Sunday, January 15, 2017

Transforming firkins

Sermon for the second Sunday after Epiphany.

How much is a firkin?
Imperial measurements are sadly dying out. It’s a shame because they are based on our human dimensions and thus fit our lives better than something that is rather more arbitrary. Both of the words inch and ounce come from the Latin word for thumb. We still think in feet. A furlong is literally a furrow-long. But what of a firkin?
Firkin comes from the Dutch word for a quarter of a barrel of beer, and is actually 72 pints (or 41 litres if you’ve gone metric).
This means that three firkins would be 216 pints. That’s a lot of water and would weigh approximately 250 pounds! That’s heavy!
And yet, six jars of this weight are brought before Jesus for Him to turn the water into wine. All 216 pints in each jar turned from water to wine - that’s clearly a miracle, isn’t it?
[PAUSE]
Yet, if we listen to Our Lord carefully, it isn’t what He does that matters to Him. He does it in response to what others do. He wants us to play a part in these miracles. There would be no wine if some servants hadn’t laboured hard to bring the water to Him. The paralysed man is let down through a roof through the faith for his friends and Jesus can respond to that faith by telling the man to take up his bed and walk, which he does. Likewise, blind Bartimaeus calls out in faith of Christ and is rewarded with his sight. What would have happened if Our Lady had said “no!” to God rather than “yes!”?
[PAUSE]
Here in Cana, it is Our Lord’s mother who has faith in her son and communicates that faith to servants who are willing to lug six jars of about 250 pounds to Jesus for Him to work a wonderful miracle. A bride and groom who aren’t even mentioned by name receive a gift of about 1,246 pints of the best wine. What a wonderful wedding gift, and what a lesson for us!
[PAUSE]
We have seen the Lord’s Epiphany – His revelation of Himself to us. Effectively, He has said to the world, “Here I am!” This is unequivocal. The presence of Our Lord in history is without parallel. We have a man who says that He is God. We have a choice of whether or not to believe Him. Many people these days will not. They demand evidence and then, when it is provided, they disregard it because it is not in keeping with their idea of the world. They do not want their worldview challenged, and yet they would demand miracles of Jesus which would break that worldview to pieces! To them, Our Lord gives only the sign of Jonah – His shameful death upon the Cross.
But what if we do dare to believe?
[PAUSE]
It is for those who are prepared to have their world challenged that Jesus performs His miracles, and in abundance. Those who are prepared to lug a thousand pints of water to Him just to see what He will do, they are the ones who receive something astounding, something good, something truly joyous! If we want a miracle in our lives then we must believe that Our Lord can do miracles and demonstrate that to ourselves by working hard in coming to Christ so that He can make that transformation in our lives. This is our Salvation, and it is a miracle that comes about not only through our Faith but our living out that Faith in response to God’s Epiphany in our lives.
This wonderful transformation is hard work. It requires a change of life, a commitment to suffering and sacrifice for the Kingdom of God, and a denial of our rights so that God’s righteousness can enter our lives. As we stand looking into the wedding at Cana, we see hard labour turned to joy overflowing. The work pays off; the miracle is there for all to see; water becomes wine, all 1,246 pints of it!

Sunday, January 08, 2017

Revealed for a reason?

Sermon for the First Sunday after Epiphany

What does the Lord’s Epiphany mean to you?

Remember, there are two aspects of the Lord’s Epiphany: the Adoration of the Magi, and the Baptism of the Lord in the River Jordan. Which do you identify with most?

[PAUSE]

God has revealed Himself to us. That is what Epiphany means: the realisation that God is in our midst. Our brothers and sisters in the Eastern Church call it Theophany which hammers it home that God has truly revealed Himself to us. The question now is, if God has revealed Himself to us, how are we to respond?

The Magi see Our Lord for who He is as they see His star in the East and travel hundreds of miles to worship Him. 

St John the Baptist sees Him for who He is when He sees the Holy Ghost descend upon Him from above and hears the voice of God declaring that Our Lord is indeed His Son.

How do you see Him for who He is?

[PAUSE]

The Magi know of the Lord through their understanding and learning. They deduce that He is born in Bethlehem and then seek to prove that they are right by going out to find Him. Is this how we encounter Our Lord? Do we believe the historical record which shows that He does exist – a record that is clearer than that of Julius Caesar? If we do, then does the historical fact of the empty tomb convince us that He is who He says He is? This is how many people first come to Christ, by understanding Him as a real life person. However, can we only worship Christ on paper? Don’t we need to dare to travel out thousands of miles and meet Him?

[PAUSE]

St John the Baptist knows of the Christ through what His parents have told him of the proclamation of his birth by the angel, and the Virgin Mary’s visit to his mother. He knows his kinsman, Jesus, and he has been told that He is the Messiah. So St John engages in his service of God by proclaiming that coming Messiah. Yet he is working only by faith, feeling his way and trusting in the testimony of others. It is not until he sees the miracle of the Descent of the Holy Ghost upon Our Lord that what he has been told by his family and friends makes sense. This is how many people first come to Christ, by trusting in the testimony of others. However, how do we know we are not being misled by someone who may not really know the Lord? Are we willing to change our lives radically on the basis of believing what someone says, no matter how close they are to us?

[PAUSE]

This is the great challenge that we face in the Church. The testimony of the Holy Scriptures and of the Holy Tradition, and the testimony of Christian men and women are ways in which people find their way into the Church. Are these sufficient reasons for people to stay in the Church? The evidence of dwindling congregations would say otherwise. The only reason that people will stay in Church is if they find what they are looking for, Our Lord Himself. The Magi find Him; St John the Baptist finds Him: we need to be able to find Him. This is why it is crucial that we churchmen and women, who are engaged in the same search, live our lives in a way that will bear witness to the reality of Our Lord Jesus Christ.

Many Protestants will speak of “having a personal relationship with Jesus”. This is something to be applauded: the better we know Our Lord, the better we can live out His will in our lives and thus bring Him closer to those who need to know Him. The way we cultivate this relationship is through our study of Holy Scripture, through our personal prayer life, through regularly meeting Christ with others in the Holy Sacraments, and through doing those things He tells us to do.

Gimmicks won’t keep people in Church. Entertainment won’t keep people in Church. Academic study won’t keep people in Church. Beautiful liturgy won’t keep people in Church. The only thing that will keep people in Church is if they find God there revealed in His Son through the Holy Ghost. Our job is to allow that to happen.

How are you going to reveal God to those who need to know Him?

Friday, January 06, 2017

Uncompromisingly compromising or vice versa?

I see lots of discussion in the Anglican world about the nature of sacraments, in particular the Eucharist.

Nothing causes more friction at a gathering of Anglicans than the mention of the word Transubstantiation. Say that, and the urbane soirée turns into the final battle in Return of the Jedi.

Is the Real Presence of Christ spiritual, physical, corporeal, or symbolic? Does it matter? Yes, of course it does, and the ink ( and blood! ) that has been spilt on this very issue shows that it cuts to the very heart of one's relationship with God. How on earth can Anglicans be reconciled if they differ so much on this issue?

Let's turn the problem around and look at on what Anglicans, and given the breadth   of what Anglicans believe, what most Christians agree on.

First, the Eucharist is important enough not to compromise one's belief on. It is commanded by Christ, and somehow bread and wine take on something of Christ in some way. For many Christians, the bread and wine take on the full identity of Christ as an objective locus of His Presence at the expense of their identity as bread and wine. There are disagreements as to how this identity is to be recognised and the nature of the locus. Is it spiritual? Is it a memorial, by which I mean something more than a simple remembring but a relication of one's experience in time? Is it physical? Is it metaphysical? It does matter what we believe, but we have to hold fast to what we believe unless the Holy Ghost compels us to believe.

This brings issues in that the one who believes in Transubstantiation could be accused of idolatry by one who believes in a spiritual presence. Yet, the one who believes in the spiritual presence could be accused of faithlessness and rejection of the words of Christ by the one who accepts Transubstantiation. Notice that I say could be accused. That doesn't mean that we have to accuse. Remember that the literal translation of Satan is "the accuser". What we must each do is to be true to our sincere belief, constantly thrashing our intellect against the Rock of Christ so that we do not become Kripkean in our dogmatism. If this means that we cannot be present at the same Altar in this Time, so be it. But we must trust in the same One Christ that we believe in with the same One Faith being members of the same One Church that we, and those with whom we disagree, are going to be together at the same altar in Heaven. Indeed, many of us believe that this happens at every valid Mass anyway!

Second, we must remember that there is no Anglican Church, no Roman Catholic Church, no Anglican Catholic Church, no Orthodox Church, there is only One Holy Catholic and Apostolic Church. That's it. Some of us may be Anglican as a noun by the doctrine of the prayer book and the formularies. Some of us may be Anglican as an adjective by history or by succession. Some of us may be Roman by location, by doctrine, or just by being in communion with the Holy Father. Again, that's just us. We can and should argue but not to convince, but rather to explain. Debates become tedious when they're very old. The Church Fathers say nothing conclusive about the nature of the Eucharist, save that Christ is really and objectively present following His promise to us. A promise that He keeps even when we do not keep ours. Christ's promise works for the salvation of the faithful be they Anglican, Roman, Orthodox, or Protestant. In Christ we are all brothers and sisters, yet we seem to accuse and abuse each other on the same level as the sons of King David!

Third, we should not compromise our liturgy. These words bind us in time with those who have gone before. If we say the prayer book rite whether it be the 1549 Canon,  or the 1928 Canon, or if we use the Missal, whether it be English, Anglican, Sarum, or even Roman, or if we use one of the ancient Orthodox liturgies then we should remember that at the very least they agree about the words of consecration. The same intention is there in every rite - to make present the body and blood of Christ. There are, indeed, some truly terrible modern liturgies out there, but they are only invalidated if they do not embrace the true Christ as proclaimed in the great Creeds of the Church. If one's intention is to dumb things down to make it "accessible" rather than allow the great words said by so many unlearned folk throughout the ages, then one is compromising one's integrity for the fashionable by introducing a disconnection. The old language is still good enough for Shakespeare: it is still good enough for the majesty of the Holy Sacraments.

Fourthly, this brings me to the fact that the old language is a source of Anglican unity for those who seek to hold that connection with the Reformers. We do have that in common, and it won't do to forget it. I remember being picked up on the words "miserable offender" by Deacon Christopher Little. I had forgotten that the word "miserable" had changed meaning. Perhaps each Christian needs to ensure that they do not compromise on the language that they speak, but commit to learning that language as thoroughly as possible. One we truly understand our own language, then we have a better basis by which we can translate for each other. It has often been said that the English and the American are separated by a common language: let Anglicans then be united by their common  language . Whether Cranmer is heretic or hero, he is certainly to be venerated for his translation and use of liturgical language.

We should not compromise on our sincere belief in Christ, but we must be prepared to suffer for that lack of compromise. If we recognise that suffering in others, then perhaps that is enough for us to come together in suffering, mutual support, mutual protection, and continue to point to that One Christ. All Catholics have the same Nicene Creed (preferably without the filioque), pray the same Our Father, and agree on 66 books of the Holy Scriptures. We all have received the same commandments from the same Christ. That should be the basis of our unity in Christ.

Empirical Epiphany

Here on the Feast of the Epiphany, we are presented with the facts. God reveals Himself to us in the historical record. He makes Himself known to the Magi, the Gentiles from the East, and to St John the Baptist, the last of the great Jewish Prophets. Here is a God who makes Himself known through a still, small voice, a burning bush, through the message of an angel, through a voice calling in the darkness, through dreams, through the words of the prophets. But why?

What really is an epiphany? It is a revelation: a passing on of knowledge hitherto inaccessible to us. There are many different academic arguments for the existence of God. All have strengths and weaknesses. However, there are two arguments for the non-existence of God: through the problem of Evil and through showing that the Divine Attributes are logically inconsistent. These have problems too. The arguments are not conclusive either way. 

However, academic knowledge is not the only type of knowledge. We know a person by interacting with them. To do so, there needs to be an introduction, a discussion, a learning of the other's language. We don't philosophise others into existence. There is no conclusive philosophical proof that your friend has a mind in the same way that you have a mind, yet it seems reasonable that they do based on your interaction with them.

However, God doesn't seem to be someone that you can meet face-to-face. 

God's existence is not self-evident otherwise we would all be theists. How can the Holy Uncreate ever truly manifest Himself to human beings? Even if He were to become incarnate, people would still be able to doubt that He is who He says He is. Why doesn't He reveal Himself to us as Christtoday, performing miracles and allowing us all to perceive Him as He is? Why has He stopped revealing Himself to us?

Or has humanity stopped looking?

Some Scientists have made up their minds. have declared that there is no way that they could be scientifically convinced of the existence of God, and have closed the door. It isn't exactly a scientific thing to do as even the laws of physics are subject to revision given evidence. The trouble is how one considers the admissibility of evidence. 

God doesn't reveal Himself scientifically, because we do not come to know people scientifically. His revelation to the Magi is initially a theoretical hypothesis, but they come to know God through seeing Him in the manger and thus recognising Him there. St John the Baptist knows Our Lord through having Him as a kinsman. What we call Science is not the complete way that we know things. There is also Recognition. We need to learn to recognise God, and His Epiphany shows us that this is possible. It comes from interaction, not through argument. It comes through living together, not by reductio ad absurdam. 

The Church has given her scientific case and defence for God's existence, knowing that this is not enough to know God Himself. We can only do so by coming to Him and seeing His Epiphany for us. 

Are we really looking out for His Epiphany? How do we communicate that?

Thursday, January 05, 2017

Regular Apostolic Unity

As regular readers will be aware, one thing confounds me about the situation with the Catholic Church is the sheer scale of fragmentation. The "alphabet soup" that describes the Anglican Continuum is certainly an embarrassment. Further, the fragmentation is somewhat exacerbated by the episcopi vagantes that ordain and consecrate priests and bishops at a whim rather than in the prayerful and long discernment of the Church. Most of these episcopi vagantes produce valid but irregular bishops and priests, though some do not mainly because they rely on aged and infirm bishops to consecrate them. I look with some distaste at one bishop being consecrated by an aged, blind patriarch who seems to have no idea what is happening. That, to me, seems like defect of intention, and would render subsequent consecrations by this ordinand highly suspect to say the least.

It is the apostolic succession that ultimately must bind the Catholic Church together. St Paul warns both St Timothy and St Titus not to let controversies over genealogies damage the body of Christ. So many times do we witness this criticism over who has valid orders and who does not. This is particularly prevalent in Anglican Orders which have the clearly politically motivated Apostolicae Curae  issued against us, despite its blatantly obvious falsity. However, until the attempts to ordain women, it was clear that Anglicans sought to preserve this succession as tightly as possible. 

The defect of intention has now rendered all ordinations in the Church of England since 1992 suspect, though it does not render the acts of true charity and love that the CofE promulgates in any way suspicious. While it may lack sacramental assurance and cannot claim to be part of the Catholic Church, Christ's commands are still taken seriously, and CofE ministers are due as much respect as any other minister of God. Yet, the fact remains that the CofE is no longer Catholic as an institution.

In the Anglican Continuum, we have the famous Chambers Succession. In 1978, Bishop Albert Chambers and Bishop Francisco Pagtakhan were due to be joined by Bishops Mark Pae and Charles Boynton to consecrate Charles Doren the first Continuing Anglican Bishop. However, Bishops Pae and Boynton were both prevented from attending due to ill-health which meant that the consecration of Bishop Doren occurred with two consecrating Bishops. However, Bishops Pae and Boynton both sent letters of consent to Bishop Doren's consecration. Bishop Pae participated in subsequent Continuing Anglican ordinations while Bishop Boynton actually joined the ACC. 

Now criticisms of the ordination of Bishop Doren clearly start with the fact that there were only two bishops present at the consecration. This is true. However, the first Apostolic Canon states "Let a bishop be ordained by two or three bishops." Of course, the standard has become that three bishops should ordinarily participate in the consecration of a bishop. Nonetheless, it is highly likely that there are bishops who were consecrated by two rather than three others. This does not throw into doubt the validity, but rather their regularity.

Regularity in this context demonstrates the rule by which the bishops live. Many of theepiscopi vagantes are regular only to themselves and their interpretation of whatever rules, canons, and polity they choose. Bishop Doren was indeed validly consecrated, however he was not regularly consecrated within the regularity defined by ECUSA. Now think about this carefully. Given that the Continuing Anglicans were desiring to stay with the Catholic definitions of sacraments and traditional understanding of Anglicanism, they clearly had objections to the regularity of ECUSA. This was not the regularity that the Catholic Church possesses, but ECUSA had moved the goal posts. Thus, it does not matter to the Continuing Anglican movement that its orders are not regular with ECUSA, but rather regular to the new body of Continuing Anglicans as put forward a year earlier in 1977 in the Affirmation of St Louis. This set up the rules for Continuing Anglicanism. Although it was a nuisance to have only two consecrators present at Bishop Doren's consecration, it did not affect its validity, but the consent that it received showed the strength of the intention of Bishop Doren and subsequently consecrated Bishops. The fact that the Chambers Succession flourished into a jurisdiction with a clear constitution, a clear purpose, and a clear desire to preserve the Catholic Faith, means that it cannot be compared with little groups of episcopi vagantes who change the names of their jurisdictions every five minutes, and who change their names and titles as often as they change their trousers.

The same is true of the Old Roman Catholic Church. They have been accused of being a product of a purported episcopus vagans, namely Archbishop Arnold Harris Mathew, but the fact remains that they have a visible regularity, an organic unity, and a government under God which seeks to continue the Catholic Faith as they have received it. That growth is testament to their validity in Christ. To the Roman Church, they may be irregular, but their bishops are as valid as any Roman Catholic bishop.

Further, a little discovery that I recently made was that one of the bishops who participated in the consecration of Bishop Chambers was Bishop Francis Rowinski of the Polish National Catholic Church whose orders are recognised by Rome. Even among the others of Bishop Chambers' consecrators were those whose consecration had been participated in by the Old Catholic Church. This reinforces what has always been said of Anglican Orders, that they are as valid as Roman Catholic Orders. 

Should this bother us? Is this just Rome's problem with us? 

We should not care that others don't recognise us as being valid only for as long as we truly seek the will of God in the World and live our lives in sacrifice to Him. Ultimately, it can only be He that validates or invalidates our ministry. Yet, the schisms within the Catholic Church are always a scandal and need to be healed for the integrity of the Church's mission to all people.

Recently, distances have been  growing between UECNA and the ACC, despite the fact that they are both inheritors of the Chambers Succession - indeed, Bishop Doren became the first Presiding Bishop of UECNA after consecrating the first Archbishop of the ACC - Archbishop James Mote. UECNA is Anglican and holds to the doctrine of the Book of Common Prayer together with its formularies. The ACC is not Anglican, but Anglican Catholic preferring to subordinate any doctrine in the Book of Common Prayer to the doctrine of the Early Church. This does mean that the ACC sees the XXXIX articles as largely irrelevant, but not unwholesome. That is something that UECNA find difficult, however the jurisdictions of the Chambers succession share that common bond. We are hewn out of the same rock despite our differences. We are children born from the same battle for orthodoxy.

As the Week of Prayer for Christian Unity approaches towards the end of the month,  I wonder whether we should start looking at the lists of those who describe themselves as Continuing Anglicans and start looking for reasons why we cannot meet regularly with a view to seeing each other as "regular". I wonder whether we can seek out all those Christians who hold fast to the doctrine of the Primitive Church in the first Seven Oecumenical Councils. Instead of G8 summits, we can hold C7 summits for those who hold the doctrine of the first Seven Councils, and C4 with those who hold the doctrine of the first four. These clearly form some common ground. Once we have some kind of visible unity among the Independent Catholic Churches both nationally and world wide, perhaps then we can start to reach out to those who reject Catholic Doctrine and seek to be on good terms with them also. 

We cannot be members of the World Council of Churches while it remains non-Apostolic and secular in its purposes and practices. We note that the Roman Catholic Church is not a member of the WCC either for the same reasons. However, we need to stop saying why we cannot be members together and start thinking actively of how we can be members together. What we need is a council of Independent Catholics recognising each others' orders as valid and regular within their jurisdictions and also appreciating our differences which have arisen from history, so that

a) we can learn to view each other as regular in a wider context;

b) that, despite the smallness of member jurisdictions, we can present a larger front with which to dialogue with larger and better established jurisdictions; and

c) that we can better protect each other, arbitrate for each other, and assist each other in a growing bond of trust in Christ's Rule.

Perhaps then, we can begin to heal the schism within the Church and present a better ikon with which to draw those who schism from the Church back into the fold. This has always been my prayer, especially as I have such good friends from all over the Christian spectrum. There are good Christians out there who need to know that they are the Body of Christ. There is a ministry out there to bring the love and grace of God into a dark world through the means of the Sacraments. Can we do it together? I pray that with the help of our Omnipotent God we can.

Sunday, January 01, 2017

Cutting out the sacrifices?

Sermon for the Circumcision of Christ

Derek has just been told off by his mummy for treading on John’s toe. John deserves to have had his toe trodden on because he poked Derek in the eye, first. Mummy tells Derek that he will not be allowed to watch his favourite programme until he says sorry to John. As you can imagine, Derek feels that this is a great injustice, and so he refuses to eat his sweets so that he’ll die from starvation and Mummy will be sorry. And what does Mummy tell Mrs Meeks from next-door?

“Oh! He’s just cutting off his nose to spite his face!”

[PAUSE]

That’s a weird little phrase. We use it to mean that Derek is literally going to damage himself for a cause that really isn’t worth the pain and suffering. Well, at least we think it’s a cause that isn’t worth the pain and suffering. For Derek, this is an important issue. He’s being made to say sorry and John isn’t. Perhaps Derek is campaigning for freedom from injustice, but then, if he truly values justice, would he go without his sweets on behalf of John if things were the other way around?

Is it really worth the sacrifice?

[PAUSE]

Today, men all around the world feel uncomfortable as we are presented with the Circumcision of Christ. It’s an unkind cut that our Jewish brothers and sisters have valued throughout the centuries. It signifies the Covenant and relationship that the Jewish people have with God. As symbols go, it literally involves cutting off a part of the body to seal one’s relationship with God in blood. That is clearly going to be painful, and will have a lasting effect on that one’s life. Again, we must ask the question: is it really worth the sacrifice?

[PAUSE]

That depends on what lies within the heart. What is our motive? Does it make us more socially acceptable? Do we become one of the in-crowd? Or do we do it because we value God and seek to be among those who cherish His Rule?

And then, Our Lord comes to circumcision. What does this say? That God wants to be socially acceptable? Well, clearly He isn’t: the Jewish authorities crucify Him. That God wants to be part of the in-crowd? Then why does He spend most of His ministry with the outcasts while scolding the “in-crowd” for their lack of sincerity and faith?

St Paul says that Abraham “received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised; that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also: And the father of circumcision to them who are not of the circumcision only, but also walk in the steps of that faith of our father Abraham, which he had being yet uncircumcised. For the promise, that he should be the heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith.”

The Jewish people identify themselves with the God-fearing Abraham through Circumcision. Thus Christ our God seeks to identify Himself with the people of Abraham. We see throughout His Holy Incarnation God’s desire to be reconciled to all His children, Jew and Gentile whether they be uncircumcised or not. So what does the sacrifice of circumcision actually do?

[PAUSE]

There is no point in making sacrifices unless the sacrifice is worth making. Again, St Paul says, “ though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing.”

[PAUSE]

Do we Christians need to be circumcised? No. Our Lord has made the sacrifice of His blood to seal the new covenant with us. He has made circumcision unnecessary. However, the Christian must learn to make sacrifices. The word “sacrifice” literally means a making-holy. That’s our job. We make the sacrifice of the Mass so that we no longer need to slaughter animals, an act that can’t take away all our sins in the first place. We make a sacrifice of our Sunday mornings so that we can meet God. We make a sacrifice of our lives by recognising Christ our King and thus reject our own will, our possessions, our statuses, our reputations, even our own flawed views of right and wrong, in order to separate ourselves out into being with God.

That’s enormous, daunting, and painful. Yet, Our Lord allows Himself to be circumcised so that He might be part of our in-crowd so that we can all be in His in-crowd. If we have the faith then we will be able to bear our sacrifices for Him and thus stand with Him in His Kingdom. If we don’t have the faith, why don’t we ask God for it?

Yes, why don’t we ask God for the faith to make sacrifices?

Friday, December 30, 2016

The last lesson (until the next one)

I’m taking a break from teaching mathematics for a while, so I thought I would just have one last gasp with some irritations from Facebook and try and convince people that these are just silly things that arise from playing fast and loose with the grammar of mathematics.

What is 5+3×2?

There are many people who believe that the answer to this problem is 16: 5+3=8 and 8×2=16. Yet, this is wrong and many a Facebook page has been curdled by disagreements about what the answer should be. Mathematics has its own grammar that comes from its understanding of structure. The structure of how numbers interact is properly called algebra. People may think that this is just using letters to stand for numbers, but the actual study of how the numbers combine and reduce is really what we mean by algebra.

What does a mathematician make of 5+3×2? Well, to see my point, let’s rephrase it in English. What are five and three lots of two? Still not sure? Try reading that sentence again, but leave a little pause after the five. What are five(,) and three lots of two? Well, three lots of two are six, and five more makes eleven. This is the correct answer. The mathematical grammar says that you must do multiplication before addition. We have to understand what three lots of two are before we add the five.

Now, let’s try reading that sentence another way. Put the pause between the “three” and the “lots”. What are five and three(,) lots of two? Ah! Now you’re asking a different question. Five and three are eight, and two lots of eight are sixteen. We’re doing the addition first. The way that a mathematician would write this is (5+3)×2, bracketing off the bit we do first.

I’ve seen some bizarre answers to things like: 1+1+1+1+1+1+1+1+1+1+1×0+1=? But apply the mathematical grammar, do the multiplication first: 1×0=0. So we now have:

1+1+1+1+1+1+1+1+1+1+1×0+1=1+1+1+1+1+1+1+1+1+1+0+1=11.

I suspect that many people might have thought the answer to be 1, but that would be the answer to:

(1+1+1+1+1+1+1+1+1+1+1)×0+1=11×0+1=1.

There are some genuine mathematical ambiguities out there. What about 1-1+1=?

Is that 1-(1+1)=-1?

No. Otherwise we’d put the bracket in to show that we are adding the 1 and 1 together first. We have to understand this as a credit of £1 plus a debt of £1 plus a credit of £1 is £1. This is why the old acronym of BIDMAS (or BODMAS or BEDMAS if you’re of an age) sometimes tricks us into getting the answer wrong. BIDMAS gives the order of operations: Brackets, Indices (Orders or Exponents), Division, Multiplication, Addition, Subtraction.

However, we see that this is a bit vague when it comes to the order of addition and subtraction. We have to see subtracting as adding a negative.

A truly ambiguous mathematical question is 6÷2(1+2). Clearly, as mathematicians, we should do the brackets first.

6÷2(1+2)= 6÷2×3.

Strict BIDMAS would now say do 6÷2=3, and thus 3×3=9.

However, what is not completely clear is whether it is intended for six scones to be shared between two families each of one and two people (Johnny and his parents, Dorothy and her parents), or if we’re trying to find out the number of eggs needed when bumping a recipe for an omelette for two people that requires six eggs up to an omelette for Johnny and his parents. If it is the former, then each person gets one scone each. If it is the latter, then nine eggs are needed.

So ambiguous statements do exist in mathematics if we are not careful. We could make that last calculation a little easier if we write:

(6÷2)(1+2)=9 or 6÷[2(1+2)]=1

Of course, strings of numbers and calculations are all rather fun to play about with, like word games which reveal much about our language. It’s making sure that we do the correct calculation when it counts.

Wednesday, December 28, 2016

Blogday 2016: Changing and the changeless

I suspect one thing that puts people off public transport is the frequent need to change and make a connection. If you have your own car, this is not something that will affect you greatly, though you’ll have your own set of problems.

However, for those of us who rely on public transport, there is always the worry that you’ll make the right connection at the right time and in the right place. Until it’s time for that change, you can at least relax and enjoy the view.

When it comes to make the change, you then have to grab your bags, make sure that you haven’t left your phone charger in the socket, join the exodus onto the platform and, in the midst of all this confusion, seek to make your way to where you should be. This is not an easy job – in fact, if you don’t know where you are, it can be quite terrifying. The great fear is that we find ourselves on the wrong train to the wrong destination hundreds of miles from where we should be. We have a fear of getting irretrievably lost from the familiar path and from the place where we know we should be.

2016 has been a year in which many of us have had to change trains in their lives. This is so true for me. I am now preparing for a move North. I have left my parish in Rochester with heavy heart and fond memories. I leave my family and my old community behind to embrace the unfamiliar; my poor wife is in the same situation. I have left my teaching job in the South East and prepare to engage in a new job with a new boss who is very demanding, but a sheer delight to work for. I face the prospect of finding a new home, a new community, and the uphill struggle of building God’s Church on bare earth.

I truly envy the Franciscan way of life which is rooted on the idea that we are all on a journey and that we must disengage with things in order to engage with God. The same idea is true in Benedictine Spirituality, yet the notion of stability to the community usually leads to a more static location, unlike the mendicant Franciscan friars. For St Benedict, possessions are for the community, not for the individual, and the abbot must be in sole charge of things. For the Franciscan, possessions are fleeting things that come and go, and we may not cling on to them. The Benedictine seeks to put down roots, the Franciscan seeks to allow God to blow her where He wills. Both are valid spiritualities beloved by God. Both challenge the materialist view of the world. Both call people back to God, accommodating different personalities.

We see the world in a state of political flux. There has been a shift to the right further than we are perhaps comfortable with, yet we knew that there was a growing undercurrent of discontent, and political ideologies always change. We have lost a large host of treasured celebrities despite knowing that Death is certain for us all. Without their passing, Art and Entertainment cannot receive a charge of the new, even if the new is discomforting and takes some getting used to.

Yet, we know that change for the sake of change is not all it’s cracked up to be. The Christian Faith does not change because all Humanity, past, present and future needs the same Salvation through the same Saviour. Thus our rule for believing cannot change – the Nicene Creed cannot be altered. This is why we should drop thefilioque, not because it’s necessarily incorrect, but because it has not been sanctioned by the Church Catholic. This staff of changelessness, this Rock of our relationship with God, remains immutable through Time and gives us something to cling to when the Winds of Change blow roughly in our lives and in the whole world.

2017 is a time in which those winds will blow hard. They will blow hard for me in my new life. They will blow hard over the great political ocean as the storm rages for control of mankind. We must see ourselves both as fleeting creatures and as possessors of Eternity. We can dare to do this as Our Lord Jesus has given us the pattern for doing so. With His Divine and Human natures inseparably entwined in His substance as God, He shows us that our fleeting lives can hold Eternity tightly. The Church is there to care for Humanity passing through Life. It is a hospital for the souls that are dashed upon the crags of sin; it is a rock on which the uncertain can cling knowing that this Faith has not changed in the history of Mankind; it is a safehouse through which one can view the turbulence of Life; it provides the sustenance of Grace that the journey needs to continue on to its very end.

In times of our upheaval, we must look carefully to ensure that the fear of the unknown does not erode our faith that all of what happens to us in our lives – happy, sad, boring, exciting, terrifying, miserable and ecstatic – become part of our souls and present to God in His Eternity. There is nothing in this life that can separate us from His love. Even the most excruciating torture will end and pass into nothingness: Love can, and indeed, lasts beyond Time. This is why we cannot allow our lives to be defined by things temporal. If all we know is misery in life, why should we allow ourselves to be defined by that misery and let Misery win? Rather, should we not learn to rise above it by seeking that Joy which lies beyond and yet breaks though into this World to announce His Existence?

I pray that the vicissitudes of 2017 will rather edify and strengthen my dear readers in the Hope of Christ. Do please pray for me in my “interesting times” as somehow I’m going to have to practise what I preach!