Mathematical Commentary on Genesis 1: 27-28

Below I tried to use mathematics to explain the biblical viewpoint on gender issues. Men have used the Bible to place women as second fiddles. Much of this debate is not centered on just verses from the Bible but the use of the word 'man' which has been used to refer to 'humankind'. The position of most women is that such use of the word 'man' to refer to 'humankind' is a travesty of the fight for discrimination against women. As a result of this, these days it is appropriate for example to say 'chairperson' instead of 'chairman' or 'headship' instead of 'headmaster' etc. It is believed that such words as 'chairman' denotes the position as the preserve for men. My exposition here is to support the argument the word man means both male and female and both are equal in the eyes of God.

This is my absolute view and I am responsible for my own comments in this article.

"So God created man in His own image, in the image of God He created him, male and female He created them. And God bless them and God said, 'Be fruitful and multiply, and fill the earth and subdue it...' Gen. 1: 27-28.

First of all what is established here is there is a relationship between God and man. For the sake of what I want to do I will explain what relation means in Mathematics.

A relation is an association between, or a condition satisfied by, ordered pairs of objects, numbers, etc such as ab=1, ........is greater than......or...... is the father of......or.......is the god of(mine).......(The Harper Collins Dictionary of Mathematics). An ordered pair is an ordered set of two elements; example {Mrs. Quansah, Adwoa} will be an ordered set for the relation 'is the mother of'. What it means is that this order cannot be changed to maintain the same relation. If the order is changed then we have what we called an inverse relation. In the example I have used {Mrs. Quansah, Adwoa}the ordered pair of the inverse relation 'is the duaghter of'' is {Adwoa, Mrs. Quansah}. So if the relation 'is the mother of' then the inverse relation 'is the daughter of'.

There are types of relations in Mathematics such as one-to-one relation, one-to-many relation, many-to-one relation and many-to-many relation. I do not want to go into the explanation and examples of these types of relations, but one-to-one and many-to-one relations are regarded as functions in mathematics. A function is denoted by using the letter f or g or h etc.

Since according to Genesis 1: 27-28, God created man in his own image we can define the relation 'the creator of' as the relation between God and man. So, man is the second element of an ordered set. The first member is God. The set is {God, man} and is defined by the rule 'the creator of'. This relation is one-to-one or injective and therefore a function. We can show if this is so. Let the first set of the ordered pair be denoted as G={g} where g=God and the second set be denoted M={m} where m=man. Let the function f denote 'the creator of' then we show that g₁, g₂  G with f(g₁) =f(g₂)=m, then g₁=g₂. So it is the same God. So this means there can only be one God.  

All we can say is that our function f is an injection of G into M. But let’s take the expression ‘of male and female’ in the verse quoted above. The question is, is the female also created in the image of God? Is the female a second fiddle of man? To look at these questions the members of our second set are now two, M={male, female}. Our ordered sets are now {g, m} and {g, f}. where male=m and female=f. g means the same as stated above.

The relation is no more one-to.one or injective. In mathematical terms it means there is more than one image of God because we can show that if g₁ , g₂  G then f(g₁) f(g₂) and hence g₁ g₂. This result would mean there might be more than one God for each to created male and female in their own image.

For the polytheist this is a good result but for the monotheist this result shakes the very foundations of his/her faith. For the monotheist female activists though happy with the inclusion of female in the proof will not appreciate the result. The monotheist male chauvinist is all the more happy. Mathematics has shown all along that he has been right in treating the woman as second fiddle but not as equal.

But the acceptance of the first proof in the line of thinking of the male chauvinist is a denial of the image of God in females. But this is a contradiction to the statement ‘male and female he created them’ and therefore his reasoning cannot be accepted. 

The implication is that God created male and female equal, that is {m} and {f} are equal sets. God named the set Man i.e. Man=male =female. The set {m, f} is not an ordered set (in this sense) since we can change the order and it will still remain the same. Whatever man can do women can do!

The proof of the invertibility of the function f :the creator of, leaves the question so what is the inverse relation (function) between God and man? If we invert the function then the ordered pair will reverse. But the first function is an important functio which places God at the center of man’s life. It is important for man to keep this relation.

Free SHS-My Thoughts.

Free SHS Education-Is it Possible?

During the IEA encounter with the electorate, the flag bearer of New Patriotic, Nana Addo Danquah Akuffo-Addo mentioned the free senior high school (SHS) education policy as one of his intended policies he will implement when given the nod to rule this country come January 2013.  This has not been the only platform on which the Hon. Nana Akuffo-Addo has stated this; he has done this on every electioneering platform since 2008.

Nana’s policy is a noble idea but not a novelty and I believe he has good intentions for the people of this country. But very characteristic of Ghanaians the debate has been politicized along NPP-NDC lines. You are susceptible to be labeled NDC or NPP depending on whether you disagree or agree with the possibility of free SHS education. Worse of all those so called party faithful, serial callers and some social commentators have taken entrenched positions on the issue depending on which side they belong.

Is this party labeling fair? Even if one belongs to a political party, does that person not have the right to speak his mind objectively without being reminded the party he belongs to? Our partisan attitude has created a gag order making it impossible for experts and professionals to speak their minds on some of these pertinent issues that confront our country. Our political landscape is fraught with politicians who have no political conviction of how they can solve our problems.

So is free SHS education possible in Ghana? In my opinion it is possible in the long term if certain pressing issues that confront our educational system are taken care of first.

A major problem facing our educational system today is the focus on quantity neglecting quality. It is obvious that the NPP’s policy on education is inherently going to perpetuate this quantitative aspect of educational policy. It is good that we all go to school but pushing everyone to go to school for the sake of getting ‘education’ is not enough. Education if properly given should equip the educated with employable skills or ability to create employment.

School drop out is not just the result of inability to pay fees. There are a lot of other factors that cause children to drop out of school. Children may drop out of school because the school system is not challenging enough. Brilliant children who exhibit unusual behaviors have been branded as ‘witches and wizards’ and are forced to drop out of school. Our social attitudes and perception of the educated have forced so many children out of school. In communities where the most respected or rich person is not an educated person children consider going to school a waste of time because they believe one can succeed without education. Certain cultural and religious practices are also contributing factors to why some children drop out of school. Therefore basing the introduction of free SHS education on a single story of inability to pay fees is not enough.

Today while basic education is free and compulsory we know that not all children are in school. We can pat ourselves on the shoulder, however, since Ghana’s basic school enrolment is rated among the best in Africa. Our primary school enrolment is about ninety-five percent. Unfortunately our students have performed abysmally in international exams in basic math and science skills. Ghana’s educational system is ranked 148^th out of 181 in the world below countries like Equatorial Guinea and Namibia.

We also know that, though basic education is free some parents have their wards enrolled in private schools that charge exorbitant fees. Such parents are prepared to pay any amount of money to have the wards educated.  The reality is that majority of the public schools are producing a lot of illiterate graduates who can not read or write. The BECE results attest to this phenomenon.  Majority of these schools are found in the rural areas. The situation is that the gap between the rich and the poor, urban and rural is widening as a result of the kind of education they are receiving. 

Our quality of education is very poor as a result of many factors. One of these is teacher quality at the basic school level especially lower primary. The NPP cannot absolve itself of contributing to the problem when they created an ad-hoc solution of employing unqualified teachers to teach in their youth employment program.  When we continue finding makeshift solutions to problems we end up creating more problems. And one such solution is employing people who cannot even write their own names to teach in the lower primary because these are children who do not know anything. We forget that these years are formative years of the child, when the foundation is weak they grow up not knowing basic knowledge required to succeed at a higher level.

Another factor is not necessary infrastructure, even though this is eminent in the rural areas, but other conducive facilities that facilitate teaching and learning. Every child needs books to augment what is taught in school. In this age of information and technology children need access to computers. The reforms that introduced the JHS and SHS concept revised the curriculum and introduced the study of ICT at the JHS level. Computer studies which was also part of the Integrated Science syllabus at the SHS as level was decoupled and introduced as a subject on its own. Majority of schools mostly at the JHS level and the SHS in rural areas cannot boast of computer laboratories to facilitate the study of the subject.

Despite the employment of unqualified teachers to fill classrooms that are empty we have teacher deficit in this country. This teacher deficit does not occur in urban areas but in the rural areas of this country. In fact schools in urban areas are choked with teachers who do less work compared to their counterparts in the rural areas. Most teachers are not ready to accept posting to the remote parts of this country because it is a disincentive to work in this part of the country. Apart form the abundance of foodstuffs there is no opportunity for those teachers in the rural areas to upgrade their knowledge and improve their personal lives.

The School Feeding program and the Capitation Grant were very important interventions introduced by the NPP government to encourage children to go to school. These programs are being continued and expanded by the NDC government. We also know that the SHS boarding fees and some other fees are being subsidized by the government for the running of secondary schools in the country. But these programs are fraught with serious problems forcing some of the schools to borrow money to run their schools. And when they schools cannot pay they are forced to closed until government pays them.

I believe that the introduction of free SHS education will only reinforced the widening gap between urban rich schools and rural poor schools. Majority of the people who attend these schools in the city are the ones who go to prestigious private schools in the city. Schools that charged exorbitant fees but affordable by the elite in our society. It is a fact that the computer selection and placement program that selects students to SHS have never picked a student who hails from a school in a rural area who had aggregate 20 and place the child in Achimota school.

The free SHS education will also create an avenue for the proliferation of private senior high schools which may be producing more quality students than the public ones. The signs are already there. We know what is happening at the basic school level. Virtually every basic private school outperforms the public schools at the BECE exams. Parents are ready to send their wards to these schools. It is no doubt that such a situation will arise with introduction of the free SHS education. We should be wary so that we do not create a society where the minority elite and their children get access to the best things of this country while the majority poor get access to the worse. Every Ghanaian child deserves the best and that does not necessary mean free SHS education.

Today JHS graduates, SHS graduates, technical and vocational graduates, polytechnic graduates and university graduates are being turned out everyday. What skills have they acquired to meet the job opportunities of today’s world? The NPP promises job creation based on manufacturing. Will our mass production of graduates through the free SHS be equipped with the right skills to be employed in the manufacturing industries? Will our universities be able to admit all qualified applicants who want to pursue high education?

Free SHS education is possible but in the long term. A better educated Ghanaian will mean a well informed Ghanaian who will make well informed choices in the interest of this nation. A better educated Ghanaian will demand good service and accountability from politicians. A better educated Ghanaian will contribute immensely to the development of this country. That is what is needed right now, to improve upon the quality of education and work progressively towards free SHS education.

Is this the Hand of God at work?

GOD WORKS IN MYSTERIOUS WAYS.

A popular Christian parlance goes like this, “God works in mysterious ways”. Indeed this is so true. The African is fanatically religious. Our religiosity is so deep that statements like this and others such as “It shall be well”, “God is in control” sip deep in our language and social fibre. Our lives are shaped and directed by these statements.  And we are criticized for the way we are; our fanaticism for religion, our superstition and belief that our fate is shaped by God or the gods. And it is rightly so, taking into evidence the evils that have engulfed the continent. There are wars spotted all over the continent and poverty has eaten deep into the crevices of our society. But we are also not a continent of derelict individuals who can buy guns and start “pumping” bullets into innocent people. Though we fight wars we do it for the “good” of our countries.

Unlike most continents our religious nature is the source of our survival. Imagine how the African will survive without God or a god. Our belief in a deity gives us hope, inspires us and informs us that though our problems are huge they are not insurmountable. This sort of thinking might have been the bane of our mediocrity but it has also strengthened us and developed our survival instincts.

I followed a discussion on Harvard Business Review through Linked, a social forum, which bothers on the reasons why it is difficult to do business in Africa. Have you wondered why Africans who stayed outside for long find it difficult starting business here in Africa while those here are successful business people? As you go from Johannesburg to the slums of Kenya, from Senegal to Ghana and then to Nigeria, there are successful individual “businesspeople” on the streets of these countries. Irrespective of the litany of reasons why doing business in Africa is difficult see the indigenous African businessperson and hears his success story.

The death of our beloved president of Ghana, the late Prof. Evans Atta Mills has generated so much debate. Sometimes when I listened to the debates on TV and radio and the ones around me which I sometimes joined I am amazed at how the death of a man can change our perceptions about him. And it has been the debate as to whether we should say good things about a man whiles he is alive or when he is dead. Especially from the angle of politics, is it alright for us to say that our opponent is such an honest and kind person if he is so whiles he is still alive? In the struggle for power, more so devoid of selflessness, the possibility is very remote. Even while the president is dead people are not very happy that he is being considered as a successful president. Some still believe that irrespective of his sterling public life he was a flop as a politician. And it is interesting and funny for people to judge the memory of the man that way.  Not now, not tomorrow but posterity will see this man of blessed memory as one of the strongest and successful presidents in the history of Ghana.

You know how people think that Nkrumah did not do much for Ghana. They say with the amount of money the colonial government left him he should have done more. They accuse the man of doling money to other African countries leaving his own people. But Nkrumah is the African of the millennium. He saw long ahead of his peers and that was his fault. A man who is ahead of his friends and a dreamer is always treated differently more so harshly. You know the story of Joseph in the Bible!

I saw the passion of Nkrumah in Atta Mills. I saw how passionate he spoke when he talked about education, unemployment and poverty. He felt it was the opportunity created by Nkrumah that gave the chance for him to attend a prestigious school like Achimota, why is that not possible today? Well it looked as if the vision of Nkrumah died with him on the 24^th of February, 1966. Since then nothing has improved, things just got worse and worse until the coup in 1981 which by then things have escalated beyond redemption.

The first coup happened on a 24^th, and the first time we have lost a president occurred on 24^th, July 24^th, 2012. Is God working in mysterious ways again?

While in the past the political terrain has been choked with the same people who kept on recycling themselves, it seems we are entering a new dawn of politics where those firebrand individuals are giving way to more tolerant individuals. The president’s death is becoming a birth canal for more technocrats who probably will put the interest of these nations before themselves to be born.

After February 24^th the military took over power and lead us on a road of ups and downs and turmoil.  

July 24^th has become the beginning of when God will intensify his work in mysterious ways for our country Ghana.  After all, our late president was a firm believer in God and His hand in the affairs of men. His death may therefore be seen as the divine hand of God working in mysterious ways. IT IS WELL!

Muddy Waters

Truly, man is like the ocean no matter how much water that flow into it, it will still want more. The ocean, however, houses many creatures and provide them shelter, food and confort. And as more water pours into it, the ocean shoulders more responsibilities because each one comes with their troubles. I am not a marine engineer or someone who has studied about the ocean but I believe the ocean does accept anything that enters it.
There are some African leaders who are never satisfied with what they have had from the corridors of power. Even when they have eaten and licked the bowl they are unhappy if there are drips around for others to also lick. Well everyone is licking anyway. That in my opinion is the reason why most of our politicians enter into politics. It is not a shame anymore for anyone to amass wealth one year after entering politics.
And these are our role models! Should we be blame if we do the same?
For our politician every vote counts during election but every voice does not count after election. It is funny how politicians can sit in a small boat and row five miles on water to a place like Nzulezu just for votes and ignore every promise they made after they have won power?
I am not getting my thoughts well, but forgive me the ocean is better than our African politician.