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Uncertainty and the Physical World


Physical World

Certainty and the Abstract World

In the last section (Mathematics and the Physical World) we saw that it was possible to make a statement in the abstract world and then prove that it is logically consistent. The most extensive example of this being mathematical proofs. Mathematical proofs give certainty. They are absolute however, that absolute certainty only applies in their abstract world. Albert Einstein said that "as far as the laws of mathematics refer to reality (the physical world) , they are not certain; and as far as they are certain, they do not refer to reality (the physical world i.e. as far as they are certain they only apply to the abstract world)." In short there is no certainty in the physical world. 

What did Einstein mean?
 To answer this question let's explore the story of fingerprints.

History of the Fingerprint


As early as 1885-1913 B.C.E. fingerprints were used as signatures with people impressing their fingerprints into the clay tablet on which contracts had been written. Similarly by 246 B.C.E. Chinese officials impressed their fingerprint in clay seals and later when silk and then paper was used the parties to the contract made a palm print on the document. At this stage people were using finger prints as a form of signature but they probably did not realize how well finger prints could identify somebody.  

In 1684 Nehemiah Grew an English physician, botanist and microscopist published a paper describing the ridge structure of skin on the fingers and plams. This was followed in 1685 by the illustration of the ridge structure of fingerprints in books published by Govard Bidloo and Marcello Malpighi. However, it wasn't until 1788 that Johann Christoph Andreas Mayer observed that although friction ridge patterns from the fingerprints of different individuals could be similar they never appeared to be the same.  

As people's mobility increased and cities grew larger it became very difficult for the authorities to identify an individual if they lied about their name. To solve this problem a Parisian police clerk named Alphonse Bertillon created in 1883 a method called anthropometry. This method used a set of anatomical measurements to define an individuals identity ans was effective but difficult. Sir Francis Galton inspired by the ideas on Evolution of his half-cousin Charles Darwin studied amongst many other things differences in human beings. He investigated Alphonse Bertillon method for identifying individuals and compared it to fingerprinting and concluded for a variety of reasons that fingerprinting was superior. Galton was the first to place the study of fingerprints on a scientific basis. He devised the first workable fingerprint classification system defining 8 broad groups: 1) plain arch, 2) tented arch, 3) simple loop, 4) central pocket loop, 5) double loop, 6) lateral pocket loop, 7) plain whorl and 8) accidental. Some examples are shown below.


Right Loop


Tented Arch

He collected over 8,000 sets of prints and in his 1892 book 'Finger Prints' he discusses using finger prints as evidence. On page 101 he states "no great reliance can be placed on a general resemblance in appearance of two finger prints, as a proof that they were made by the same finger, though the obvious disagreement of two prints is conclusive evidence that they were made by different fingers." However based on the minutiae of the many types of difference he had found in fingerprints Galton went onto calculate that "as the number of the human race is reckoned at about sixteen thousand millions, it is a smaller chance than 1 to 4 that the print of a single finger of any given person would be exactly like that of the same finger of any other member of the human race." (page 110 -111). If you include the prints from other fingers on the hand the chance decreases even further. 
It was Sir Francis Galton's work that paved the way for the law courts to accept fingerprints as evidence. 

The Success of Fingerprinting

Fingerprinting has been very successful. It was first used as evidence to convict a criminal in 1892. An Argentinian police office, Juan Vucetich, had studied Galton's work and used his fingerprint identification method to show the bloody fingerprint found at the crime scene could only have been Francisca Rojas'. Fingerprinting proved both practical and effective. The first Fingerprint Bureau opened in Calcutta in 1897. It was soon followed by many others. The number of fingerprints being stored grew rapidly. In 1902 Dr. Henry P. DeForrest pioneers the first systematic use of fingerprints in the U.S. by the New York Civil Service Commission for testing. Soon the U.S. prison system, Army, Navy etc were all using fingerprinting.  The U.S. Congress consolidated the National Bureau of Criminal Identification and the U.S. Justice Department's Bureau of Criminal Identification and established the Identification Division of the FBI in 1924.  By 1946 the FBI had processed  100 million fingerprint cards. 

Fingerprint identification proved both practical and effective. Law enforcement agencies found it to be critical tool in fighting crime. The FBI published a book call "The Science of Fingerprints". In the introduction J. Edgard Hoover wrote "
Of all the methods of identification, fingerprinting alone has proved to be both infallible and feasible. ... While many cases of mistaken identification have occurred through the use of these older systems, to date the fingerprints of no two individuals have been found to be identical. "

By 1971 the FBI had 200 million fingerprint cards. The need to compare suspect's fingerprints to so many record cards drove the adoption of computers for both storing the fingerprint records and for automating fingerprint identification. The automated fingerprint identification system (AFIS) was developed. 
Many of the 200 million cards were found to be duplicates and in total there were fingerprint records for between 25 to 30 million individuals in the crime records. The FBI's Integrated Fingerprint Identification System (IAFIS) in 2009 had more than 54 million individual computerized fingerprint records for known criminals. 

The very success of fingerprint identification and the resulting huge fingerprint databases has increasingly revealed a problem. 

There was a common perception that fingerprint evidence gave certainty. Once the fingerprints matched then the job was done. You had your proof. This perhaps relates back to the early days of fingerprinting. At the time it was widely understood that science proceeded using the inductive method. 

'The Inductive (Scientific) Method

  • State the Question: What information do you wish to obtain?
  • Make Observations: Gather information that will help answer your questions by researching, making, and recording direct observations of the subject
  • Form a Hypothesis: After gathering an adequate amount of information, apply what you have observed to form an educated guess or prediction of what the answer to your question is
  • Test: Test your hypothesis by performing an experiment that includes a variable
  • Analyze: Examine the results of your experiment to understand what they imply
  • Draw a Conclusion: Based on the interpretation of your results, develop a general principle as an answer to your question.'

When fingerprint identification was first introduced to law enforcement Science had been very successful. The hypothesis science created were stated as laws. For example Newton's laws of motion. Fingerprint identification applied scientific method and so by both association and because of its effectiveness the hypothesis of fingerprint identification took on the status of a scientific law.  
This confidence and association is reflected in the FBI's publication 'The Science of Fingerprints'. The FBI were not only presenting fingerprint identification as scientific but they also said in the introduction that it was 'infallible'. They were not saying there were no errors but that these errors were very few and that they were caused by humans making mistakes not the underlying science of fingerprint identification. The underlying science was infallible.

Problem of Induction

In spite of the huge success of fingerprint identification there was a problem and this lay at the foundation of how a theory was proved in the physical world. David Hume observed that logically more and more supporting evidence does not prove a theory yet one piece of negative evidence will logically disprove the theory. The problem of induction is often illustrated with the following example:
  • A naturalist is observing different types of birds 
  • Generalizing from her observation she states "all swans are white"
  • As a good scientist she now tests her theory. She travels all over the country and makes many, many observations. All the swans she observes are white.
  • Conclusion: theory proven "all swans are white"
The naturalist might have observed 1,000 or 10,000 or 100,000 white swans however, logically she cannot say the theory is proven. What about the other swans she has not observed. There might be a Swan that is not white. If however, during her work she finds just one black swan she can now logically say that theory "all swans are white" has been disproved. So although logically you cannot prove something in the physical world you can logically disprove it. This takes us back to Foundation Idea 3: Evidence that challenges an idea is much more significant than supporting evidence.

There are two major consequences:
1) Scientific theories about the physical world are conjectures to be tested. They are not laws and they cannot be proved absolutely.  
2) and, although they are conjectures by testing and trying to falsify them their usefulness in the physical world can be measured. This allows us to rank ideas. Those that substantially fail testing can be set aside. 

J Edgar Hoover's assertion of the 'infallibility' of fingerprint identification

If scientific theories are not laws but very well tested and useful conjectures then where does this leave J Edgar Hoovers assertion that fingerprint identification was 'infallible'. Logically it means that fingerprint identification cannot be 'infallible'. This has been shown to be true. 

Brandon Mayfield and the Madrid bombing

After the Madrid bombing of March 11th, 2004 the Spanish police sent fingerprints to international law enforcement agencies. The FBI Latent Print Unit reported a "100 percent positive" and an "absolutely incontrovertible match" against one of 20 fingerprint candidates returned in an automated IAFIS search. However, the Spanish National Police examiners concluded the print did not match and after two weeks they identified another man who matched. In the meantime on the evidence of the FBI's fingerprint identification Mayfield an American convert to Islam had been arrested. In January 2006 a U.S. Justice Department report was released and it concluded the FBI work was sloppy but it cleared them of more serious allegations. On November 29th, 2006 the FBI agreed to pay Mayfield $2 million USD and they stated that Mayfield had erroneously been linked to the 2004 Madrid bombing through a fingerprinting mistake and that they had taken steps to ensure this did not happen again.

Treatment of negative evidence

There is an important difference in how negative evidence is treated. If you believe that fingerprint identification is infallible and you have say 12 matching points and one point that does not match. It is very tempting to argue that the 12 matches out weigh the 1 non match and conclude that you have matched the identity. However, as Galton pointed out '... the obvious disagreement of two prints is conclusive evidence that they were made by different fingers' He was talking about large fingerprint characteristics. However, what is true for large characteristics is also true for small features.  Even a small feature difference of two print is strong evidence that they were made by different fingers.

So for fingerprint identification a large number of matching characteristics and no non matching characteristics gives a very high probability that the prints came from the same person. However, if the fingerprints match on a large number of characteristics but do not match on one characteristic then you have strong evidence that this is not the same person.


It is very easy to conclude that because no idea about the physical world can be proved then all ideas are equality valid.However, this is not the case. Ideas can still be compared. An idea that has survived a range of tests is more true than a idea that has failed one or more test. Further an idea that may have failed a test may still be a close enough approximation to be very useful in application to physical world problems.

There is a curious relationship: the more useful an idea is the more it excludes but at the same time the more generally it applies.


All ideas about the physical world are conjectures. Einstein realised this when he said  "No amount of experimentation can ever prove me right: a single experiment can prove me wrong."  (a paraphrased translation of Einstein's work "Induction and Deduction")
This conclusion has important implications in other areas. For example if we look at the business world. In this case business theories (products, services, strategies, investment plans etc) are tested in the physical world of the market place (in as far as the market place addresses physical world requirements and problems). We have already seen that there is no absolute proof for theories about the physical world. Therefore, like scientific theories business theories are conjecture and they should be treated as such.