George Boole and Childhood Mortality in the Cork Union Workhouse

 Anthony Ryan1,2, Desmond MacHale3, Yvonne Cohen4

1Department of Neonatology, Cork University Maternity Hospital
2Department of Paediatrics and Child Health, University College Cork, Cork, Ireland
3School of Mathematical Sciences, University College Cork (UCC), Ireland
4Chartered Accountant, Declan O'Connell & Co, Cork, Ireland

‘Probability is expectation founded on partial knowledge’.

George Boole

In 1855, George Boole, founder of Boolean algebra and the foundation Professor of Mathematics in Queens College Cork (now UCC) prepared a treatise on childhood mortality at the Cork Union Workhouse (CUW). Although the essay was purely mathematical, Boole, a family man with five young daughters, was socially aware and empathetic with the plight of the poor. We present excerpts from the treatise (available in Desmond MacHale’s biography of Boole1 and on, while exploring Boole’s social philosophy, along with a brief history of the CUW.

Boole began by stating his aim:

In the Cork Union Workhouse in the year 1855, 167 children died. During the same year the average number of children in the house was 139. Required the probable percentage of deaths in the year among children not removed alive.

Unusual for a scientist, Boole did not clearly define his study population. The term “children” can imply a range of years anywhere between birth and adulthood. Considering the Victorian Romantic ideal of childhood as a time of innocence, and the need to differentiate children from adults in the Workhouse daily roll-call, it is reasonable to conclude that the Boole reference to children was from birth to twelve but possibly 15 years. Boole, also, did not indicate how his data was acquired.

The setting of Boole’s study was the CUW, in Skahabeg North Townland, Co. Cork. It was designed by the Poor Law Commissioner's architect George Wilkinson and was one of the largest of the 143 workhouses built in Ireland, accommodating up to 2,600 inmates2. It was completed in 1841, having cost £12,800 to build and £8,000 to outfit3. The workhouse was an isolated place built outside the 1840’s boundaries of Cork City. The gabled entrance, still standing today, was built in a Tudor domestic style, with Tudor arches and hood mouldings over the windows. Entry into the workhouse was generally seen as a journey of no return, reserved for the destitute, the starving and the dying, and, even today, it remains a reminder of an especially difficult period of Irish history, the Great Famine. From the outset, the CUW catered for pregnant women, initially with a 10-bed facility, and also included a Fever hospital catering for the regular outbreaks of smallpox, cholera and typhus from the tenement lanes of Cork City.

Boole continues.

We suppose the state of things uniform as regards the causes affecting mortality. This is a necessary ground of calculation. Of course children who had been exposed a long time to the prevailing influences of the place might be more likely to die within a given time than those who had been exposed for a shorter time owing to the weakening of the powers of life. On the other hand they might be less likely owing to their systems having become accustomed to such (noxious) influences, but in the absence of information in such points, we can only reason on the supposition of the causes influencing mortality being unison for all and during the whole time.


Boole’s assumption of a steady rate of childhood mortality throughout the year was necessary for mathematical purposes, but was not true in reality. It is likely that children in a closed institution such as the CUW died mainly from childhood infectious diseases and from sporadic epidemics of diphtheria, cholera, typhus and smallpox, compounded by malnutrition, considering that the Irish famine hit County Cork particularly badly. In addition, there is a known seasonal influence on infant mortality with higher rates in the winter months. Boole, who showed an interest in maternal health when his wife was pregnant4, also shows some understanding of child health in suggesting that the weakening of the powers of life (e.g. through malnutrition) increases mortality. We know now, for instance, that vitamin A deficient children have a higher mortality from measles5. In addition, debilitation in utero and early infancy has been shown to decrease survivability in later adult life6. Boole also showed a grasp of the concept of acquired immunity: in 1863 he had one of his daughters vaccinated against smallpox with Jenner’s cowpox lymph7.

However Boole lived in the pre-Lister-Pasteur era. His concept of what we now know are infectious organisms was that of the miasma (μίασμα, ancient Greek: "pollution") theory, which held that diseases such as cholera, typhus and the plague were caused by a noxious form of "bad air", emanating from rotting organic matter. This explains why Boole took his own family out of the “noxious influences” of Cork City to the cleaner airs of the villages of Blackrock and Ballintemple1.

Boole’s second mathematical assumption was as follows:

Now the probable proportion of children not removed alive which die within a year being very short is equal to the average number of children who die within such period divided by the average number in the house, I say ‘within a very short period’, because if the period be not very short the proportion of the deaths, and the longer the period the greater the proportion will be of those children admitted after commencement of the period - the greater also will be the effect of ‘removals’. While he refers to “removals”, Boole is including children who died as well as those “removed alive”, since he was well aware that, despite the high walls, inmates could leave voluntarily.

Let the year be divided into a large number of equal portions, each therefore small, and let the number of these portions be represented by ρ. Let also n be the number of children in the actual care 167 who die in the year and a the average number in the actual care 391, in the house. Then n/ρ will be the average number dying within one of those short periods referred to.

Boole arrives at the following equation (A) and continues:

And the probable percentage of annual deaths not removed alive will therefore be 100{1 - (1- n/aρ) ρ}      (A)

We have seen that p must be a large number. Theoretically it should be infinite, for by making the period infinitesimal we completely eliminate all probability of error arising from the change produced by the admissions of new inmates or removal of old ones alive. Now, if we make the p infinite, the formula (A) assumes the form 100 (1-e -n/a) (B), where e is the base of Naperian logarithms, viz: 2.718281828….

I will illustrate these formulae by calculating the probable percentage of deaths in a year among children exposed continuously to the state of things which prevailed in the Cork Workhouse in 1855*….,

n = 167, a = 139, p = infinity. Then from (B) percentage = 69.88. And this is the true value.

Boole’s stark conclusion was that children entering the CUW had a 70% chance of dying there. What made him interested in this matter? George Booles’s consistent underlying philosophical sentiments were those of a non-conformist, liberal humanitarian. He believed in God (but not the Trinity) such “that the laws of the material universe are the expression of His will, their unfailing certainty is the symbol of His Immutableness; their wondrous adaption is an argument of His Universal Presence”8. He was actively involved in promoting social reform. He joined a crusade to appeal the Corn Laws that artificially raised the price of bread, and he abhorred the evils of prostitution8. As the founder of Boolean logic, he was also a believer in the ability to think clearly and with the goal of pursuing the truth. Yet, practical ethics appeared to give him more solid gratification than mathematics as “ethics appeals to both emotion and reason”.8 In a footnote to his comment above on “the conditions prevailing at Cork Workhouse in 1855”, he noted, perhaps over-optimistically: *Happily, through the benevolent exertions of one individual, no longer prevailing”. We do not know to whom he was referring, but it may have been Professor D.C. O’Connor, the first medical attendant at CUW and the first professor of Medicine (1849-1888) at Queen’s College Cork. However, he resigned from the CUW, to become the first doctor at the newly founded Mercy Hospital, just a year after Boole’s treatise was written.

What happened to the CUW? In 1870, the Sisters of Mercy at St Mary’s of the Isle took charge of the Union Hospital9. In 1898, the Workhouse name was changed to the Cork District Hospital. In the 1920s, all workhouses in the Irish Free State were abolished and the CUW emerged as the Cork County Home and District Hospital. A 51-bed maternity unit was opened in 1952, when the name was changed to St Finbarr’s Hospital. In 2007, this maternity unit was amalgamated with the Erinville and the Bons Secours maternity hospitals to form the Cork University Maternity Hospital in Wilton. St Finbarrs remains as a center for elderly care, rehabilitation and blood bank facilities. However, it is still looked upon with trepidation as the Skahabeg Workhouse by the older citizens of Cork and Munster, while retaining a vast repository of memories, symbolism, iconography and cultural debate with its plaques, ruins and haunted memories10.

Conflicts of Interest Statement
The authors of this study do not have conflicts of interest to declare.

Correspondence: Prof Tony Ryan, Department of Neonatology, Cork University Maternity Hospital, Wilton, Cork, Ireland.

Telephone: 00353 21 4920500,                                             

Email:  [email protected]


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