Episode 8 on 100% probability
A few of you were making fun of someone contradicting themselves between 100% sure and probably the case. Although he may well not be aware of this it's actually not technically problematic.
I've only ever seen probability defined as the limit of an infinite sequence if an event has probability one it's not necessary for it always to occur. Merely that, over an infinite number of trials, it fails a finite number of times.
I think I may have made a post about something related some time ago. ;)
Just listened to the podcast where you replied to this (yeah yeah I have a backlog) and fuck you guys too. :P
But seriously I do have a few verbal-diarrheatic paragraphs to write. Before commencing however I will say that if you were the non-science podcast I listen to I wouldn't bother writing what I have. I am perfectly comfortable acknowledging that in colloquial language probabily zero is considered as synonymous with impossible. However you are purportedly a science based podcast in which case you may want to consider that in your case 'technically correct' is the goal, not some irritant in your way.
Now that's out of the way...
First is that I kind of get the impression you think I write in while snootily laughing into my tumbler of port about how stupid you are for not knowing what I've written. However this isn't the case, if for no other reason than because I'm a beer drinker and it's hard to snootily laught into beer. Other than that I first came across the probability results in a 3rd year Computability Theory paper about how infinitely often given an algorithm uniformly at random to solve a particular problem a faster one exists. At the time I sure as hell didn't know about it and thought 'Wow! This is a fantastically cool counter intuitive result. Why don't more people know about it?' and thus decided to fix the latter part of the statement one person at a time.
Second, and this is something you might want to use to argue against anyone who brings it up again in the future... if anyone brings it up again in the future, is that I was talking to a professor at a recent conference and he disagreed with me but I think that it was because his approach was from a more applied sense. If you have a statistical model which you think produced a set of data but don't know the parameters of that model often what you'll do is come up with some that maximise the probability of obtaining the data given the model with those parameters, the so called maximum likelihood model. As such, since data is typically of finite length, you don't lose any important detail by treating probability zero as impossible. Consider if you were to set all probabilities to zero the likelihood of the model would also be something like zero (but remember not impossible!) and so basically any other model would be preferred to this one if you were trying to maximise the likelihood. Whether or not the maximum likelihood model is a good choice in a particular circumstance is often an interesting question in its own right.
Thirdly I have noticed something and I want to know if it's just confirmation bias on my part. Based on the podcasts I listen to if a presenter says something relating to a natural or social science and someone with some related knowledge writes in typically the presenter will have a mea culpa or clarify what they meant and generally be gracious in the face of correction. However it does seem that if the mistake is with regards to mathematics or statistics the response is quite like what your podcast's was where such a correction is somehow considered 'too pedantic' and discarded. Has anyone else noticed this and if so thoughts as to why it might happen?
Lastly, based on the other podcasts I listen to, your news seemed to be much more upto date this week. Good job. :)