the scale of our axes:

  • If we chose Granular but are too “zoomed in”, we have accidentally defined four new species of Shih Tzu.
  • If we chose Course but are too “zoomed out”, we have accidentally defined Mammal as its own species.

The point is that scale matters, and we should define species on a scale that makes good biological sense. The most popular scale is that defined by successful interbreeding (i.e., produce fertile offspring). For greater distances (large genetic dissimilarity), such interbreeding is impossible. We therefore constrain the size of our specie clusters by maximum interbreeding distance.

The approach just outlined is the one in use today. However, any man-made criteria for categorizing reality has its stretch points. For example, consider ring species.

Population Genetics- Ring Species (2)

Consider the Larus gulls’ populations in the above image. These gulls habitats form a ring around the North Pole, not normally crossed by individual gulls. The European herring gull {6} can hybridize with the American herring gull {5}, which can hybridize with the East Siberian herring gull {4} which can hybridize with Heuglin’s gull {3}, which can hybridize with the Siberian lesser black-backed gull {2}, which can hybridize with the lesser black-backed gulls {1}. However, the lesser black-backed gulls {1} and herring gulls {6} are sufficiently different that they do not normally hybridize.

Genetic Drift Is Random Travel

Landscapes without movement aren’t very interesting. With our brand-new concept as Species As Clusters, let’s see if we can make sense of travel.

Consider the phenomenon of population bottleneck. Many factors may contribute to population reduction (e.g., novel predators). Often, the survivors are just lucky. Descendants of the survivors tend to be more similar to them than the average genome of the original species. By this process, bottlenecks induces change in the species as a whole:
Population Genetics- Genetic Drift (1)

Why wouldn’t such movement cancel itself out in the long run? The reason why resides in the size of gene-space. For our genome is length two, mutations cancelling each other out would be a fairly common occurence. Would cancelling out increase or decrease on a genome of length 1,000? Surely less. How much less (a forteriori!)  the case for genomes with three billion molecules. By the extreme dimensionality of gene-space, then, we are witness to non-cancellative genetic movement!

  • Genetic Drift Is (Random) Travel.

Importantly, it is not the individuals that travel (modify their genomes), but the species as a whole.

  • Species Are Vehicles.

Viewing the species itself as actor, rather than the individual, is an important paradigm shift of population genetics.


In this post, I introduced the following metaphor:

  • A Genotype Is A Location.
  • Organisms Are Unmoving Points
  • Birth Is Point Creation, Death Is Point Erasure
  • Genome Differences Are Distances

We then strengthened our metaphor with the following considerations:

  • A Species Is A Cluster Of Points
  • Species Are Vehicles
  • Genetic Drift is (Random) Travel.

We are left with the image of specie vehicles clumsily moving around gene-space. But genetic drift is not the only mechanism by which species navigate gene-space. In our next post, we explore a more sophisticated property of living things.