Four. One in.

The same genetic code is present in all your cells, the same as when you were first created, the single cell we call zygote.  Each sperm and egg carries a single set of 23 chromosomes,  half of each parental pair.  Actually, it is one in four chromosomes, as first there is a duplication before the split into sperm or egg.  Each of the four strands is a random, but different, mix of DNA that is half each from mum and dad’s DNA.  Mitochondrial DNA is only from mum.  But you really don’t need to know any of that, do you?

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Two. Start 2 x 2

develop_zygote_cleavage_stages_blastula_etc.pngOnce the first sperm enters the egg, the egg closes off its outer wall so that no other sperm can enter.  The winner takes all (with the odd failure!).  This is the start of you;  and you are who you are, because of the specific egg and sperm that won the race.  Your unique genetic code resulted from the unique combination of sperm and egg that became you.

(I used to wonder,  who would I would have been if my mum had married someone else; what would I have been like.  But, that would not have been me.)

It doesn’t take long before that one cell splits into two almost identical cells, and that doubling keeps going until you become hundreds of trillions, a newborn baby that emerges from your mother’s womb about nine months later.  But let’s go back to the start of you.

When the sperm and egg combine combine, each comes with a single set of  23 chromosomes.  When they combine to create a new human, it starts with a single  cell, now called a zygote, with the full set of 23 pairs of chromosomes.

Doesn’t that word sound full of colour and meaning?  Chromosomes contain the ‘instructions’ that create each cell, coded in the 4-letter alphabet of DNA (molecules of De-oxy-ribo Nucleic Acid).  All life is made of cells, and DNA and its precursor RNA (Ribo Nucleic Acid) is central to making and controlling each cell.  Each one of our trillions of human cells has nearly exactly the same genetic code.

That genetic code is created form the unique pairing of sperm and egg.  And here we learn that 1+ 1 = 1 since 1 sperm and 1 egg make a single zygote that then becomes a baby in mothers’ womb.  For humans, as for all other mammals.  One could also argue that  1 + 1 = 3, for mummy and daddy create out of themselves a new baby.

It seems obvious here, but may be hidden: arithmetic demands you use numbers that refer to the same thing.  You cannot add up or do any other operations on number and expect a meaningful answer.  The arithmetic of reproduction is meaningful, but it is not useful for an arithmetic where the answer to 1 + 1 is not reliable. So, whenever you see two or number used or compared; ask yourself, what’s the unit in each case.  Is it the same; and a quick way to see that is to imagine what does single unit look like.

When you are a single cell and divide into two cells, are the two the same? They seem to be, yet one is destined to become embryo, the other the placenta. Each cell divides by first creating two sets of 23 paired chromosomes; so your cells enter the Noah’s ark of life two by two.  And the power of multiplication of just keeing dividing by two to create the trillions of cells that you became as a new baby.

This is the power of compound interest, the exponential factor that is behind biology as well as human society.  This is the power of mathematics.  When my father taught me chess, he told me of the story of the ruler who was so pleased to play the game that we wished to reward the person who taught him. He just asked for a single grain of rice to start, but to be doubled on every square of the chess board, which has 64 squares.  The ruler was happy to agree. A single grain multiplied a few times did not seem so much.  But before covering half the board, the number is over 4 trillion, more rice grains than the ruler had.

You grew from one cell that kept dividing. It takes a while to start after fertilisation, the moment that the sperm enters the egg, and the two cells to become one, the zygote.  It takes a little more than a day for zygote your to start dividing, first into two equal cells.  These two cells divide into four, the four into eight, then by the time you have become 16 cells, you are called a morula. As your cells keep dividing, you become a blastula that enters the lining of your mother’s womb, and into a gastrula, with three layers of cells that will make your inside, outside and middle (respectively), though not in exactly the way you might think.

Somehow equal cells have become different, and that difference continues to develop as your cells develop into at least 200 different types of cells that a human is made of.  All of them from one single cell, who at this stage in your story is a few hundred cells of each of these three types: endo-,  ecto-, and mesoderm.   Can you relate to yourself, when you were just a single cell or the three layers of cells?

 

 

 

 

One. Odd Odds

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Here, I found this pretty picture: a tiny fraction of the hundreds of millions spermatozoa (sperm cells) swimming as fast as they can, to be the first to enter the egg cell.  Guess who won?

This is how you started: you won the race against incredible odds.  Odds is an odd word, but then so is odd; why does it need two ‘d’s: od would look odd, but sounds the same.  It is derived from a peak of land, then became a triangle, then for not-paired, being the third point. Odd being left on its own, somehow became probability, for the odds is just another way of saying what’s the probability.  The minor difference is that odds is stated as 1 in some number; and odds against when that number is less than 1; and probability is generally stated as a decimal or percentage.  In history, all probabilities have become 0 or 1; until we know whether the event happened or not, its chance of happening, or probability will be a number between 0 and 1, like 0.5 which is exactly in the middle.  Here the odds are even; like whether you get heads or tails when you toss a coin.  But let’s get back to your story.

If another sperm had won, it would not have been you.  Strange thought, but well done for winning that race with bigger odds against you than winning the lottery:  one sperm in 100 to 500 million just for that race; but you might not even been able to enter that race, if your mother had become pregnant with the egg she released the previous month.  So, what is the probability that YOU are here, instead of the brother or sister that could have been here instead?  And if your parents had not met; and so on.

You need to be careful not to mis-use probabilities.  They have no bearing on history; it already happened; it’s either 0 or 1; and even though the prior probability was so close to 0 that the one that you call you should be here; the probability is actually 1, because you are here.

Want to do some arithmetic? If not, skip the square brackets.

[Let’s round out to saying there are 16 sperm in the picture, and there were  128 million (128,000,000) sperms competing for that egg.  Now if you happen to know that 16 = 2^4 and 128 = 2^7, then you know that 128 divided by 16 is the same as subtracting the exponents of the common base.  The ^ symbol means ‘to the power of, or ‘exponent’.  It’s the number of times the number is multiplied by itself. So, 128/16 =2^7 -2^4 = 2^(7-4) = 2^3 = 8.  And there  was a 1 in 8 million chance that ‘your’ sperm won. What’s that probability? But now that you’re here, its odds are 1 in 1 – it already happened.]

[[{Ever heard of log tables?  Before we had calculators, they were used to simplify complex calculations by converting a number (x) to its ‘exponent’ (y) or logarithm: [x = 10^y].  Adding the logs is the same as multiplying the numbers; subtraction division.  The result is found in the anti-log table where the resulting exponent(y) is converted back to a number (x). }]]

In epidemiology, the science of disease distribution and determinants, careful use of data is vital.  The Texas sharp-shooter fallacy: shoots first in the wall, then draws the target around the bullet hole.  To state that you have beaten the odds to be here is kind of like that.  Can you see the analogy?

Once something has happened, what does it mean to calculate the odds of it happening.  The lady who just won the lottery did not beat the odds, she just won.  Even though winning was incredibly unlikely, and very much against the odds to the tune of one in close to a billion; those odds no longer carry any information once she won; and somebody had to win!

Knowledge is very slippery, so is logic.  Words are the problem.  They aren’t real; and they can never fully describe reality.  We can just get close. Shall we try?

 

Pre-amble

We, the People, seek to order: a more perfect union of peoples, Justice, peace and prosperity; a secure life and liberty to pursue our individual goals, including happiness.

This paraphrase of the 1787 US Constitution explains what we want from government.  Democracy demands active citizens, knowledge is a pre-requisite.  Numbers count.

Vaccines are designed to prevent infection by preparing the immune system to ward off the specific bug each vaccine targets.  There are different types of bugs that cause serious illnesses and so, different types of vaccines to protect against these.

I am trying to develop a story to explain how vaccines work and why these marvels of science are considered so dangerous by a small fringe.  And to tell this story properly, we will need to understand the cognitive illusions created by our minds, and the biases that can make us certain of our view, even after we see evidence against it.

In the process we need to learn about numbers; the first lesson is that numbers can lie.

 

Smallpox the First: a human triumph!

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Lady Mary Wortley Montague (1689–1762)

Source: Reidel 2005, Photo courtesy of the National Library of Medicine.

Smallpox the First

Did you hear the good news? Smallpox is dead!  The smallpox virus was murderous.  It killed more people than war.  In the 20th century alone, smallpox killed between 300 million (300,000,000 or 3*10^8) and half a billion (500,000,000 or 5*10^8) people.  The first disease conquered by humans: How did we vanquish this angel of death?

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What’s a vaccine to you?

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A vaccine against ignorance?  “Humanity certainly needs to be immunized with a vaccine for ignorance, and we propose that that vaccine is education. But education would have to be coupled to restrictions on people, agencies, and corporations determined to follow the profit motive, and in so doing, undermine the intelligence of the populace.”

Vaccines have been so good at preventing disease, that the above article uses ‘vaccine’ metaphorically to describe prevention of ignorance.  And has been used to describe other preventive interventions: what would you like a vaccine for?  Something to stop what you don’t want.  I would like a vaccine to be more kind and less mean; to love.  Sadly, we have not yet discovered that.  But education and changing the economic system could help.

The picture above uses shapes, sizes, and colours to show different bugs; and the hand as defence that stops them. Vaccines stop harmful bugs by preparing our defences. A vaccine does not protect against bugs in general, only the specific bug that it targets. It does this by ‘looking like’ the bug to our immune system.

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