Rainbow of Colors: Monkey See

Color vision is something I take for granted. I forget that a significant portion of the population does not see the range of colors that I can. And I have no way of appreciating the range of colors that birds and bees can see. The natural history of primate color vision makes for an interesting story.

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We see color because the cones in our retinas make three different versions of proteins called opsins. These proteins are responsible for initiating impulses to the brain, and they have differing sensitivities to different wavelengths of light. It is by comparing the signal strength between the three opsins that our brains are able to interpret color. Since we have three types of opsin proteins (S, M and L), we are trichromats.


(Figure shows spectral sensitivities of the opsins in different organisims [1].)

Although there are several types and causes of color blindness, the most familiar cause is genetic and mainly affects men. This is because two of the three opsin genes are located on the X chromosome. Since females have two X chromosomes it doesn't matter if one of them has a defective opsin gene. But if a male has a defective opsin on the X chromosome, he's out of luck.

Color vision appears to have been the norm for most animals--including fish--but most placental mammals are dichromats, apparently because they lost two unnecessary opsins while adopting a nocturnal lifestyle early in their evolution. Most primates are different, however, and this is where the story gets interesting.


There is a basic divide among the monkeys and apes: there are the Old World Monkeys (OWMs) and Apes (including humans), and then there are the New World Monkeys (NWMs). NWM males are dichromats, but some females are trichromats. How can this be? Well instead of having two different opsins on the X chromosome, there are different variants (allels) of the one opsin gene on the X chromosome circulating in the population. Since females have two X chromosomes, they can have two variants of that opsin at once. Such females are called 'allelic trichromats'. Males are stuck with either one or the other variant, and thus remain dichromats. The exception is the howler monkey, which at some point had a gene duplication occur such that the X chromosome has two copies of the opsin gene. One of the opsins mutated such that it has a slightly different wavelength sensitivity, making howler monkeys 'true trichromats,' like us.

OWMs and Apes are true trichromats. The reason for this is similar to the howler monkey. At an early point after the split from NWMs, a gene duplication occured on the X chromosome leading to the existence of two opsin genes of slightly different peak sensitivity. However this was an earlier and separate event from that of the howler monkey. (In the figure above and to the left [2], the arrows indicate lineages that are true trichromats. Red lineages indicate those with a high precentage of OR pseudogenes, as explained below. Click to enlarge.)

All of this is interesting for a number of reasons, including issues of phylogeny, biogeography and so forth, but the story goes one step further. A group of scientists were studying the olfactory receptors (ORs) in primates. These proteins are to smell, what opsins are to vision--except that there are a greater variety of ORs. Specifically, they looked at the proportion of OR genes that are broken (pseudogenes) in a variety of primates and found something interesting. OWMs and Apes have a higher percentage of OR pseudogenes than NWMs, with one exception: the howler monkey. The figure to the right (click to enlarge) shows the percentage of OR pseudogenes in different primate species [2]. Humans have the highest percentage, but note that the only species above 20% are true trichromats. It is too early to say whether there is a causal relationship, but the correlation is striking and suggests that as primates gained better color vision, selective pressure for smell was relaxed, which allowed increasing numbers of ORs to become broken and unused.

As I look out my window, fall colors are on full display. Limited as they may be in comparision to some other animals, I'm grateful for my senses.

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1. Vorobyev, Ecology and Evolution of Primate Colour Vision (pdf), Clinical and Experimental Optometry, 2004, 87:4-5. The same issue of this journal has several additional articles on color vision, freely available here.

2. Gilad et al., Loss of Olfactory Receptor Genes Coincides with the Acquisition of Full Trichromatic Vision in Primates, PLoS Biology, 2004, Vol. 2 Issue 1.

See "The Howler Monkey's Tale" in Richard Dawkins' Ancestor's Tale for a popular-science treatment of primate color vision.

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Failures of Alternative Medicine go Unnoticed

I touched on alternative medicine a couple of posts ago. NBC's Robert Bazell recently published a commentary titled, "Ignoring the failures of alternative medicine."

Last week’s study showing that the widely touted and sold supplement DHEA does nothing to slow the effects of aging was only the latest major piece of research with powerfully negative results from the National Institutes of Health Center for Complimentary and Alternative Medicine. Previous placebo-controlled trials proved the uselessness of St. John’s Wort for depression and saw palmetto for enlarged prostates, shark cartilage for cancer, echinacea for the common cold and glucosamine plus chondroitin sulphate for arthritis. [emphasis added]

But it doesn’t matter much — few seem to care....

No doubt some of the thousands of products sold as dietary supplements work well, but the industry that sells them has neither motivation nor desire to know which ones work and which don’t.

For one physician-scientist-blogger's view, see Orac's take.

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Report: David Calderwood and Voices from the Dust

I recently attended a presentation given by David Calderwood, author of Voices from the Dust. Brother Calderwood served a mission in Uruguay and has subsequently lived in, and traveled to, South and Central America throughout his career. After retiring he returned to graduate school at the University of Texas at Austin to study at the Institute of Latin American Studies where he earned an M.A. Over the years he has collected over 70 chronicles written by Spanish and Portuguese explorers, priests, and soldiers. He was apparently a popular speaker at the recent CES Education Week at BYU.

What follows is my report of his talk, according to my notes.

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The main theme of Bro. Calderwood's talk was that Spanish and Portuguese chronicles, written in the 15-1600's but not published until at least the late 1800's, contain descriptions of native history and folklore that correspond with the Book of Mormon.

Early in the talk he said that researchers are tied to "make-believe histories." The first is evolution and that there was no creation. The second is that Native Americans migrated from Asia 15,000 years ago and that there were no significant outside contacts until Columbus. (He did not specify whether he objected to the early migration, or just the isolation.)

He spent most of the time talking about interesting elements in various chronicles. I will provide names (where I have them) and some of the things they described.

Miguel Cabello Valboa (1586): recorded legends of the earth shaking, the sun being darkened, and the graves being opened.

Felipe Huaman Poma De Ayala (1609): legends of natual disasters including volcanoes, fire from heaven, sand flattening a city, earthquakes and tidal waves.

Diego de Landa: described baptism in the Yucatan. Bro. Calderwood said that the practice was more widespread and that the Maya term "caput sihil" means to be born again or anew.

Martin de Murua: described Incan religious cleansing that involved confession. Bro. Calderwood said that they had rules that correspond well with the Ten Commandments, and that some of the punishments also correspond (eg. adultery punished by stoning). As part of purification, people would say, "I have confessed my sins to my father, the Sun."

Fernando de Montesinos: His reports are ignored by many scholars because they seem outlandish. His writings include a reference to a transition from government by kings to wise men (judges). Describes how ancient records were used to eradicate homosexuality from the civilization [apparently through repentance].

Pedro de Cieza de Leon: wrote that the Chachapoya indians were the whitest he had seen, and that their women were beautiful.

Bro. Calderwood described other documents refering to white indians, and said that there are still white Amerindians in some places. He also showed iconography depicting white and dark figures. In the picture he showed, it appeared that the dark figures were conquering the white figure.

Alonso de Ercilla Y Zuniga: Araucanos used implements of war including bow and arrows, swords, and scimitars. Bro. Calderwood made a point of telling us that Alonso had seen Old World scimitars.

He related a story about a Jewish rabbi in the 1600's named Aaron Levi [I think], who lived in South America. During his prayers he kept having the thought that Native Americans were Jewish. He was introduced to a group who claimed Abraham, Issac, and Jacob as their patriarchs and said that Joseph lives in the middle of the ocean, divided in two parts.

He also discussed metallurgy and the skill with which some ancient American cultures could manipulate gold, silver, and copper. He also mentioned their skill with cloth and their ability to make a fiber derived from animal hair that was likened to silk.

All in all I thought that the presentation was interesting. At first glance it seems remarkable that the various chronicles contain things that really seem to reasonate with the Book of Mormon. Yet without having studied the material myself--and again, having not read his book--I was at times a little skeptical of the connections he was making. For example, he showed some complicated iconography and explained the interpretation of many of the elements. Since they were of a religious nature it was pretty easy to draw connections to the Book of Mormon. But beyond that, he then pointed our attention to a figure whose meaning is unknown, and suggested that the meaning comes from a particular part of the Book of Mormon. There were a couple of other instances of the same type of thing, and I found myself skeptical that it is really that easy.

It seems to me that it is rather easy to fool ourselves on an issue like this, and although the intent of his talk was to build faith, I did not see evidence of skepticism except as applied to mainstream thought. But if there are real connections to be made, there must also be a host of false positives as well. If LDS scholarship is to have a credible voice, it must separate out the wheat from the chaff. I look forward to seeing how his book fares in the FARMS Review.

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Stewart Article in FARMS Review

I recently blogged on David Stewart's essay on DNA and the Book of Mormon, and expressed concern about elements of it. Today I see that it has been published in the latest FARMS Review. My quick look at it did not detect any editing differences from the FAIR version.

Stewart may make some good points, but I don't think FARMS has done itself any favors by publishing the essay in its present form.


By the way, Frank Salisbury also has two reviews dealing with evolution in this issue (here and here.)

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Expiration of the Rising Generation

Dang. I had this post pretty much composed two months ago, and now I see that Blogger of Jared has taken up the issue. Well, here is my take.

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In April of 1843, Joseph Smith said the following:

were I going to prophecy I would prophecy the end will not come in 1844 or 5 or 6. or 40 years ["more" crossed out here] there are those of the rising generation who shall no taste death til christ comes. I was once praying earnestly upon this subject. and a voice said unto me. My son, if thou livest til thou art 85 years of age, thou shalt see the face of the son of man.--I was left to draw my own conclusions concerning this & I took the liberty to conclude that if I did live til that time ["Jesus" crossed out here] he would make his appearance.--but I do not say whether he will make his appearance or I shall go where he is.--I prophecy in the name of the Lord God.--& let it be written. that the Son of Man will not come in the heavens till I am 85 years old 48 years hence or about 1890.

[bracketed items above are from the text at the link]

Earlier, in February of 1835, Joseph had said,

...it was the will of God that they should be ordained to the ministry and go forth to prune the vineyard for the last times, or the coming of the Lord which was nigh, even fifty six years should wind up the scene. [link]

It seems clear that Joseph thought, based at least in part on the criptic answer to his prayer, that the Second Coming would occur around 1890-91.

In Mormon Doctrine (entry: "Second Coming") Elder McConkie wrote that a young man with at least one child on the day of Joseph's speech might live another 50+ years and father additional children in his old age with a younger wife. The children born in old age would still be part of the 'rising generation', having older siblings that were alive in 1843. These later children could easily live past the year 2000.

Using McConkie's explanation, when can we consider the 'rising generation' to have passed? Here is a spreadsheet I put together. I used 110 years old as the maximum mortal age. (Click to enlarge.)




So I guess it is within the realm of biological possibility that one of McConkie's 'rising generation' will be with us until 2048. I expect to be retired by then--if the Second Coming has not yet occured.

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Providential Plants: The Ridiculous

This video clip from a creationist video co-hosted by Kirk Cameron (of Growing Pains fame) has been making its way around the internet. In the moments preceeding the clip, the other host outlines a scenario where a soda can came into existence via natural and random forces, and then says that to think such a thing is an insult to intelligence. Then he give us the "athiest's nightmare":

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In case you were unable to watch the clip, here is a summary. The banana shows evidence of design because:

1. It fits well in the hand.
2. It has a non-slick peel.
3. It has a color scheme to let you know when it is ripe.
4. The peel has a tab and perforations allowing for easy removal, and it hangs gracefully over the hand. Oh, and it is biodegradable.
5. The banana has a pointed end for "ease of entry," is the right size for the human mouth, and is curved toward you.
6. It is chewy and easily digested.

This argument is silly enough on its own, but to top it off the banana he is holding (and that we are most familiar with) is a domesticated type--wild bananas are tough and full of seeds (or so I understand). Evidently the banana needed some human-selected improvement before it became such a powerful witness to God's genius.

Is God glorified by this?

(If you are so inclined, you can watch the whole video here.)

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Providential Plants: The Danger

My last post used Alma 46:40 as a starting point to discuss the role of God in medicinal plants and I mentioned that some people take such scriptures literally. In discussing what science may look like in the millennium, John Pratt (of Meridian Magazine) cites the scripture above and then writes [1]:

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It will probably be discovered in the millennium that the modern practice of trying to extract the one "miracle ingredient" from a plant has overlooked the fact that the Creator has put a combination of chemicals and enzymes together for a certain purpose. Note also that the scripture does not say "to mask symptoms," which seems to be the modern quick-fix method of taking medicine for relief without getting to the cause of the problem.

In my view this is wrongheaded. As stated before, organisms do not produce substances solely as a favor to other organisms. Furthermore, although reductionism in medical science may not always be a virtue, understanding the molecular actions of drugs is important. But beyond that, this passage gives the impression that ancient healers had wisdom and understanding surpassing modern doctors, or that we would be better off with less precision in our drug research. There is no doubt that traditional healers hit on some useful discoveries, but it is demonstrable that the lion-share of medical success has come in recent decades through the application of scientific knowledge. There may be room for legitimate criticism of quick-fix mentality, but our ability to understand and treat the real causes of disease is unparalleled in history. If God really prepared such a pharmacopoeia for the use of man, I can't help but wonder why he didn't provide more information about it.

But is there harm in the providential view? Certainly not in and of itself. However some adopt the mindset that 'natural' (whatever that means) is equal to 'good' and become consumers of alternative medicine. The alternative medicine industry is not subject to the same oversight and regulation that mainstream medicine is, which means that as long as the producers of such products word their claims carefully they do not have to prove the efficacy--or even the safety--of their products [2,3]. In my view privileging alternative medicine (such as 'natural' dietary supplements) over mainstream medicine in the pursuit of God's natural cures is a mistake that can be harmful to health.

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1. One of my first posts on this blog was a review of this article.
2. For a critical summary of natural supplements see here.
3. Overview of Dietary Supplements, FDA, 2001

Unlike drug products that must be proven safe and effective for their intended use before marketing, there are no provisions in the law for FDA to "approve" dietary supplements for safety or effectiveness before they reach the consumer. Also unlike drug products, manufacturers and distributors of dietary supplements are not currently required by law to record, investigate or forward to FDA any reports they receive of injuries or illnesses that may be related to the use of their products. Under DSHEA, once the product is marketed, FDA has the responsibility for showing that a dietary supplement is "unsafe," before it can take action to restrict the product's use or removal from the marketplace.

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Providential Plants

The germ theory of disease is a modern understanding. Consequently there is little to go on in the scriptures to help us understand the illnesses that afflicted the people. The Book of Mormon has one statement on this topic that I've noticed.

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Alma 46:40

And there were some who died with fevers, which at some seasons of the year were very frequent in the land—but not so much so with fevers, because of the excellent qualities of the many plants and roots which God had prepared to remove the cause of diseases, to which men were subject by the nature of the climate—

The description of the fevers as seasonal suggests something like a mosquito-borne virus to me. And evidently there was a folk medicine industry that produced (real, perceived, or a mix) results. And there we hit a dead end.

So I want to turn to another aspect of this verse--the providence of God in providing treatments. There are other scriptures that carry a similar message. A prominent one is D&C 59:16-21 [1]. In the broader theological context this seems somewhat contradictory to me: we are in a fallen world (where the ground is cursed) yet we are in a providental and designed world (where God has given us solutions for our problems--in this case treatment for illnesses).

Now consider the following passage from Origin of Species:

Natural selection cannot possibly produce any modification in any one species exclusively for the good of another species... If it could be proved that any part of the structure of any one species had been formed for the exclusive good of another species, it would annihilate my theory, for such could not have been produced through natural selection. Although many statements may be found in works on natural history to this effect, I cannot find even one which seems to me of any weight. It is admitted that the rattlesnake has a poison-fang for its own defence and for the destruction of its prey; but some authors suppose that at the same time this snake is furnished with a rattle for its own injury, namely, to warn its prey to escape. I would almost as soon believe that the cat curls the end of its tail when preparing to spring, in order to warn the doomed mouse.

I think that these competing ways of seeing the world each have their place, and each have their excesses. On the one hand, we understand that in the natural world organisms do not expend energy to produce things merely as a favor to other organisms. Antibiotics are produced by fungi for their own fight against bacteria, not for our medical use. And plants produce flowers and fruit to get their pollen and seeds spread, not just to give us something nice to look at or eat. In the rich biological diversity of this planet it seems like a natural coincidence that some organisms will make substances useful to our health, just as some make substances harmful to our health. Taken to excess, these principles might lead us to be ungrateful toward God (if we believe in him at all)--we've solved our own problems without his help, thank you very much.

On the other hand God tells us that the earth is here to be inhabited and that we should be grateful for it and the potential that its materials offer us--something I think holds whether or not he intervened to ensure that medicinal plants exist. Furthermore, we should be grateful to live in a prosperous environment that makes scientific research possible, and for any direct inspiration of scientists.

But I am framing things from my point of view. There are those who take Alma 46:40 at it's word--that God did prepare plants for medical use--and I want to discuss this some more in a separate post.

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1. It is interesting to me that the Word of Wisdom was given 2 years later, which put qualifiers on these verses.

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Book of Mormon: Everything But the Timing

I'm late noticing this, but FAIR has posted a presentation given at its 2006 conference by David Stewart (a medical doctor) on the Book of Mormon--DNA issue. Stewart's basic thesis appears to be that the reason Native American genetics resemble that of Asians is because some of the Asians are actually descended from the lost tribes of Israel. Thus, Native Americans (through Lehi et al.) have a common ancestry with some Asians, rooted in Israel. Stewart therefore has no use for a limited geography model. However his own presentation contains elements that contradict him.

(My following comments should not be interpreted as disbelief in Book of Mormon historicity.)

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1. He acknowledges that the timing doesn't work (yet). This is because archeological and genetic evidence place the colonization of the Americas back around 15,000 years ago, and he is moving much of that up to 600 B.C.

2. He acknowledges that, based on mtDNA data, there has been genetic continuity from ancient Native Americans to today's. In other words, the common ancestry of mtDNA lineages in Native Americans and Asians appears to be genuinely ancient (although correspondingly ancient Asians have not been examined).

3. He argues that Jewish genetics have been so scrambled over the centuries that we should not expect to see direct correlation between Lamanite DNA and modern Jewish--or even Near Eastern--DNA. Yet at the same time his thesis requires that the genetics of the lost tribes have remained in tact enough that we can find correlation between it and Lamanite DNA. Do we have good reason to think such would be the case?

Stewart makes clear the timeframe that most scientists accept for the migration to America. Nevertheless the reader might be confused about the message of the quote from a paper by Mark Seielstad regarding "problems with early dating". In the paper they argue for a migration time of 15,000-18,000 years before present. This date is later than those proposed in some mtDNA studies (>20,000 years before present), and more in line with archeological and linguistic evidence. In this context 'later' and 'earlier' are relative terms that are still far removed from the time of Lehi, as Stewart correctly notes.

I couldn't help but notice this sentence: "To my knowledge, critics to date have not been able to generate a single peer-reviewed publication in a scientific journal on Book of Mormon DNA issues." I think Stewart is confused about where the burden of evidence lies at the moment. The scientific community--rightly or wrongly--understands Native American origins quite differently from what is told in the Book of Mormon. The Book of Mormon scenario must be on the scientific table before any serious journal is going to publish criticism of it. What Murphy and Southerton have done is to make the (somewhat) broader LDS community aware of the prevailing scientific view (with some accompanying polemics).

Finally, Stewart concludes:

There is still much we do not know about the genetics of ancient and modern populations, but careful study demonstrates that the teachings of LDS prophets are fully consistent with existing DNA data.

I agree with the first part of the sentence. It seems to me the second part--as he has argued for it--is only true if you grant some generous assumptions and ignore inconvenient evidence.

The genetic issue is a thorny one. In the face of uncomfortable data some abandon the Book of Mormon while others remain patient. Stewart's intent is to make room for faith, for which I commend him. Nevertheless I think his proposal faces significant hurdles. I would urge caution.

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Quantitative Chiasmus

This news is a little old, but I wanted to bring it to the attention of any who might be interested. Recently Dialogue published a paper online that uses a quantitative approach to investigate chiasmus in one of Joseph Smith's letters. The work is an extension of a previous BYU Studies article by the same authors.

The authors seek to put probablilities on chiastic passages to determine whether they are a result of chance or intention and they make for interesting reading. Their methodology has not gone unchallenged, and you can read the back-and-forth at Dialogue.

(There was also some discussion of this topic at By Common Consent.)

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Matzke on Flagella, Etc.

Nick Matzke of the NCSE, and regular contributor to The Pandas Thumb, has been a busy guy. He played an important role (behind the scenes) in the Kitzmiller v. Dover Area School District case, and I want to highlight some things he has written recently.

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1. Having been profiled in Seed Magazine, Matzke gives a few additional insights into his role in the Dover case, including how they learned that the book at issue in the case had been originally written as a creationism text. This evidence undercut the defense's case that intelligent design is science, not religion.

2. He recently gathered up published measurements for hominin cranial capacity and made a couple of nifty charts. (Original posts here and here.)



3. He has co-authored a paper in the current issue of Nature Reviews Microbiology where he takes on ID arguments about bacterial flagella. Unfortunately a subscription is required to read the article, but Nick has posted additional comments here.

Having read the paper, I will just list some of the key points made.

a. ID arguments tend to treat the flagellum as an essentialist type, however there are a diversity of flagella.

Therefore, there is no point discussing the creation or ID of 'the' bacterial flagellum. Instead, one is faced with two options: either there were thousands or even millions of individual creation events, which strains Occam's razor to the breaking point, or one has to accept that all the highly diverse contemporary flagellar systems have evolved from a common ancestor.

b. Some of the core flagellar proteins show sequence similarity that indicates common ancestry via gene duplication. In some cases, related proteins are involved in other non-flagellar processes, suggesting that flagellar proteins could have been co-opted from other functions.

c. While the exact (historical) steps to building a flagellum through variation and natural selection are impossible to know, looking at the range of differing flagella may provide clues.

d. Ideas for research are put forward, like--for example--using phylogenetic analysis to reconstruct ancient proteins and evaluating them for function.

An alternative, more radical, option would be to mdel flagellar evolution prospectively, for example, by creation random or minimally constrained libraries and then iteratively selecting proteins that assemble into ever more sophistocated artificial analogues of the flagellar filament.

4. Finally, I just couldn't help but point this out--I think it may be one of the silliest things I've read all year. (If you're in a hurry, head to the quote at the bottom.)

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New York Masons

Today the New York Times had an article (registration may be required) discussing efforts of Masons to open up a little in order to encourage membership. The article had this accompanying picture:

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What there is, inside the [New York] grand lodge headquarters, are a dozen ornate rooms where some 60 lodges still hold meetings regularly.

Those dozen rooms have no windows. Leading the way into one of them, the Grand Master, or leader of all Masons in New York State, Neal I. Bidnick [seated], said the layout was no different from any other lodge room in the world, with an altar and candles in the center. At the one end are two pieces of stone, each about the size of a cinder block--one uncut, the other finished.

"We take a good man and polish the rough edges,"” Mr. Bidnick said. (The Masons do not admit women.)

Aside from anything else, the architecture reminded me of this.

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Benjamin Silliman: Geology, Genesis, and Old Ideas

In a recent discussion of Joseph Smith and the day-age theory of creation, I mentioned an appendix to an 1839 geology text that was written by Yale professor Benjamin Silliman. I wanted to highlight it again because it makes for some interesting reading. The appendix was a discussion of various ways to reconcile Genesis with geology, and it shows that a number of the issues and approaches that get discussed today have actually been around for a long time.

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One of his first orders of buisness was to deal with the idea that God created fossils in situ.

With such persons we can sustain no discussion, since there is no common ground on which we can meet: we must leave them to their own reflections, for they cannot be influenced by reason and sound argument, and can, with or without evidence, believe any thing that accords with their prepossessions. And yet we have known such individuals - those who either deny the best established facts, or endeavor to avoid their effect by making the most absurd suppositions, inconsistent alike with the truths of science, and with candor and fair dealing in argument.

Silliman then presented and discussed five proposals, rejecting all but one:

1. "The present crust of the planet has been regularly formed between the first creation "in the beginning," and the commencement of the first day." This is essentially a version of the gap theory of creation, which became very popular in the early twentieth century.

2. "The present crust was formed from the ruins and fragments of an earlier world, re-arranged and set in order during the six days of the creation." This is a form of catastrophism, however it also reminds me of Joseph Smith's 1841 comment about the earth having been formed from broken-up planets.

3. "It has been supposed that the succession of geological events may have happened in the first ages of the world, after the creation of man, and before the general deluge."

4. "It has been supposed that a general deluge will account for all geological events." Although Silliman rejected this view as "entirely inadmissible," it was later promoted in the writings of Seventh-day Adventist George McCready Price, was further popularized by Whitcomb and Morris in The Genesis Flood, and has since remained part of the young-earth creationist framework.

5. "The divisions of time called days in the Genesis are not necessarily restricted to twenty four hours, but may be understood to be periods of indefinite length." As discussed before, this is the day-age theory and appears to be Silliman's preferred explanation.

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