Wednesday, September 22, 2010

1+1=2+ɛ... +δ

I have a confession to make. I've been unduly withholding information from you. But I think time has come to fill you in and I hope the following will clarify some things about my recent absence and brevity. During the last months, I've been more of a bumblebee than a bee: Yes, I'm pregnant! Here's a short summary of what was written between the lines.

Late April, due to an overactive Icelandic volcano, Stefan and I had to take a 3000 km road trip from Sweden to Germany and back. Unlike other primates, humans belong to the category of "nonseasonal breeders." Nevertheless, for as long as there's birth statistics, 10-20% seasonal variations in human live births have been documented. Confusingly though, the seasonal peak has changed over decades and seems to depend on age and other demographic factors as well. So spare me the comments about spring feelings. For what humans are concerned, "spring feelings" is a cocktail.

Briefly before my trip to Perimeter Institute in May, I got a positive result on the pregnancy test. Pregnacy tests are sensitive to the human chorionic gonadotrophin (hCG) hormone that is detectable after implantation of the fertilized egg. Modern pregnancy tests are amazing accurate. You can now also have them with a digital display and they provide estimates for the weeks after conception. They work up to 4 days before the missed period. In a few years, pregnancy tests will probably have a speech output and automatically submit the result to your twitter feed.

I dubbed the little clump of rapidly dividing cells Epsilon.

My stay at Perimeter Institute in May was mildly speaking scientifically not very productive. I started getting very sick briefly after my arrival. It's a miracle I managed to sit through the workshop on the Laws of Nature - and to even write a blogpost about it. My flight back to Stockholm was a nightmare. I spent 14 hours holding onto a sick bag, pressing a lemon scented face towel to my nose, trying to escape the food smell. Folk wisdom says nausea during early pregnancy is worse with girls and twins.

A word on counting the pregnancy length. Historically, the length of the pregnancy is not counted from conception on (typically unknown), but from the first day of the last menstrual period. This is known as "gestational age" and used by all doctors, books, and most other references (with a few exceptions). The gestational age, which I'll also use in the following, is approximately two weeks longer than the actual age of the embryo, also known as "embryonic age."

At about 7 weeks, the heart starts beating.

Back in Stockholm, at about 8 weeks, I went to the first ultrasound exam. The doctor didn't speak English too well. "You know," he said, "you have twilights." - "I have what?" He turned the screen around and showed me the image (see left). "Twins!" I said. And so to Epsilon was added Delta. If you haven't seen an ultrasound image before, dark means little reflection (sonolucent). Here, the black ovals are basically liquid-filled: the amniotic sacs. In the lower one you see very nicely the umbilical cord. The embryos are about 18 mm (crown to rump).

A twin pregnancy has advantages and disadvantages. There's a long list of possible additional complications with multiple pregnancies, which is why it's automatically considered a "high risk pregnancy." The advantage is the mother gets additional screenings to prevent these complications.

Just in time for our summer workshop, the nausea finally started fading. Clothes started getting a little tight though, as an observant eye might have noticed on the conference photo.

The average length of a human pregnancy is 40 weeks (gestational) and it's roughly divided into 3 trimesters, each bringing its own challenges. The first trimester ends at week 12, the second at week 27. From 9 weeks on, the embryo is called a fetus. The risk of miscarriage during the first trimester is very high, estimates range from one in 8 to one in 5 pregnancies that end by spontaneous abortion in that early stage. In the first 12 weeks, all the major organs are formed and working, though it takes several more months for them to mature - the last organ to fully mature is the lung. If anything goes wrong in the critical first steps, the embryo is not viable. Some reasons for miscarriage are known and are treatable, but by and large the doctors don't know much and can do even less at these stages. This is my second pregnancy. The first one ended in a miscarriage at 11 weeks. Of course I knew the statistics. But I didn't realize what it means till it happened to me and I suddenly learned how many people I knew had made the same experience before.

At 14 weeks, I went to the second ultrasound. The doc found two placentas, which means it could be fraternal or idential twins, but more likely fraternal. In the ultrasound image to the left you see them lying on top of each other, both heads to the right. (I've blurred out some details in the header for privacy reasons.) Crown to rump length is about 8 cm.

After that, Epsilon and Delta got too large to fit on a single ultrasound image. Then, the docs start measuring the sizes of single organs instead. The next ultrasound, "the big one" as they call it, is at 20 weeks. With this ultrasound, the fetus' organs are screened to detect possible problems. The outcome is some sort of risk assessment. In our case, the doctors didn't find any reason for concern. Kidneys and bladders were working properly. They did an ultrasound of the hearts, and measured the blood flow. They showed us the main arteries, the brains, the stomachs, the legs and hands. I was less impressed by the technique itself than by the resolution and, most of all, by what the doctor managed to read out of the pictures. We had this "big ultrasound" done in Germany (it has to be done by some particular week in case a severe problem calls for a late abortion), so Stefan could come and watch.

The doctor told us Epsilon and Delta are two girls.

Since then, Epsilon and Delta, and so my belly, have been steadily growing. The little ones are well and kicking (both me and each other), while I'm having some trouble coping with the adjustment. My sudden hospitalization some weeks ago was very likely related to the pregnancy, though the actual problem remained mysterious. Worse, only a week later I had the questionable honor to spend another night in a hospital, this time for a completely different reason. Again the doctors insisted on many tests but eventually found nothing in particular. The pregnancy bible tells me helpfully that I should be feeling great during the 2nd trimester. Well, so much about statistics.

In any case, my employer is informed now, the wheels of bureaucracy are turning, and if everything works out alright I'll go on maternity leave mid of November. As you know, Stefan lives in Germany while I live in Sweden, so our situation is a little complicated. The health insurance issues are a big annoyance, and that's only part of the problem. Luckily though, both the Swedes and the Germans are very generous with parental leave, so we'll have some time to reorganize our lives. For now, Stefan is moving into a larger apartment while I'm enjoying the pleasantries of maternity wear.


  1. This is the best news of the day! A big congrats to you and Stefan! Hmm, maybe there's something in that volcanic ash? Twins! Hoo boy, wait till you get home from your successful deliveries! The expression "a good night's sleep" will mean more to you than it ever did before! lol

    Our first pregnancy ended in miscarriage as well. About 25% of them do, which surprised us that it was that high.

    One thing I'll miss is Christine telling you/implying you have children. Now you've done it! Mission accomplished, Christine! :-)

  2. Yes Congrats Bee and Stefan.

    My wife was very sick in the beginning too, Bee. Any fast movement that would knock her off her equilibrium, or, the wrong food ,and she was throwing up as well. That was thirty three years ago and three children later, it is something as a male I will never forget:)

    So many things change, and as I look back it was such a beautiful time to bring life into the world and the children change you in so many ways.

    All the best you two.

  3. Oh wow! Congratulations!

    :) :) :) :) :) :)

  4. Wow, congratulations to you both. Man, an epsilon and a delta! :) That's awesome.

  5. So many things change, and as I look back it was such a beautiful time to bring life into the world and the children change you in so many ways.

    Beautiful prose, Plato, and so true.

    Bee, you're going to get a lot of unasked for advice. If there's any conflicting advice, talk to the two experts: your babies' future grandmothers.

    Twins! How does "one-and-a-half" jobs sound, Stefan? I don't know how expensive socialized education is for European parents, but America isn't socialized (yet) and it's killing us. Stefan, take the change out of your pocket, stick it in a jar, and write "Grad School - Zurich Polytechnic" on it. Visit and deposit often. It is never ever too early to start saving for college, and you'll have two going at once! My 2 and last cents. Congrats again! Woo hoo! Now you've done it. :-)

  6. Congrats! ;-)

    Now you just need to an alpha, beta and gamma for a complete set! :-D

  7. Hi Bee, hi Stefan,

    congratulations! This is great news. And twins, this is fantastic!

    Best, Kay

  8. YAY! So glad everything is going (relatively) well. Congrats to you and can't wait to "meet" Epsilon and Delta!

  9. Congratulations from me, too.
    My youngest sister is actually called Delta.
    She is the fourth girl of my parents, and was a "small increment", so what better name?

    All the best to you, I only have one piece of parental wisdom to impart: "It gets easier".

  10. My congratulations to the two of you. :)

  11. Geekiest pregnancy announcement ever -- congratulations!

    I do hope the sisters keep their names; may their futures be limitless.

  12. Yes, I'm pregnant!

    How did that happen? Oh yeah... biology. See what happens when you engage interdisciplinary research? Productivity! German efficiency, too.


    Now you must resist the temptation to formally name them Scylla and Charybdis, Lapis and Lazuli, or Lorelei and Katzenelnbogen. Their middle initials are already graven in bytes.

    It is never too early to begin buying their toys. 2-D Penrose tiles, 3-D wooden blocks are nice,
    (swallowing hazard)

    spirallohedra 858 hits
    Google Images
    spirallohedra 296 hits

    Buy diapers by the full case, possibly direct from the manufacturer.

  13. Hello Bee,
    I try to think of some names which have some
    connection to volcanos....
    - Hephaistos ? No,
    - Vulcanus ? No
    - Spock ? Not really!
    No Girls names at all- maybe You should choose
    something fitting in the tradition of Your families.
    (please avoid the 10 now most popular names
    in Germany!)

  14. "The purpose of Life is to create Life"
    -- Biology

    A note on Bonobo "non-seasonal breeders":

    "Big applause for Bonobo's female-led societies. Bonobo women stick together to protect/support each other against males. #WSF10 [ 2010 World Science Festival ]
    12:25 PM Jun 5th via TweetDeck

    Vanessa Woods [ Duke University ] going over the difference between Chimps and Bonobos. #WSF10"

    Bonobo Society: Amicable, Amorous and Run by Females/NATALIE ANGIER

    "Nature's raucous bestiary rarely serves up good role models for human behavior, unless you happen to work on the trading floor of the New York Stock Exchange. But there is one creature that stands out from the chest-thumping masses as an example of amicability, sensitivity and, well, humaneness: a little-known ape called the bonobo, or, less accurately, the pygmy chimpanzee. Before bonobos can be fully appreciated, however, two human prejudices must be overcome. The first is, fellows, the female bonobo is the dominant sex, though the dominance is so mild and unobnoxious that some researchers view bonobo society as a matter of "co-dominance," or equality between the sexes. Fancy that."

    "As de Waal puts it in his book, "The chimpanzee resolves sexual issues with power; the bonobo resolves power issues with sex." Or more coyly, chimpanzees are from Mars, bonobos are from Venus. All of which has relevance for understanding the roots of human nature. De Waal seeks to correct the image of humanity's ancestors as invariably chimpanzee-like, driven by aggression, hierarchical machinations, hunting, warfare and male dominance."

    "De Waal said that many men grow indignant when they learn of the bonobo's social structure. "After one of my talks, a famous German professor jumped up and said, 'What is wrong with these males?' " he recalled. Yet de Waal said the bonobo males might not have reason to rebel. "They seem to be in a perfectly good situation," he said. "The females have sex with them all the time, and they don't have to fight over it so much among themselves. I'm not sure they've lost anything, except for their dominance.""

  15. ~ Repeating from Facebook:
    Wow, Bee! Congratulations to you and Stefan! Can't resist a reference to "pair production", how appropo for anyone in QM (and not quite planned, correct?) For names, consider picking among these: Emmy, for Emmy Noether. Try Ada, from the lady who helped invent computing. Or to strike a "blow" for women not being given enough credit: Mileva, Einstein's wife who reportedly helped him a lot with SRT but got little credit, or Jocelyn for Jocelyn Bell Burnell who did most of discovering the Pulsars but didn't share the Nobel award with Antony Hewish. Sophia, for "wisdom"? Hypatia, the Neoplatonist scholar killed by an ignorant mob in the late Roman Empire, Alexandria Egypt?

    Or perhaps less tasteful, consider names inspired by things in physics: Photina, Axiona, Quantia, Quantine; etc, Electria, etc. Some will chuckle.

    OTOH, maybe forget "making a statement" and pick names you like.

    BTW my long-term GF is not able to have children so I vicariously interface and enjoy parenthood through the birth announcements and children of others (also from teaching.)

    PS, aren't epsilon, delta etc. sometimes used in that curious frontier form of math, the surreal numbers and non-standard analysis (roughly, use of infinitesimals beyond just as intermediaries to get results.)

  16. Congratulations; and thank you for the interesting information related to pregnancy, ultrasounds and human sexual behavior!

    Best wishes!

  17. AHA! WOW!

    I've told you so! And twins! Girls!

    The world will now completely change for you and Stefan.

    A brave, great new world!

    Congratulations for you too!!

    And, see, I've told you so.

    It was about the right time.

    All the best,

  18. Hi Steven

    Mission accomplished, Christine! :-)

    Yeah! Great!

    I'm very happy for them!


  19. Hi again Sabine,

    I was not sick during my pregnancy... But I suppose you will get better by now.

    Have a great time, and let us know how it is like to feel *two* babies moving inside. Pedro used to kick me pretty strong right when I was about to sleep. Ah, good times! Enjoy this great period of a woman's life.

    Pedro and Fabiano send you best wishes! I've just told them the news.


  20. Best advice I can give you is this. There are many books about raising babies. I read many of them, and was absolutely terrified. It was a vast relief to find that the actual experience was far, far better than the books indicated. [Perhaps that is the intention?] My son is a pain in the ass sometimes, but nowhere near as bad as those books would have you believe.

  21. Does ultrasound provide enough identification that Epsilon and Delta can be recognized and one knows who is whom through birth?

  22. Hi All,

    Thanks so much for the kind wishes.

    Hi Garrett,

    The Germans are quite restrictive with what are allowed first names. I doubt Greek letters will be legally acceptable. So, no, we'll not keep the names. Also, Epsilon sounds to me like a boy's name.

    Hi Christine,

    They're not yet kicking too strongly. It's just enough so Stefan can see the kicks. I'm not sure how I could tell a difference between one and two babies kicking, except possibly that they're not usually both moving, ie, sometimes the one on the left side is active, sometimes the one on the right side.

    Hi Rastus,

    Will make sure to stay away from such books ;-)

    Hi Arun,

    I don't think you can tell them apart on the ultrasound. But they are in two separate sacs, so they can't move around freely. One is on the bottom right, and the other one is on the top left, and while they can turn around in the sacs, they'll pretty much have to stay in these spots till delivery.



  23. Hi Steven,

    Higher Education in Germany used to be tuition free. Nowadays, many universities have some fees (it depends on the state), but these are moderate. There are of course private universities where you can pay your ass off if you want to, but the ideal that access to higher education should not depend on a family's social status is still mostly valid in Germany. There's also disadvantages to this, but I think the advantages weigh heavier.

    The most annoying disadvantage of tuition free higher education is that after high school, a lot of people who don't really know what to do with their lives think they'll go and study something. These folks, typically unmotivated, clog up the classrooms till they drop out after one or two semesters. The other disadvantage is lacking money for maintenance and extravagancies, ie compared to the average US campus, German Universities are plain ugly. Best,


  24. Congrats Bee! My mother is a twin and my grandmother said they were her easiest babies as they entertained each other. I wish you the very best!

  25. Hi Bee,

    Congratulations to you and Stephan! If your experience matches my own, this marks a wonderful place in life for each of you, both as individuals and as a couple, as now you soon will have realized to have extended yourselves with your creation of unique beings common only to you both. So once again let me extend my best wishes and congratulations to the beginning of something that never existed before, with that being you all as a new family.



  26. Hi Bee,

    Just as a follow is to say that your tale has reminded me how science has now changed even the memories that families can share, as not only can those born be shown photos of how they were when they came into the world, yet before when they were still forming to make their entry. I wonder in time if it will become the tradition to have such images displayed proudly and meaningfully in frames on ones mantle?



  27. Congratulations! I am the father of 14 year old identical twin boys (and a 10 year old boy). My twins were born while I was finishing my PhD at MIT in physics...

    My not-so-brilliant insight is the blindingly obvious fact: Your life will soon get _very busy_. (Although I do recall pleasant occasions eating takeout pizza while rocking twins in car seats on the floor in front of the sofa that were pretty sedate.)

    Just remember that things will pretty much get monotonically easier as time goes on for the first few years, at least. And it will all be worth it...

  28. Bee,

    You seemed fine when I talked to you in May. Regardless, congratulations!

    I guess you're carrying on the Perimeter Institute tradition on having only female children.

    Again, congratulations!

  29. Good luck with your (hopefully) twins

  30. Congratulations! WOW.

    Ever notice that "WOW" with one rotation, in either of two different ways = MOM!

    Twins! Less entropy compared to one at a time. It's good.

    Funny that for all the advanced math there is, it's simple multiplcation which can be the most amazing. :-)

  31. Bee/Stefan - late to the party as always, congrats on the impending fission! And while you may jest now with the names Delta and Epsilon, I think they would be great! (Not to mention the added advantage of an easy way to mark their clothes and belongings to prevent confusions)

  32. Bee/Stefan - late to the party as always, congrats on the impending fission!

    Nicely put, Snowboarder, and let us never forget the eventual fission started with a fusion. :-)

    I have many suggested names for the twins (Twins!), but I think we'd all love to hear of others, because the best I can come up with at the moment is Heidi and Brunhilda, two very nice German names. Or Scandinavian. I can't tell the difference.

  33. Missed the important announcement earlier.


  34. Congratulations, Bee and Stefan! I missed the announcement, too... I've been silently reading here since we exchanged emails a few years ago, and am so happy for you (all). What wonderful news! TWINS! :-D

  35. You tweeted:
    is on bed rest and not happy about it.

    Hi Bee,

    I hope you're fine; certainly twins require you to rest at some point.

    This is your first *real* exercise in patience. Others will come, but it's all worthwhile. It's a new responsability in your life; everything you have seen before pales before the new responsabilities that will come. So, be ready.

    It's a new world, but a very special one, and all that really matters in one's life! You will first act instinctively, you will be busy. But then a wonderful thing will happen: you will start to experience a different kind of love, it will come slowly and steadly, and it's different from any other kind of love you have felt before. It will grow with time and make you a different person.

    You will see that many things that you used to do unconcerned with other commitments will no longer be possible. Things that you have never bored before like your time will have to be shared.

    But as I said, it's all worthy and great!

    It's wonderful to have children, and you will have two at the same time! A very unique experience!

    Take care,


COMMENTS ON THIS BLOG ARE PERMANENTLY CLOSED. You can join the discussion on Patreon.

Note: Only a member of this blog may post a comment.