[thedoc (OP)]

Donald piniach asked the Naked Scientists:
   How many times must a fertilized ovum divide to form a normal term baby? Does this account for the placenta and apoptosis? How many cells are in a newborn? How fast is the cell division curve in each month?
What do you think?

[evan_au]

Since no-one has tried to answer this question, I'll do a rough back-of-the-envelope estimate...

How many cells are in a newborn?

One estimate puts the number of human cells in a 70kg male at 37 trillion cells, or 37x10¹².
See Dr Karl's summary: http://www.abc.net.au/science/articles/2015/11/10/4346790.htm

Assuming that individual adult cells are roughly similar mass to the cells in a newborn, the number of cells in a 4kg newborn is this number times 4/70, or 2x10¹² cells.

This ignores the huge number of commensual bacteria which live in adults (and it seems, a smaller number which have already colonized a newborn).

How many times must a fertilized ovum divide to form a normal term baby?

The minimum number of divisions to reach this number is LOG₂(2x10¹²) = LOG₁₀(2x10¹²)/LOG₁₀(2) ≈ 41 divisions.

This does not account for apoptosis, which will require additional divisions to produce the cells which subsequently die.

Does this account for the placenta?

Part of the placenta forms from the fertilized egg, and part grows from the mother's tissue. So it partly includes the placenta. 

The placenta functions as a fetomaternal organ with two components: the fetal placenta (Chorion frondosum), which develops from the same blastocyst that forms the fetus, and the maternal placenta (Decidua basalis), which develops from the maternal uterine tissue

How fast is the cell division curve in each month?

41 divisions in 9 months averages out at 0.9 per week (or a bit faster, if you account for apotosis).

A blastocyst at 6 days after fertilization has 200-300 cells; this represents about 8 divisions.
So in the first week, divisions happen more than once per day.
See: https://en.wikipedia.org/wiki/Blastocyst

[evan_au]

The minimum number of divisions to reach this number is LOG₂(2x10¹²) = LOG₁₀(2x10¹²)/LOG₁₀(2) ≈ 41 divisions.

The podcast used a slightly different method for arriving at the same answer.

Most people don't have access to a calculator that can do LOG₂(x)

• Most scientific calculators can do LOG₁₀(x)
  
• Many scientific calculators can do the "natural logarithm" ln=LOG_e(x), where e=2.718281828....
  
• You can simulate it in a spreadsheet by calculating 2^n=x, and try different values of n until you hit the target number for x.
  
• ...or even by using the "Goal Seek" function in a spreadsheet
  
• ...or (even easier) just type into Google: "What is log2(2e12)?", and the answer is "40.8631371386" ≈ 41 divisions.

You can convert logarithms in one base to logarithms in another base.  The method described in the podcast was:
LOG₂(2x10¹²) = LOG_e(2x10¹²)/LOG_e(2)
= ln(2x10¹²)/ln(2) ≈ 41 divisions.