Posted: Mar 02, 2010 3:06 am
Frequently Occurring Fallacies No. 2: The 'Serial Trials' Fallacy
For the second of the fallacies that tends to appear in reality-denial attempts to dismiss the validity of evolution, I have decided to cover the Serial Trials Fallacy. This usually, but not always, accompanies the One True Sequence fallacy above. However, the nature of this fallacy arises via an entirely different mechanism.
Typically, what happens is that a probability calculation is constructed, usually on the basis of assumptions that are either left unstated altogether (conveniently preventing independent verification of their validity), or if they are stated, they usually fail to survive intense critical scrutiny. However, even if we allow these assumptions to remain unchallenged, the appearance of the Serial Trials fallacy means that destruction of the validity of the spurious probability calculation is easy even without resorting to the effort of destroying those other assumptions.
Basically, the Serial Trials Fallacy consists of assuming that only one participant in an interacting system is performing the necessary task at any one time. While this may be true for a lone experimenter engaged in a coin tossing exercise, this is assuredly NOT true of any system involving chemical reactions, which involves untold billions of atoms or molecules at any given moment. This of course has import for abiogenesis as well, against which bad probability calculations and the Serial Trials Fallacy are routinely deployed. I shall concentrate here on abiogenetic scenarios, but what follows applies equally to nuclear DNA replication and any absurd arguments based upon bad probability calculations and the Serial Trials Fallacy that mutations cannot occur in a given amount of time.
The idea is simply this. If you only have one participant in the system in question, and the probability of the desired outcome is small, then it will take a long time for that outcome to appear among the other outcomes. But, if you have billions of participants in the system in question, all acting simultaneously, then even a low-probability outcome will occur a lot more quickly.
For example, if I perform trials that consist of ten coin tosses in a row per trial, and this takes about 20 seconds, then I'm going to take a long time to arrive at 10 heads in a row, because the probability is indeed 1/(210) = 1/1024. In accordance with a basic law of probability, namely that if the probability of the event is P, the number of serial trials required will be 1/P, I shall need to conduct 1,024 serial trials to obtain 10 heads in a row (averaged over the long term of course) and at 1 trial every 20 seconds, this will take me about six days, if all I do is toss coins without any breaks for sleep, food or other necessary biological functions. If, however, I co-opt 1,024 people to perform these trials in parallel, at least one of them should arrive at 10 heads from the very outset. If I manage by some logistical wonder to co-opt the entire population of China to toss coins in this fashion, then with a billion people tossing the coins, we should see 1,000,000,000/1024, which gives us 976,562 Chinese coin tossers who should see 10 heads in a row out of the total 1,000,000,000 Chinese.
Now given that the number of molecules in any given reaction even in relatively dilute solutions is large (a 1 molar solution contains 6.023 × 1023 particles of interest per litre of solution, be they atoms, molecules or whatever) then we have scope for some serious participating numbers in terms of parallel trials. Even if we assume, for the sake of argument in a typical prebiotic scenario, that only the top 100 metres of ocean depth is available for parallel trials of this kind (which is a restriction that may prove to be too restrictive once the requisite experimental data are in from various places around the world with respect to this, and of course totally ignores processes around volcanic black smokers in deep ocean waters that could also fuel abiogenetic reactions) and we further assume that the concentration of substancers of interest is only of the order of millimoles per litre, then that still leaves us with the following calculation:
[1] Mean radius of Earth = 6,371,000 m, and 100 m down, that radius is 6,370,900 m
[2] Volume of sea water of interest is therefore 4/3π(R3-r3)
which equals 5.1005 × 1016 m3
1 litre of solution of 1 mmol l-1 will contain 6.023 × 1020 reacting particles of interest, which means that 1 m3 of solution will contain 6.023 × 1026 particles, and therefore the number of particles in the 100 metre layer of ocean around the world will be 3.0730 × 1043 particles. So already we're well into the territory where our number of parallel trials will make life a little bit easier. At this juncture, if we have this many interacting particles, then any reaction outcome that is computed to have a probability of greater than 1/(3.073 ×1043) is inevitable with the first reaction sequence.
Now, of course, this assumes that the reactions in question are, to use that much abused word by reality denialists, "random" (though their usage of this word tends to be woefully non-rigorous at the best of times). However, chemical reactions are not "random" by any stretch of the imagination (we wouldn't be able to do chemistry if they were!), which means that once we factor that into the picture alongside the fact that a parallel trial involving massive numbers of reacting molecules is taking place, the spurious nature of these probabilistic arguments against evolution rapidly become apparent.
The same parallel trials of course take place in reproducing populations of organisms. Of course, the notion falsely propagated by reality denialists is that we have to wait for one particular organism to develop one particular mutation, and that this is somehow "improbable". Whereas what we really have to wait for is any one organism among untold millions, or even billions, to develop that mutation, for evolution to have something to work with. If that mutation is considered to have a probability of 1/109, then we only have to wait for 109 DNA replications in germ cells to take place before that mutation happens. If our working population of organisms is already comprised of 1 billion individuals (last time I checked, the world human population had exceeded 6.6 billion) then that mutation is inevitable.
So, next time you see a spurious probability calculation appearing that purports to "disprove evolution", look out for two salient features, namely:
[1] Base assumptions that are either not stated altogether (thus conveniently preventing independent verification) or base assumptions that fail to withstand critical scrutiny, and
[2] The Serial Trials Fallacy above.
For the second of the fallacies that tends to appear in reality-denial attempts to dismiss the validity of evolution, I have decided to cover the Serial Trials Fallacy. This usually, but not always, accompanies the One True Sequence fallacy above. However, the nature of this fallacy arises via an entirely different mechanism.
Typically, what happens is that a probability calculation is constructed, usually on the basis of assumptions that are either left unstated altogether (conveniently preventing independent verification of their validity), or if they are stated, they usually fail to survive intense critical scrutiny. However, even if we allow these assumptions to remain unchallenged, the appearance of the Serial Trials fallacy means that destruction of the validity of the spurious probability calculation is easy even without resorting to the effort of destroying those other assumptions.
Basically, the Serial Trials Fallacy consists of assuming that only one participant in an interacting system is performing the necessary task at any one time. While this may be true for a lone experimenter engaged in a coin tossing exercise, this is assuredly NOT true of any system involving chemical reactions, which involves untold billions of atoms or molecules at any given moment. This of course has import for abiogenesis as well, against which bad probability calculations and the Serial Trials Fallacy are routinely deployed. I shall concentrate here on abiogenetic scenarios, but what follows applies equally to nuclear DNA replication and any absurd arguments based upon bad probability calculations and the Serial Trials Fallacy that mutations cannot occur in a given amount of time.
The idea is simply this. If you only have one participant in the system in question, and the probability of the desired outcome is small, then it will take a long time for that outcome to appear among the other outcomes. But, if you have billions of participants in the system in question, all acting simultaneously, then even a low-probability outcome will occur a lot more quickly.
For example, if I perform trials that consist of ten coin tosses in a row per trial, and this takes about 20 seconds, then I'm going to take a long time to arrive at 10 heads in a row, because the probability is indeed 1/(210) = 1/1024. In accordance with a basic law of probability, namely that if the probability of the event is P, the number of serial trials required will be 1/P, I shall need to conduct 1,024 serial trials to obtain 10 heads in a row (averaged over the long term of course) and at 1 trial every 20 seconds, this will take me about six days, if all I do is toss coins without any breaks for sleep, food or other necessary biological functions. If, however, I co-opt 1,024 people to perform these trials in parallel, at least one of them should arrive at 10 heads from the very outset. If I manage by some logistical wonder to co-opt the entire population of China to toss coins in this fashion, then with a billion people tossing the coins, we should see 1,000,000,000/1024, which gives us 976,562 Chinese coin tossers who should see 10 heads in a row out of the total 1,000,000,000 Chinese.
Now given that the number of molecules in any given reaction even in relatively dilute solutions is large (a 1 molar solution contains 6.023 × 1023 particles of interest per litre of solution, be they atoms, molecules or whatever) then we have scope for some serious participating numbers in terms of parallel trials. Even if we assume, for the sake of argument in a typical prebiotic scenario, that only the top 100 metres of ocean depth is available for parallel trials of this kind (which is a restriction that may prove to be too restrictive once the requisite experimental data are in from various places around the world with respect to this, and of course totally ignores processes around volcanic black smokers in deep ocean waters that could also fuel abiogenetic reactions) and we further assume that the concentration of substancers of interest is only of the order of millimoles per litre, then that still leaves us with the following calculation:
[1] Mean radius of Earth = 6,371,000 m, and 100 m down, that radius is 6,370,900 m
[2] Volume of sea water of interest is therefore 4/3π(R3-r3)
which equals 5.1005 × 1016 m3
1 litre of solution of 1 mmol l-1 will contain 6.023 × 1020 reacting particles of interest, which means that 1 m3 of solution will contain 6.023 × 1026 particles, and therefore the number of particles in the 100 metre layer of ocean around the world will be 3.0730 × 1043 particles. So already we're well into the territory where our number of parallel trials will make life a little bit easier. At this juncture, if we have this many interacting particles, then any reaction outcome that is computed to have a probability of greater than 1/(3.073 ×1043) is inevitable with the first reaction sequence.
Now, of course, this assumes that the reactions in question are, to use that much abused word by reality denialists, "random" (though their usage of this word tends to be woefully non-rigorous at the best of times). However, chemical reactions are not "random" by any stretch of the imagination (we wouldn't be able to do chemistry if they were!), which means that once we factor that into the picture alongside the fact that a parallel trial involving massive numbers of reacting molecules is taking place, the spurious nature of these probabilistic arguments against evolution rapidly become apparent.
The same parallel trials of course take place in reproducing populations of organisms. Of course, the notion falsely propagated by reality denialists is that we have to wait for one particular organism to develop one particular mutation, and that this is somehow "improbable". Whereas what we really have to wait for is any one organism among untold millions, or even billions, to develop that mutation, for evolution to have something to work with. If that mutation is considered to have a probability of 1/109, then we only have to wait for 109 DNA replications in germ cells to take place before that mutation happens. If our working population of organisms is already comprised of 1 billion individuals (last time I checked, the world human population had exceeded 6.6 billion) then that mutation is inevitable.
So, next time you see a spurious probability calculation appearing that purports to "disprove evolution", look out for two salient features, namely:
[1] Base assumptions that are either not stated altogether (thus conveniently preventing independent verification) or base assumptions that fail to withstand critical scrutiny, and
[2] The Serial Trials Fallacy above.