The Monty Hall Problem

This is a strange one. I can't think of another theoretical maths problem quite like it. The answer is so counter-intuitive that generations of gifted mathematicians have got it wrong and undoubtedly generations to come will too. It goes like this:

Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 3 and the host opens Door 1, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

So is it better to stick with your original choice or switch to the other unopened door? At first it seems the obvious answer is that it makes no difference what you do. Its a 50/50 choice, right? Well, no, wrong actually. You are always better off switching to the other unopened door. You might not believe it but it's been tested time and again and the conclusion is always the same.

Switch.

I know what you're thinking. I thought the exact same thing. But the fact remains that I was wrong, and so are you. Here's why:

When you first make your choice it's a 1/3 chance that you have picked the door with the car behind it. When Monty opens one of the other doors and offers you the switch, by sticking with your original choice nothing has changed, so your odds are still 1/3. However, if you switch you are effectively getting both the opened door and the other unopened door, meaning yours odds have become 2/3.

Again, I know what you're thinking. "If I stick it's also a 2/3 chance because I now know what's behind one of the doors". But again, you would be wrong. Another way to think of it is to imagine 1,000,000 doors instead of just three. When you choose one door you have a 1/1,000,000 chance of winning. Monty then proceeds to open 999,998 of the other doors, all of which show goats, leaving just one other unopened door. If you now stick, your odds are still 1/1,000,000 because the new information makes no difference to the choice you originally had. If you switch your odds jump to 999,999/1,000,000, because you essentially have been given every door except your original choice. The same rationale holds for 3 doors.

The below figure should explain it:

Hopefully it now makes sense. If not, don't worry. You are in good company. As cognitive psychologist Massimo Piattelli-Palmarini says "... no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer."

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Grand, Slam, thank you Mam

First Irish Grand Slam victory since 1948. Couldn't have been any sweeter....

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Nature review: The AIM2 inflammasome

Sensing and destroying foreign microorganisms is essential for the survival of multicellular organisms. The last decade has seen great advances in our understanding of how the body detects and eliminates invading pathogens. Central to this progress was the discovery of the Toll-like receptors (TLRs), a family of germline-encoded membrane receptors that are responsible for detecting microbes. Crucially, these receptors allow the innate immune system to discriminate between 'self' and 'non-self', an ability long known to be utilised by memory T and B cells of the adaptive immune system. The TLRs function by recognising bacterial or viral motifs, called pathogen associated molecular patterns (PAMPs). These PAMPS are essential for the structural integrity of the microbes and so are highly conserved in bacteria, viruses and other microbes. Different TLRs have evolved to detect specific PAMPs, enabling a wide range of directed immune responses to be induced.

Complementing the membrane bound TLRs are several cytoplasmic pathogen recognition receptors which have evolved to recognise intracellular microbes. For example, viral RNA can be detected by TLR3, TLR7, TLR8 and the cytoplasmic receptors RIG-I and MDA-5. Until recently, TLR9 was the sole receptor for viral DNA, however Fernandes-Alnemri et al (1) and Hornung et al (2) have independently published evidence in Nature (Vol 458, March 2009) that the cytoplasmic receptor AIM2 (absent in melanoma 2) also recognises viral DNA, leading to activation of a multi-protein complex called the inflammasome. The inflammasome is responsible for cleaving the proinflammatory cytokines pro-IL1β and pro-IL18 to their active forms, resulting in the recruitment of inflammatory cells to the site of infection. Cleavage of these pro-inflammatory precursors is achieved through the inflammasome-mediated activation of caspase-1, an enzyme that has been extensively studied in both immunology and cancer research.

Figure from Schroder et al (3).

An inflammasome-activating DNA receptor had previously been implicated in the DNA-induced interferon pathway, thus both studies initially searched databases for pyrin domain-containing receptors. The rationale for this was that the hypothetical DNA receptor would require a pyrin domain to bind the inflammasome protein ASC (apoptosis-associated speck-like protein containing a CARD), such as is the case for a family of cytoplasmic pathogen recognition receptors called the Nod-like receptors (Nods). Using this starting point, both groups of researchers identified AIM2, a member of the interferon-inducible HIN-200 family, and showed the ability of the receptor to activate the inflammasome and caspase-1 following synthetic dsDNA stimulation (1,2). Furthermore, Hornung et al also observed a role for AIM2 in innate immunity to dsDNA vaccinia virus (2). These results were corroborated in cells with decreased expression of AIM2, achieved through siRNA or shRNA. Following stimulation of AIM2-deficient cells with dsDNA, decreased caspase-1 activation and IL-1β processing were observed in comparison to AIM2-expressing cells (1,2). AIM2 was also discovered as a cytoplasmic dsDNA receptor independently in a third study by Bürckstümmer et al (4) published in Nature Immunology, in which a combination of genomic and proteomic screens were used to identify the receptor.

This combined work shows that cytoplasmic DNA binds directly to AIM2 resulting in a strong proinflammatory response. This novel mechanism by which our immune system can sense viral or bacterial infection may have therapeutic applications. For example, targeted activation of AIM2 could assist in the elimination of invading pathogens. However, this finding also has implications for autoimmunity, as AIM2 will presumably also sense 'self-DNA' released by apoptotic cells. Thus, inappropriate activation of AIM2 could lead to the overproduction of inflammatory cytokines and type I interferons known to be associated with autoimmune disorders. This makes AIM2 a potential therapeutic target, as blocking the receptor may inhibit the onset of inflammation. It will also be interesting to scan autoimmune patients for single nucleotide polymorphisms or SNPs in the AIM2 mRNA, as it has been shown that mutations in the NLRP3 inflammasome result in constitutive activation, resulting in enhanced and prolonged activation of caspase-1 and secretion of IL-1β.

1. Fernandes-Alnemri et al. AIM2 activates the inflammasome and cell death in response to cytoplasmic DNA. Nature 2009 Mar 26;458(7237):509-13.
2. Hornung et al. AIM2 recognizes cytosolic dsDNA and forms a caspase-1-activating inflammasome with ASC. Nature 2009 Mar 26;458(7237):514-8.
3. Schroder et al. Innate immunity: cytoplasmic DNA sensing by the AIM2 inflammasome. Curr Biol. 2009 Mar 24;19(6):R262-5
4. Bürckstümmer et al. An orthogonal proteomic-genomic screen identifies AIM2 as a cytoplasmic DNA sensor for the inflammasome. Nat Immunol 2009 Mar;10(3):266-72.

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We meet at last!

Darwin: 200th birthday in February.
Me: 29th birthday in February.

Darwin: A baldy slaphead.
Me: A baldy slaphead.

Darwin: Wrote Origin of Species and is widely credited with being one of the greatest minds of all time.
Me: Eh........hmmm.......(tumbleweed).......*bird sounds*

Official score:
Darwin 3 - Rhiggs 2

This ain't over Charles, not by a long shot......!!!!



Picture taken by Kev R at the Natural History Museum in London (07/03/09)

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Intelligent Design Flaw

Well, there are many reasons why this particular branch of pseudoscience is wrong and their core arguments have been refuted time and again, but I'm just going to focus on one aspect of ID here. Specifically, I am addressing the infinite regress of designers necessary for ID to hold true. Now IDists may claim that this infinite regress isn't a necessity (ie the designer is eternal) but this isn't the case if you follow ID logic to its conclusion...

ID proponents claim that "Intelligent design holds that certain features of the universe and of living things are best explained by an intelligent cause". This seems reasonable for such things as Mt Rushmore, mousetraps and computers but IDists claim it also applies to 'living things' such as eyes, flagella, immune systems, etc. The problem is that we already know the designer in the case of the former examples, but crucially we do not have such knowledge for the latter.

Now, ID states that "one need not fully understand the origin or identity of the designer to determine that an object was designed". Instead, we can infer design from our experience: "Such research begins by observing the types of information produced when intelligent agents act. Scientists investigating design then seek to find objects which have those same types of informational properties which we commonly know come from intelligence."

Herein lies the problem.

Human knowledge of design is derived from experience of.........wait for it..........human design. There is no evidence to suggest that knowledge of human design can extrapolate to supernatural design. This is simply not an assumption that can be made, although the ID crowd are happy to do so. I'm not saying that supernatural design does not exist, although I doubt that it does, but just that knowledge of human design does not qualify us to recognise it.

So, if we base our knowledge of design on human design, as ID proponents do, then we must logically base our knowledge of intelligent designers on humans. So if ID is true, this means that intelligent designers (humans) are themselves designed by a intelligent designer. But crucially this 'earlier' intelligent designer is subject to the same criteria and so must also have been designed. This inevitably leads to an infinite regress of designers and a continual begging of the same question. As was famously said to Bertrand Russell, "But it's turtles all the way down!"

I'm not trying to show that ID is wrong here (although it is). Instead I'm trying to show that if ID were true, based on our current knowledge, we must conclude that there has been a never-ending series of intelligent designers, which creates a paradox. So, if one were to claim ID as evidence of God, this would mean that God was created by an intelligent designer, meaning there is a higher higher power. Now since most if not all IDist are practicing Christians, the implications of their theory actually directly contradicts their faith. Either they don't realise this or they are burying their heads in the sand.

Come to your own conclusions. I have.

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Ready, Set.........

Gooooooo!!!!!!!!!!

This being my first post, I guess I should explain why I've thrown myself into the blogosphere. Well, the reasons are two-fold:

Firstly, and most importantly, it is my desire to start training for a career in science communication. So this blog is really an outlet for me to hone my writing skills......or should I say acquire some writing skills to begin with! Secondly, I regularly read a variety of blogs and often have my own opinions on what is being discussed, but rarely express them. Here I will attempt to do just that.

As this is mainly a self-improvement project, I don't really expect anyone else to read any of this. So I guess I'll just be mostly talking to myself..........Which is what I'm doing right now........Talking to myself........I'd better get used to it......

Anyway, if you do happen to stop by and read then feel free to leave comments.

All the best,

Rhiggs

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