Banner
    The Fallacy Of The Average
    By Patrick Lockerby | March 17th 2010 11:09 AM | 12 comments | Print | E-mail | Track Comments
    About Patrick

    Retired engineer, 60+ years young. Computer builder and programmer. Linguist specialising in language acquisition and computational linguistics....

    View Patrick's Profile
    The Fallacy Of The Average


    A fallacy is a pattern of logical reasoning which appears on its surface to be a pattern of sound reasoning.  The fallacy of the average is based on the false notion that the effect of a thing averaged out on a large scale is equivalent to an effect of the same thing on a small scale.

    A drop of rain falling anywhere in the Pacific is self-evidently insignificant as a matter of scale.

    But what if that single drop of rain falls into the mains supply circuit of a radio?


    If I have a box of screws and wish to know their average length, I need only take some random sample and measure each screw in the sample.  Using sound statistical methods, I can determine the likelihood of anyone picking a screw at random of a specific length range.

    It may be that the average screw is 15.5 mm long.  It seems to be self-evident that if I pick three screws at random, then they will measure, end-to-end 46.5 mm.  In reality, that is a most unlikely outcome if the box is of mixed sizes.

    Again, if I have a box of 1,000 10 mm cubes, 70% of which are of copper and 30% of zinc, then I most definitely do not have, on average, a box of 5.84803548mm3 brass cubes.


    A fallacy of the averagely overheated human

    The fallacy: compared with all the salt in all the oceans, the amount of salt in human sweat is so trivial that it can be ignored for all practical purposes at the scale of human society and climate.

    This fallacy of averages tells us that human sweat is insignificant compared with natural sources of atmospheric salt.  However, global averages take no account of clustering.  What is the effect of the accumulated sweat of a large human population in an urban heat island?


    Boulder, Colorado at night.
    The reddish glow from the city lights of Boulder, Colo., is the result in part of the light being scattered by haze particles. UW scientists have discovered unexpected chemistry involving the pollutants that make up the haze.


    The smell of salt air, a mile high and 900 miles inland.
    Vince Stricherz March 10, 2010
    "It's there. We know it's there. But we don't have a good handle on where that chloride comes from," said Joel Thornton, a University of Washington associate professor of atmospheric sciences and lead author of a paper documenting the findings, published March 11 in Nature.
    http://uwnews.org/article.asp?articleID=56206


    How many euros does a breach of European regulations cost?

    The European regulation 94/27/CE of June 30th, 1994 requires that for items in direct contact with the skin, the amount of nickel release shall be lower than or equal to 0.5 mg/cm2 week.

    1 euro and 2 euro coins have been shown to release from 240 to 320 times more nickel than regulations allow, due to human sweat, according to a September 2002 Nature article.




    -----
    [1] - credit to Henry Cox for suggesting that human sweat in an urban heat island might account for at least some of the atmospheric sodium chloride discovered by the researchers at Boulder, Colorado.

    Comments

    adaptivecomplexity
    So why Boulder and not Denver? Or do you find the same result anywhere you have a large population of people living in the arid, high-elevation climate of the Rocky Mountain states?
    Mike
    logicman
    So why Boulder and not Denver? Or do you find the same result anywhere you have a large population of people living in the arid, high-elevation climate of the Rocky Mountain states?
    I don't know, Michael, I just happened across that particular bit of research

    I surmise that in any large urban environment you are going to find sweat-related problems.  Certainly, human sweat is a factor in London's underground railway engineering.

    It is also a factor in mobile phone design.  Those babies have to be tropicalised to survive many hours of being pressed against sweaty earholes.
    adaptivecomplexity
    Those babies have to be tropicalised to survive many hours of being pressed against sweaty earholes.
    As well as laptops - my keyboard has to withstand hours of pounding from my sweaty fingers.
    Mike
    You're forgetting one thing, Patrick. When a person perspires, the water in the perspiration evaporates leaving the sodium chloride behind. There's no way it can get into the atmosphere by means of perspiration.

    If it weren't the case that salt water leaves its sodium chloride content behind when it evaporates from the oceans, then we would not have any fresh water bodies of water at all any where on the planet. The same applies to human perspiration.



    Sodium chloride in water can only be transported by means of wind and not by evaporation. We're all perspiring all of the time, 24/7--even when we're not "sweating" (i.e. the rate of perspiration exceeds the rate of evaporation). And with 6 billion plus people on the planet, I would imagine that if what you're suggesting were true, then we would have high salinity everywhere in the world where people live in densely populated areas--especially during hot weather. But that is not the case or at least I've seen no evidence suggesting that.



    I'll admit the nitryl chloride in the air in Boulder, Colorado is a mystery, but I can assure that it has nothing to do with human perspiration.
    logicman
    If it weren't the case that salt water leaves its sodium chloride content behind when it evaporates from the oceans, then we would not have any fresh water bodies of water at all any where on the planet. The same applies to human perspiration.
    Sorry Eric, but I must disagree.

    When any solution evaporates it tends to carry over small quantities of the solute as aerosol particles.  In the environment these aerosols tend to have a gradient of atmospheric distribution around their source.  NaCl particles cause corrosion of iron and steel in coastal regions.

    The chemistry of sea salt aerosol and its measurement
    M. P. Paterson&R. S. Scorer
    http://www.nature.com/nature/journal/v254/n5500/abs/254491a0.html

    SeaSalt Aerosol Particles
    https://www.ecd.bnl.gov/steve/pres/angels_pin_vgphs.pdf

    The formation of hollow sea-salt particles from the evaporation of drops of seawater
    Roger J. Chenga, Duncan C. Blancharda and Ramon J. Ciprianoa
    http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V95-48CNMKP-3...
    jtwitten
    Michael is right. The bigger issue with your hypothesis is that the phenomenon does not appear to correlate with population density or temperature, which would be predicted by your hypothesis. Your hypothesis cannot currently be considered plausible in the face of this issue.

    Furthermore, aerosols are very different from evaporation. In evaporation, a substance in the liquid state undergoes a state change to a gas. Aerosols are very small droplets of liquid, which may evaporate. The studies you reference do not show salt "evaporating". Instead, they address salt in the atmosphere and salt particles in aerosol following evaporation of the water within which they were originally dissolved. Standard sweat evaporation does not generate aerosols. Perhaps Boulder has an increased frequency of pugilistic contests. . . 
    by Lance Iversson (San Francisco Chronicle)
     
    I agree completely, Josh on both points.
    logicman
    Aerosols are very small droplets of liquid, which may evaporate ...
    The term 'aerosol' as used in climate science is much more generic: it is not confined to liquid droplets.

    Aerosols are airborne ions, non-gaseous molecules and particles.  Any small aerosol, if energetic enough, can become airborne in a local bubble of warm air - especially humid air.  The atmosphere is a global scale ion transport mechanism.  ssNa+ is one of the most common ions.   The source of the Na is irrelevant: all that is needed is a mechanism of evaporation.

    SSA is found far from the sea in precipitation in Greenland and Antarctic ice cores.  The amount depends to a high degree on sea-ice extent and temperature.


    Atmospheric chemical cycles represent an area of climate science not widely known.  Sea Salt Aerosol - SSA - is probably the most widely studied airborne chemical.  There are quite literally many hundreds of papers available on the topic.


    Standard sweat evaporation does not generate aerosols.
    When human sweat evaporated to atmosphere condenses in confined spaces, surfaces must be protected against the corrosion due to the NaCl content of the condensate.
    jtwitten
    That is not the way aerosol is used in the context of the studies you cited.  This technical detail does not address the major issue, which relates to the lack of correlation between population or temperature and the pollution.
    rholley
    Have a look at Particle Sizes in Saturn's Rings and tell me how one would make an average out of that!

    And which sort of average?  A number average might indicate that 99% of the particles are smaller than 1 cm, but a weight average might suggest that (say) 10% or even more of the material is in chunks big enough to sit on!
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    logicman
    Robert: I somehow missed your comment until now.

    You cite an excellent example of how an average might be cherry picked to prove a point.
    The creature we call man is basically a universal phenomenon that he is not only unique in our earth. This statement can be found in different sources in literature.
    Speaking of the universe, one way to look at it may go something like the following. Suppose we have 2 points A and B in space. Actually there are innumerable numbers of such points so that the whole universe is filed with this point. This is to say that the whole universe has equal quality throughout. This is the most logical supposition we consider seriously.