Over mijn deelname aan FameLab eerder dit jaar heb ik verschillende blogposts geschreven. Ook de opnames van de Belgische finale staan al enige tijd online. Maar blijkbaar ben ik vergeten de opname van mijn pitch ook hier te plaatsen.
Terwijl ik tijdens de voorrondes uitlegde hoe zeepbellen aan hun kleuren komen, deed ik in de finale een poging om in drie minuten antwoord te geven op volgende vraag:
“Wat is waarschijnlijkheid?”
Geen sinecure, gezien ik vorig jaar een heel vak heb gegeven over deze en aanverwante vragen uit de filosofie van de kansrekening. ;-)
Het was in het Engels, maar er staan Nederlandse ondertitels bij. Bij deze dus, mijn drie minuten over kansrekening:
[error]Opgelet, de ondertitels zijn niet door mij gemaakt en er zit een cruciale fout in. Ik zeg “70 trillion“, maar ik gebruik short scale. In het Nederlands correspondeert dat niet met “70 triljoen”, maar ‘slechts’ met “70 biljoen” (70*10^12)![/error]
Transcriptie van de Engelstalige versie: na de vouw.
[Fake phone call] O ow, someone’s calling me now? What are the odds of that?!
Well, I could give you a probability, a numbers on a scale from zero to one, but what would that number mean? There is no such thing as a probability-meter?!
Let’s consider the probability that it will rain next Monday. There is no weather station that measures that probability. All that can be measured are the current weather conditions. We need to combine all those measurements, with a model: a set of equations. And to arrive at probabilities, we need to run and rerun the simulations many times and look at the fractions of simulations that predict rain for Monday.
If we use different equations in the model, we’ll arrive at different probabilities. So, probabilities depend on some model, but also on a perspective: the probability for rain next Monday will be revised each day based on new evidence.
To illustrate this, I will now compute the probability that you were born. Based on the evidence that you are present here today, the probability that you were born is one. How reassuring.
But, I will now drastically reduce the evidence to what was available at an earlier point in history. If I just take into account the identity of your biological parents and compare their chromosomes to yours, there is a match probability of only one in 70 trillion.*
This value depends on my model: had I chosen to take into account the date and time you were born as well, the probability would have been even smaller.
It also depends on the perspective. If we go even further back in time, we lose track of nearly all of the evidence for your current existence, and the probability for you to be born gets ever closer to zero.
There are just so many alternative scenarios and on most of them none of us are born – >pop< >pop< >pop< –With a probability ever so close to one this room would have been empty.
Yet, we have been born, and we managed to gather here today, against all odds. So, we are all living proof that improbable events do happen.
*Assumptions and computation leading to this number:
- Your biological parents both had 46 chromosomes (this is true for most though not all humans).
- None of their chromosomes were exactly equal (one chromosome contains many genes; the chance of two being exactly equal is very small, except if your parents were close family).
- Each parent contributed one gamete (egg cell or sperm cell), with 23 chromosomes out of their set of 46 chromosomes.
- There are 2^23 or about 8.4*10^6 (8.4 million) combinations of chromosomes for each parent (which we assume to be equally likely).
- So there are (2^23)^2 or about 70*10^12 (70 trillion in short scale) combinations of gamete chromosomes of your parents, only one of which corresponds to your set of 46 chromosomes (again, true for most though not all humans).
This computation does not take into account crossing over of genes between chromosomes (which can happen during meiosis, and which implies that your genes need not correspond completely with either of your parents’s chromosomes) nor various epigenetic factors.