Human embryology again

Returning to the topic of human embryology, here is a human fetal timeline for the first 16 weeks post fertilisation (obstetricians count from the LMP = last menstrual period, which adds about 2 weeks). It is a little disturbing quite how much scientific misinformation is being circulated in regard to the topic. False information is not conducive to honest debate, and is highly corrosive of the trust people have in professionals such as scientists (it’s also unethical on both religious and Kantian grounds). In particular, contrary to what some have suggested:

• the fetal or embryonic heart begins beating at about 21 days after conception, as any textbook will point out
• as the table shows, after a few weeks, the fetus or embryo is not “too small to see with the naked eye”

Fetal length data in the table is mostly from here. Except where indicated, linked images are subsequent to miscarriage or to surgery to resolve ectopic pregnancy, so may be distressing to some readers.

Week post fertilisation	Week post LMP	Fetal length	Image
1	3	0.01 cm / 0.005 inches	8–cell image
2	4	0.02 cm / 0.008 inches	–
3	5	0.1 cm / 0.04 inches	heart begins beating at 21 days
4	6	0.5 cm / 0.2 inches	image on flickr
5	7	1 cm / 0.4 inches	image on wikimedia
6	8	1.6 cm / 0.6 inches	image on flickr
7	9	2.3 cm / 0.9 inches	image on flickr
8	10	3.2 cm / 1.3 inches	–
9	11	4.1 cm / 1.6 inches	–
10	12	5.4 cm / 2.1 inches	–
11	13	6.7 cm / 2.6 inches	ultrasound image
12	14	14.7 cm / 5.8 inches	–
13	15	16.7 cm / 6.6 inches	–
14	16	18.6 cm / 7.3 inches	–
15	17	20.4 cm / 8 inches	ultrasound image
16	18	22 cm / 8.7 inches	–

Below (from here) is a chart of heart development:

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Modal logic, ethics, and obligation

Recently, I posted about necessary truth, the logic of belief, and epistemic logic. I would like to follow up on that one more time by discussing deontic logic, the logic of obligation and moral action. We can capture this concept using the 4 rules of D4 modal logic. The first 3 of these are the same as those I used for belief. I am replacing the previous modal operators with  Ⓞ  which is intended to be read as “it is obligatory that” (hence the O in the circle):

• if P is any tautology, then  Ⓞ P
• if  Ⓞ P  and  Ⓞ (P ⇒ Q)  then  Ⓞ Q
• if  Ⓞ P  then  Ⓞ Ⓞ P
• if  Ⓞ P  then  ~ Ⓞ ~P

where  ~ Ⓞ ~P  is read as “~ P is not obligatory,” i.e. “P is permissible.” For those who prefer words rather than symbols:

• if P is any tautology, then P is obligatory
• if P and (P implies Q) are both obligatory, then Q is obligatory
• if P is obligatory, then it is obligatory that P is obligatory
• if P is obligatory, then P is permissible

For these rules as they stand, the only things that are obligatory are necessary truths like 2 + 2 = 4. This is because you can’t get an “ought” from an “is.” Apart from the first rule, there is no way of introducing a  Ⓞ  symbol out of nowhere. Consequently, if we are to reason about ethics and morality, we must begin with some deontic axioms that already contain the  Ⓞ   symbol. For people of faith, these deontic axioms may be given by God, as in the 10 Comandments, which include:

Ⓞ  you do not murder.
Ⓞ  you do not commit adultery.
Ⓞ  you do not steal.
Ⓞ  you do not bear false witness against your neighbor.

Immanuel Kant famously introduced the categorical imperative, a deontic axiom which Kant thought implied all the other moral rules, and thus provided the smallest possible set of deontic axioms:

Ⓞ  [you] act only according to that maxim whereby you can, at the same time, will that it should become a universal law.

Others have suggested the greatest happiness of the greatest number as a principle. Fyodor Dostoevsky, William James, and Ursula Le Guin are among those who have explained the problem with this:

“Tell me yourself, I challenge your answer. Imagine that you are creating a fabric of human destiny with the object of making men happy in the end, giving them peace and rest at last, but that it was essential and inevitable to torture to death only one tiny creature – that baby beating its breast with its fist, for instance – and to found that edifice on its unavenged tears, would you consent to be the architect on those conditions?” (Fyodor Dostoevsky, “The Grand Inquisitor,” in The Brothers Karamazov, 1880; 4.35 on Goodreads)

“Or if the hypothesis were offered us of a world in which Messrs. Fourier’s and Bellamy’s and Morris’s Utopias should all be outdone and millions kept permanently happy on the one simple condition that a certain lost soul on the far-off edge of things should lead a life of lonely torture, what except a specifical and independent sort of emotion can it be which would make us immediately feel, even though an impulse arose within us to clutch at the happiness so offered, how hideous a thing would be its enjoyment when deliberately accepted as the fruit of such a bargain?” (William James, “The Moral Philosopher and the Moral Life,” 1891)

“Some of them understand why, and some do not, but they all understand that their happiness, the beauty of their city, the tenderness of their friendships, the health of their children, the wisdom of their scholars, the skill of their makers, even the abundance of their harvest and the kindly weathers of their skies, depend wholly on this child’s abominable misery.” (Ursula K. Le Guin, “The Ones Who Walk Away from Omelas,” 1973; reprinted in The Wind’s Twelve Quarters, 1975; 4.05 on Goodreads)

The meaning of deontic statements can be described using Kripke semantics, which exploits the idea of possible worlds (i.e. alternate universes). To say that some statement is obligatory is to say that the statement would be true in better possible worlds (we write w₁ → w₂ to mean that w₂ is a better possible world than w₁).

In any given world v, the statement  Ⓞ P  is equivalent to :

• P  is true in all better worlds w_i (i.e. all those with v → w_i)

Likewise, in any given world v, the statement  ~ Ⓞ ~P  (P is permissible) is equivalent to:

• P  is true in at least one better world w_i (i.e. one with v → w_i)

The rules of deontic logic imply two conditions on these arrows between possible worlds:

• if  w₁ → w₂ → w₃  then  w₁ → w₃  (i.e. chains of arrows are treated like arrows too)
• in every world v there is at least one arrow  v → w  (i.e. chains of arrows don’t stop; this includes the case of  v → v)

A number of philosophers have suggested that deontic logic leads to paradoxes. In all cases that I have seen, these “paradoxes” have involved simple errors in the use of deontic logic – errors that become obvious when the deontic statements are translated into statements about possible worlds.

There are limitations to deontic logic, however. For example, if we say that it is obligatory not to steal, this means that, in all better possible worlds, nobody steals. If we also say that it is obligatory to punish thieves, this means that, in all better possible worlds, thieves are punished. However, if it is obligatory not to steal, better possible worlds have no thieves, so the two statements do not combine well.

Some people would, no doubt, suggest that fiction like that of Dostoevsky is a better tool than logic for exploring such issues. In cases where the writer is a genius, they are probably right.

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In this post series: logic of necessary truth, logic of belief, logic of knowledge, logic of obligation

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Fetal heartbeat and political debate

Following the recent Dobbs v. Jackson Women’s Health Organization decision in the US, that nation is struggling with two moral/philosophical questions:

• Is the unborn human fetus a person, and if so from when?
• Does the unborn human fetus deserve legal protection, and if so from when?

These are independent questions – a puppy or kitten is not a person, but nevertheless has legal protection from animal cruelty. The now-repealed Roe v. Wade (1973) and Planned Parenthood v. Casey (1992) decisions essentially answered the second question as “yes, from viability.”

These questions are moral and philosophical, not scientific. However, scientific questions do arise in the debate. Is the fetus alive? Yes, obviously. Is it human? Well, it has different hemoglobin from adult humans, but the fetus is obviously Homo sapiens. Does the fetus have a heartbeat? Surprisingly, that seems to be controversial, although every textbook I have seen agrees that the heart is functional very early (how else would the developing fetus get oxygen and nutrients?). To quote some sources:

• “The heart is the first organ to develop. In the human embryo, the heart begins beating at about 21 days after conception [i.e. 5 weeks after LMP = last menstrual period].” (Anatomy and Physiology of the Circulatory and Ventilatory Systems, page 2)
• “The fetal–placental circulation begins at about 9 days postfertilization … A functional circulation is established by the end of the third developmental week [i.e. 5 weeks after LMP].” (Fetal MRI, page 405)
• “In a developing embryo, the heart has developed enough by day 21 post-fertilization to begin beating [i.e. 5 weeks after LMP]. Circulation patterns are clearly established by the fourth week of embryonic life. It is critical to the survival of the developing human that the circulatory system forms early to supply the growing tissue with nutrients and gases, and to remove waste products.” (Anatomy and Physiology 2e)
• “Circulation of fetal blood in the placental circulation begins approximately 21 days postfertilization in humans [i.e. 5 weeks after LMP].” (Handbook of Developmental Neurotoxicology, page 68)
• “1. Fetal heart development begins during the first month of gestation. At about 21 days of gestation, the fetal heart begins beating, and blood begins circulating [i.e. 5 weeks after LMP]. Between the second and seventh weeks of gestation [i.e. 4 to 9 weeks after LMP], the primitive fetal heart undergoes a series of changes that create the four-chambered heart and its great arteries. 3. During gestation, the lungs are nonfunctional, and fetal oxygenation occurs via the placenta.” (Pediatric Nursing, page 223)

In my view, accurate discussion of the scientific facts is a necessary preliminary to addressing the moral and philosophical questions.

Doppler ultrasound is routinely used to detect fetal heartbeat and the velocity of fetal blood flow. The scientific principle known as the Doppler effect allows the detection of motion. It is the principle behind speed cameras, and it allows bats to “hear” the fluttering wings of a distant insect. During first-trimester screening (at around 11 to 13 weeks after LMP), professional Doppler ultrasound devices are sensitive enough not only to detect fetal heartbeat, but to detect blood flow abnormalities in various parts of the fetal circulatory system.

Fetal heartbeat at 13 weeks (from here). S is the ventricular systolic wave, D the early diastolic, A the atrial contraction.

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Some thoughts on Roe

The hot topic at the moment is the recent “repeal” of Roe v. Wade by the US Supreme Court. This topic involves not only legal, but also moral, social, and scientific issues. This blog being a science blog, it’s appropriate to comment on the scientific issues here, and to that end I have produced the chart of human prenatal development above. Horizontal bars show fetal size on a logarithmic scale, and the two images are from Wikimedia and from USAID. Confusingly, two time scales are in regular use for prenatal development, one starting at the last menstrual period, and the other at fertilisation (around 2 weeks later). The chart shows both.

Roe v. Wade had, in fact, largely been overturned by Planned Parenthood v. Casey in 1992. The majority of people in the US (around 63%) believe that abortion should be legal in some cases but illegal in others (although views vary widely between demographic groups and from state to state). Roe v. Wade claimed a constitutional right to an abortion based on a constitutional right to privacy, and attempted to draw a cutoff for abortion legality based on the trimester of pregnancy:

1. “For the stage prior to approximately the end of the first trimester, the abortion decision and its effectuation must be left to the medical judgment of the pregnant woman’s attending physician.
2. “For the stage subsequent to approximately the end of the first trimester, the State, in promoting its interest in the health of the mother, may, if it chooses, regulate the abortion procedure in ways that are reasonably related to maternal health.
3. “For the stage subsequent to viability the State, in promoting its interest in the potentiality of human life, may, if it chooses, regulate, and even proscribe, abortion except where necessary, in appropriate medical judgment, for the preservation of the life or health of the mother.”

Planned Parenthood v. Casey rejected both of these ideas, grounding a right to abortion instead in the due process clause of the 14^th Amendment (“nor shall any State deprive any person of life, liberty, or property, without due process of law”), and drawing a new legal line solely based on viability (the age at which the unborn baby can survive outside the womb) rather than on “Roe’s rigid trimester framework.”

The Supreme Court of the United States: the Roberts Court

Viability has some appeal as a guideline, since many people consider it problematic to kill an unborn baby which could be delivered by caesarean and then cared for successfully in the neonatal intensive care unit down the hall. However, as the recent judgement by the Roberts Court in Dobbs v. Jackson Women’s Health Organization notes, viability “is heavily dependent on factors – such as medical advances and the availability of quality medical care – that have nothing to do with the characteristics of a fetus.” In fact, the viability threshold has been dropping at around a week per decade, sitting now at around 22 or 23 weeks (see the chart). Dobbs also took issue with the constitutional aspects of the decision in Casey, overturning it (and what was left of Roe), so that “the authority to regulate abortion is returned to the people and their elected representatives.” Some of “the people” have been very happy about this, while others have protested.

Another scientific (or rather, technological) issue relevant to the decision in Dobbs has been the widespread use of obstetric ultrasonography in the United States. Janelle Taylor notes that “the obstetrical exam has come to incorporate rituals of showing and telling and giving out pictures” (we have all seen them on Facebook). Such images have greatly influenced how the fetus is viewed by the population at large. Unsurprisingly, such images have also lent support to pro-life campaigners, since they give a very clear face to the unborn. This article in The Atlantic notes that “in recent years, pro-life activists have been more successful in using that tool [scientific evidence] to shift the terms of the policy debate.”

More complex has been the debate on whether the unborn human can feel pain. Even in adults, pain is complex, with two separate human pain systems, one more precisely localised, and the other more affective (it “hurts” more). No real scientific consensus currently exists on when a fetus can feel pain (indeed, how could you really prove a hypothesis here?). Various stages are reported in the literature, some as early as 14 weeks, and this literature has been heavily cited as part of the ethical debate on abortion. Other writers have, rather disturbingly, suggested that only adult human beings can truly feel pain. The debate in the US and elsewhere is ongoing.

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Social Media, Marketing, and the Fyre Festival

In traditional Christian theology, Satan is the ultimate marketing genius. Not being able to create, Satan has no actual product to sell – merely illusions. However, being a fallen angel, he does have supernatural intelligence. He also has a large crowd of “influencers” willing to endorse the nonexistent product. The book and film of Stephen King’s Needful Things illustrate the concept brilliantly, as the main character (played to perfection by Max von Sydow) uses his supernatural marketing genius to con people into trading their souls for useless bits of junk:

Of course, that kind of marketing is an ideal that mere human beings cannot achieve. Beneath the ridiculous Kendall Jenner advertisement, Pepsi has an actual product to sell. It may only be flavoured sugar-water, but that’s not a product to be sneered at – I remember a hot day in rural Thailand some decades ago when it was the only safe thing to drink.

Yet we may be closing in on what Max von Sydow could do. Browser history analysis and sophisticated predictive algorithms can stand in for the supernatural intelligence. YouTube helps to sell the illusion. And Instagram provides influencers galore. The recent Fyre Festival is perhaps the closest approach ever to the ideal. The musicians, accommodation, and food promised to the paying clientele do not appear ever to have been organised (although there apparently were a few waterlogged tents and cheese sandwiches). But the promo was great.

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A fable about science and climate change

This post will tell a simple fable. The characters are fictional, although the scenario is based on reality. At the end of the fable are some questions that puzzle me.

The smelter at Davy before it closed (photo: Jmchugh)

Billy-Bob Smith lives in the small town of Davy in the US South. He worked in the aluminium smelter there, until pressure from environmentalists closed it down. He is now unemployed (and rather bitter).

Aluminium production is very energy-intensive (the metal has been called “crystallised electricity”), and the smelter at Davy was fed by coal-fired power. Its demise is part of the general decline in US aluminium smelting (see the chart below, produced from this data).

Of course, demand for aluminium doesn’t just go away – world aluminium production is actually increasing. The plant at Davy was replaced within the year by a new plant in China, which was also fed by coal-fired power. In fact, in 2015 about two-thirds of Chinese electricity production (900 GW) was coal-fired. Chinese coal-fired power generation is projected to increase by 20% to 1100 GW in 2020 (making up about 55% of overall Chinese electricity production in that year, given the non-coal power plants that will also be coming on line). For comparison, the new coal-fired capacity being added in China each year is roughly equal to the entire generation capacity of Australia.

Billy-Bob Smith is very cynical about the environmentalists who effectively outsourced his job to China, with (as he correctly points out) no net benefit to the planet, and no net reduction in carbon emissions. In fact, Billy-Bob believes that the environmental activists in his state were funded by the Chinese government to destroy American jobs. Needless to say, he voted for Donald Trump in the recent US election.

Coal-fired power plant in Shuozhou, China (photo: Kleineolive)

Alicia Jones is a professor of atmospheric physics at a university not far from Davy. She has made significant advances in climate modelling, improving the way that radiative forcing is handled in computer models. There is even talk of nominating her for a Nobel Prize one day. Outside of her university work, she regularly gives talks to schoolchildren on the threat of climate change and the need to address the problem before it’s too late. She also frequently appears on local television. She was part of the group which lobbied to close down the smelter at Davy, in the recent US election she voted for Jill Stein, and she has marched several times in Washington, DC.

US Green Party presidential candidate Jill Stein (photo: Tar Sands Blockade)

My questions are these:

1. What makes an intelligent person like Alicia Jones believe that simply moving carbon emissions to China actually addresses climate change?
2. Being fully aware of the usefulness of computer modelling, why did Alicia Jones not do any economic modelling on the expected follow-on effects of closing the Davy plant?
3. Is virtue ethics, deontological ethics, or consequentialism the best ethical framework for handling questions of this kind?
4. In general, does the expertise of scientists lend any credibility to their economic, political, or philosophical pronouncements? Should it do so?
5. What does it say about Alicia Jones’ ability to communicate scientific issues that over 50% of people in her state (people like Billy-Bob) do not believe in anthropogenic climate change at all? What does it say about scientific communication in general?
6. Do problems with peer review affect the public perception of science?
7. What does it say about the education system in the USA that Billy-Bob does not even believe that the earth is warming? After all, many US cities have temperature records going back over a century. Mean temperatures for Newport, RI, for example, show a 1.7°C rise between 1893 and 2016 (see chart below – the blue line is a cubic interpolation, while the red line is the result of loess smoothing).
8. What can be done to improve this particular debate?

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On fairy tales

“About once every hundred years some wiseacre gets up and tries to banish the fairy tale,” C.S. Lewis wrote in 1952. The wiseacre of our time seems to be Richard Dawkins who, two years ago, told the world that fairy tales could be harmful because they “inculcate a view of the world which includes supernaturalism” (he had said similar things in 2008). In a later clarification, he added that fairy tales could “be wonderful” and that they “are part of childhood, they are stretching the imagination of children” – provided some helpful adult emphasises that “Do frogs turn into princes? No they don’t.”

But many scientists grew up with, and were inspired by, fantasy literature. For example, Jane Goodall tells of growing up with the novel The Story of Doctor Dolittle (as I did!). In fact, many science students and professional scientists avidly read fantasy literature even as adults (as they should). The booksthatmakeyoudumb website lists, among the top 10 novels read at CalTech and MIT, Harry Potter, Dune, and The Lord of the Rings. And Alice in Wonderland was written by a mathematician.

This is a science blog, so I have a strong emphasis on scientific truth, which tells us many important ecological and physiological facts about, for example, frogs. Without science, we’d all still be struggling subsistence farmers. But there is actually more than scientific truth out there.

There is also mathematical truth. Are the links in this frog network all equivalent? Yes, they are – but that is decided by mathematical proof, not by scientific experiment. It is in fact a purely abstract mathematical question – the background picture of the frog is actually irrelevant.

And there is ethical truth. Is it OK to eat frog’s legs? Science does not give us the answer to this (although logic can help us decide if our answer is consistent with our other beliefs), but fantasy literature often helps us to explore such ethical questions. Tolkien’s The Lord of the Rings is one superb example. Would you “snare an orc with a falsehood”? Would you attempt to take the One Ring and “go forth to victory”?

There is metaphorical truth. A frog may, in spite of what Dawkins says, be a handsome prince – there’s more to the universe than can be seen at first glance. Or, as Antoine de Saint-Exupéry put it, “What is essential is invisible to the eye.” Children often learn this important fact from fairy tales.

And there is even religious and philosophical truth. Does the frog-goddess Heqet exist, for example? Does the universe exist? Is there a spoon? The methods of philosophy are different from the methods of science, and some amateur philosophers simply state their beliefs without actually justifying them, but philosophy is actually very important. Science itself is based on certain philosophical beliefs about reality.

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Fetal pain: what does the science say?

Recent years have seen increased attention on the unborn fetus – in particular the question of the fetus feeling pain. Much evidence on this question has come from caring for premature babies in a neonatal intensive care unit (NICU). The modern NICU has allowed babies born as early as 22 weeks (55% of pregnancy) to survive. At 23 weeks, one US hospital reports a 71% chance of survival.

Gestational age at which premature babies had a 50% chance of survival, taken from a range of published studies, together with (for 2015) the hospital mentioned above. The data fits an exponential decay, dropping to 22 weeks by 2040 (although this may not actually be achievable).

Medical staff are generally convinced that premature babies in the NICU can feel pain, and the same is presumably true for unborn babies of the same age. Further attention on unborn babies has resulted from increasingly ubiquitous fetal ultrasounds, from numerous television documentaries on premature babies, and from books, web sites, and apps that encourage pregnant women to track their baby’s development. These have all contributed to the current interest in fetal pain. A 2005 JAMA review on fetal pain was unfortunately tarnished by allegations of conflicts of interest. However, there is a considerable body of other scientific literature on the topic of fetal pain. So what does the literature say?

A premature baby being cared for aboard the US Navy hospital ship Comfort

The question of fetal pain is unfortunately confused by uncertainties regarding the role of the cortex in feeling pain, uncertainties about how the fetal nervous system functions, uncertainties about whether “feeling pain” requires knowing the exact location of the pain, and uncertainties about whether “consciousness” is required to truly feel pain. Furthermore, there are actually two separate human pain systems, one primarily affective (concerning the “hurt” of pain), and the other more discriminative (concerning the location of pain).

A newborn baby, a puppy, and a lobster. Which of these is “conscious”? Which of these can feel pain? Is it acceptable to kill any of these by boiling them alive? Where on this spectrum do human fetuses lie?

However, developmental evidence suggests that the ability to feel pain might begin surprisingly early. Neural pathways to the spinal cord form at 8 weeks. The cerebral cortex begins to form at 10 weeks, although initially it is not connected to the rest of the brain (the cortex continues to develop during pregnancy and long after birth). By 25 weeks, pain-related nerve signals are certainly reaching the cortex. Electroencephalograms have been recorded from 21 weeks. Hearing appears to begin at 18 weeks. At about the same age hormonal stress responses are observed during surgery in the womb. In adults and older infants, such responses are associated with pain. Premature babies show strong responses to pain, and failure to administer analgesia to babies in the NICU undergoing surgical procedures is considered unethical. Surgeons are beginning to administer anaesthesia and analgesia to unborn babies at similar developmental stages as well.

A fetus at 14 weeks

It is widely accepted that the fetus can feel pain from at least 26 weeks, but the threshold at which interventions cause distress may be as early as 20, or even 15, weeks. Obviously, it is extremely difficult to be certain where the threshold lies, since fetuses cannot verbally describe their pain. Yet the same is true for newborn infants and animals, and it has long been accepted that pain in infants and animals is nonetheless real. One surgeon recommends fetal analgesia and sedation for invasive procedures from 23 weeks (coincidentally, the current viability threshold), and a number of other surgeons agree, although some set the threshold several weeks earlier or later. One of the more rational responses I’ve seen says “Scientific data, not religious or political conviction, should guide the desperately needed research in this field. In the meantime, it seems prudent to avoid pain during gestation.” After all, even the possibility of causing unnecessary pain requires preventative action. This would apply both to surgical procedures and, a fortiori, to second- and third-trimester abortion procedures which involve crushing and/or tearing the limbs from a living fetus.