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uyumadan · 6 months

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Şimdi size bu oldukça enteresan işlem sonucu hakkında bir şeyler anlatacağım. Sabırla okursanız bunun 10 parmaklı bir canlı olmamızla dahi bir ilgisi olduğunu göreceksiniz.

Bir programlama dili geliştirilirken genellikle ona ilk olarak aritmetik işlem yapabilme desteği eklenir. Bu işlemin yapıldığı yer de bir internet tarayıcısı olan Chrome'un, web sayfası üzerinde JavaScript dilini çalıştıran konsolu.

Burada göreceğiniz üzere çeşitli işlemler beklediğimiz sonuçları vermekte. Ancak 0.1 + 0.2 işlemi bize 0.30000000000000004 gibi tuhaf bir sonuç döndürüyor. Aslında bu durum yalnızca o örnek özelinde gerçekleşmiyor, aşağıda görebileceğiniz üzere sayısız kombinasyon mevcut

Bunun nedeni aslında bir tık karmaşık, fakat açıklamaya çalışacağım. Açıkladıktan sonra da bunun öngörülemez bir sonuç olmasının sonuçlarından birkaç örnek vereceğim. Yazılımcılar elbette program yazarken böyle bir durumla karşılaşmayı beklemez. Bunun nedeni biraz da evrimsel ve kendi geliştirdiğimiz bilişim devrimi ile alakalı aslında.

Biz sayıları yazıp okurken, aktarırken onluk tabanlı kullanırız. Bunun tek bir nedeni var, bizler 10 adet parmağa sahibiz ve bizim için saymanın sınırı 10'dur. Tüm el parmakları bittiğinde ayakkabılarımızı çıkarıp ayak parmaklarımızla 20'ye kadar saymamız, belki de yalnızca bir cinsiyet için bu sayının 21'e çıkması sıodjkgwelg neyse, bu çok makul bir seçenek olmadığı için sayı sistemlerimizi 10'a ve onun katlarına dayandırdık. Sayarken 9'u geçtiğimizde solda bir basamak daha türetiyoruz, soldaki basamak artık sınıra ulaştığında onun da solunda bir basamak türetiyoruz. Böylece onlar, yüzler, binler şeklinde basamak sistemlerimiz var oluyor.

Başka bir konuyu daha araya sıkıştırayım. Asker bir millet olan Türkler daha Orta Asya'dayken asker gruplarını 10'lu sisteme göre belirlerdi. Bundan dolayı onbaşı, yüzbaşı, binbaşı gibi rütbelerimiz çok uzun zamandır var. Hatta diğer dillerde pek karşılaşamayacağımız bir durum da var, Türklerde 10000 (on bin) sayısı için de bir isim var, "tümen" şeklinde ifade ediliyor.

Ben konuyu uzatmayı severim, bilirsiniz. Bu konuyla ilgili de aklıma gelen her alakalı konuyu araya sıkıştıracağım. Romen rakamları beşlik sisteme göre yazılır. V şeklinde yazılan 5 sayısından sonra 6'yı VI, 7'yi VII şeklinde ifade ederiz. Bugün kullandığımız saat ise 60'lık sisteme göre ifade edilir. Çünkü taban olarak 60'ı seçmenin avantajı 10'da olmayan kadar fazla tam bölene sahip olmasıdır. Sümerler de 60'lık sistemi benimsemiştir bu yönünden dolayı.

Hadi konumuza dönmeyi deneyelim. Evreni anlamak için dahi kullandığımız matematiğimizde 10'luk sistemi kullanıyor olsak da bilgisayarları icat ederken 2'lik sistemi tercih ettik. Bunun çok temel bir nedeni var; elektronik bileşenler aracılığıyla iki tane durumu çok rahat kullanabiliyorduk. Bir bileşende yani komponentte elektrik varsa buna 1, yoksa 0 diyebilirdik. Bir lambanın açık veya kapalı olması gibi. Bugün kullandığımız tüm dijital sistemler, tüm işletim sistemleri, bu postu okumanızı sağlayan internetin her şeyi taşıdığı her veriyi 0 ve 1 şeklinde iletir, o şekilde barındırır. Sonsuz ihtimal ifade edebilen kuantum bilgisayarların veri birimi olan qbit'lerde bu durum değişecek.

0.1 ve 0.2 sayıları bizim 10'luk sistemde yazdığımız, 10⁻¹ basamağında 1 ve 2 rakamlarını barındıran sayılar. Asal sayıları bilirsiniz, temel olarak bölemediğimiz sayılar, bir bütünün en küçük parçaları diyebiliriz onlara. Tüm sayılar asal sayıların birbirleriyle çarpılması sonucu oluşur. Hatta bu durumu bugün WhatsApp gibi yazılımların da kullandığı uçtan uca şifreleme yöntemlerinde kullanıyoruz. Aşırı büyük iki asal sayının üzerinde yapılan işlemler sonucu şifreleme ve şifre çözme anahtarları elde ediyoruz. Bu şifrelerin çözülebilmesi için tahmin edilmesi, elde edilmesi çok zor olan bu çok büyük asal sayıları kullanıyoruz. Bu tarz asal sayıları üretip satan firmalar mevcut. Şifreleme uygulamaları için bu sayılar şart.

10 ise 2 ve 5 şeklinde iki asal çarpana sahip. 1/2, 1/4, 1/5 ve 1/8 gibi sayılar bu yüzden 10'luk sistemde adamakıllı bir şekilde ifade edilebiliyor. Ancak 1/3, 1/6, 1/7, 1/9 gibi sayılar ise sonsuza kadar devam edecek ondalık bir yapıya sahip. İlk ve orta öğretimde devirli ondalık sayılar şeklinde öğrendiğimiz durumu sergiliyorlar. Bu sayıların asal çarpanları 10'luk sistemin aksine 3 ve 7 sayıları.

İkili sayı sisteminin ise tek asal çarpanı 2'dir, bu nedenle temiz bir bölüm ancak 1/2, 1/4, 1/8 gibi sayılarda gerçekleşebilir. 0.1 yani 1/10 ve 0.2 yani 1/5 gibi sayılar 10'luk sistemde güzelce ifade edilebilirken 2'lik sistemde tıpkı deminki sayıların 10'luk sistemde yaptığı gibi 2'lik sistemde başımıza bela olacaktır.

Burada problem bizim ikilik sistemde devirli bir hale gelen 0.1 ve 0.2 gibi sayıları onluk sistemde yazıp, bilgisayarın ikilik sistemde üzerinde işlem yapmasına izin verip tekrar onluk sisteme çeviriyor olmamız. Sonucunda devirli bir sayı elde ediyoruz ve bunun nedeni bizim o göremediğimiz, arada gerçekleşen ikilik sistemde yapılan işlem.

Ta en başta söylediğim gibi, bir insan bunu tahmin edemez. E bunun da çeşitli sonuçları oluyor elbette. Örneğin bir alışveriş sitesi kodlandığınızı düşünün. Bu sistemde 0.1 ve 0.2 gibi çeşitli vergi oranları olabilir, boyutlar olabilir, fiyatlar olabilir, bunların toplanması gerekebilir. Örneğin bir ürünün fiyatı döviz kuru neticesinde 323.1, diğerinin 535.2 şeklinde otomatik olarak hesaplanmış ve toplanmış olabilir. Ancak biz şimdi en temel halinde Google'da çeşitli aramalar yaparak bunu gözlemleyelim. inurl ifadesi Google araması yaparken sayfa adresinde bu ifade geçsin anlamına geliyor. inurl:products diye aratırsanız çıkan sonuçların hepsinde adres çubuğunda products ifadesi yer alacaktır.

Bu yazıyı yazmayı sabah planlamıştım, o yüzden aramayı iş yerinde yapıp ekranı telefonla çektim. Ondan dolayı fotoğraflar sik gibi görünüyor.

Başka bir şeye bakalım. 0.2 ile 0.4'ün toplamı olan 0.6000000000000001 ifadesiyle benzer bir arama yaptığımda da şu sonuç çıkıyor:

İşte böyle. Hadi ben gidiyorum.

Düzenleme: Lan şeyi söylemeyi unutmuşum, neredeyse tüm programlama dillerinde bu durum var. https://0.30000000000000004.com/ adresinde örnekler verilmiş.

Hadi şimdi gittim

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frmartinshomiliesandreflections · 1 year

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21st November >> Fr. Martin’s Gospel Reflections on:

Matthew 12:46-50 for the Feast of the Presentation of the Blessed Virgin Mary

And On

Luke 21:1-4 for Monday, Thirty Fourth Week in Ordinary Time.

Feast of the Presentation of the Blessed Virgin Mary

Gospel (Except USA)

Matthew 12:46-50

My mother and my brothers are anyone who does the will of my Father in heaven.

Jesus was speaking to the crowds when his mother and his brothers appeared; they were standing outside and were anxious to have a word with him. But to the man who told him this Jesus replied, ‘Who is my mother? Who are my brothers?’ And stretching out his hand towards his disciples he said, ‘Here are my mother and my brothers. Anyone who does the will of my Father in heaven, he is my brother and sister and mother.’

Gospel (USA)

Matthew 12:46-50

Stretching out his hands toward his disciples, he said, Here are my mother and my brothers.

While Jesus was speaking to the crowds, his mother and his brothers appeared outside, wishing to speak with him. Someone told him, “Your mother and your brothers are standing outside, asking to speak with you.” But he said in reply to the one who told him, “Who is my mother? Who are my brothers?” And stretching out his hand toward his disciples, he said, “Here are my mother and my brothers. For whoever does the will of my heavenly Father is my brother, and sister, and mother.”

Reflections (7)

(i) Feast of the Presentation of the Blessed Virgin Mary

Today’s feast commemorates the presentation of the child Mary in the Temple of Jerusalem by her parents. We seldom think of Mary as a child. All the images of Mary we are familiar with are either of Mary as an adult or of Mary in heavenly glory. Yet, when we are first introduced to Mary in the gospels at the moment of her annunciation, we should probably think of her as a very young woman, no more than a teenager. She must have grown up as a child in a very faith-filled home. Otherwise she would not have emerged as a woman of such strong and generous faith at the time of the annunciation. Today’s feast celebrates the fact that as a very young child Mary’s parents presented her to the Lord in the Temple, gave her over to the Lord’s purpose for her life. It was as if her parents were saying, ‘Lord here is our child. We know that she belongs to you more than she belongs to us’. Mary’s parents were recognizing that her relationship with the Lord was even more significant that her relationship with them. Today’s feast reminds us that the most important relationship in our lives is our relationship with the Lord. Every day we try to present ourselves to the Lord, offering ourselves to him. Every day we pray that God’s purpose for our lives would come to pass and that God’s will would be done in our lives. In the gospel reading Jesus declares that those who do the will of his Father, in whose lives God’s will is done, are his brothers and sisters and mother. It was above all Mary who did the will of Jesus’ heavenly Father. In the prayer that Jesus gave us to pray, the Lord’s Prayer, we pray, ‘Father in heaven, your kingdom come, your will be done on earth as it is in heaven’. Heaven is that state where God’s kingdom has fully come, where God’s will is fully done. To the extent that we do the will of our heavenly Father here and now, something of heaven comes to earth. When we allow God’s purpose for our lives to shape us, as Mary did, then we create an opening for God’s kingdom to come among us.

And/Or

(ii) Feast of the Presentation of the Blessed Virgin Mary

The feast of Mary’s presentation in the temple in Jerusalem as a child celebrates an important truth about Mary: From the beginning of her life, she was dedicated to God, given over to God’s purposes. Because of her dedication to God from an early age, she was called by God to become a greater temple than the magnificent temple in Jerusalem. If the temple in Jerusalem was the house of God, the place where God was believed to be present in a special way, Mary became the house of the Lord in an even greater way, because she carried the Lord in her womb until she give birth to him. God came to dwell in her, through Jesus, because she was open to God’s presence from the earliest years of her life. She is the prime example of the group that Jesus refers to in this morning’s gospel reading as those ‘who do the will of my Father in heaven’. Today’s feast celebrates the fact that from her childhood Mary did the will of God, and was therefore ready to become the temple of God’s Son at the time of God’s choosing. We too are called to do the will of the Father in heaven so that we too can become temples of the Lord, people who carry the Lord’s presence to others, as Mary did. Writing to the church in Corinth, Paul says, ‘Do you not know that you are God’s temple?’ We ask Mary to pray for us now so that we may always do the will of the Father and so become temples of God as she was.

And/Or

(iii) Feast of the Presentation of the Blessed Virgin Mary

Mary’s presentation was celebrated in Jerusalem in the sixth century. A church was built there in honour of this mystery. The Eastern Church was more interested in the feast, but it does appear in the West in the 11th century, and in the 16th century it became a feast of the universal Church. The feast stresses an important truth about Mary: From the beginning of her life, she was dedicated to God. She herself became a greater temple than any temple made by hands. God came to dwell in her in a marvellous manner and sanctified her in advance for her unique role in God's saving work. God came to dwell in her, through Jesus, because she was open to God’s presence from the earliest years of her life. She is the prime example of the group that Jesus refers to in this morning’s gospel reading, those ‘who do the will of my Father in heaven’. Today’s feast celebrates the fact that from her childhood Mary did the will of God, and was therefore ready to become the temple of God’s Son at the time of God’s choosing. We too are called to do the will of the Father in heaven and, thereby, to become temples of God, people who carry God’s presence to others. We ask Mary to pray for us now so that we may always be faithful to that calling.

And/Or

(iv) Feast of the Presentation of the Blessed Virgin Mary

Today we commemorate the presentation of the child Mary in the temple at Jerusalem. This feast celebrates the consecration of Mary’s life to the Lord. From the beginning of her life, she was dedicated to God by her parents, given over to God’s purposes for her life. According to the gospels of Matthew and Luke, in her teenage years, Mary was called by God to become a greater temple than the magnificent temple in Jerusalem in which she was presented as a child. The temple in Jerusalem was the house of God, the place where God was believed to be present in a special way. God wanted Mary to become the house of the Lord in an even greater way, because she was to carry the Lord in her womb, until she gave birth to him. God came to dwell in her, through Jesus, God’s Son. Because she was open to God’s presence from the earliest years of her life, she said ‘yes’ to this wonderful calling. She gave herself over to God’s will for her life. She is the prime example of the group that Jesus refers to in this morning’s gospel reading as those ‘who do the will of my Father in heaven’. Today’s feast celebrates the fact that from her childhood Mary had always done the will of God, and was therefore ready to become the temple of God’s Son at the time of God’s choosing. In this morning’s gospel reading Jesus declares that this true family are those who do the will of his Father in heaven. We look to Mary to show us what it means to say ‘yes’ to God’s call in our lives. Insofar as we can enter into Mary’s ‘yes’, we too will become temples of the Lord, like her. The Lord will be formed in us and we will offer him to the world by our lives, as she did.

And/Or

(v) Feast of the Presentation of the Blessed Virgin Mary

When we hear the word ‘presentation’ in a religious context, we tend to think of the presentation of Jesus in the Temple of Jerusalem, the fourth joyful mystery of the Rosary. The church celebrates the feast of the presentation of Jesus on the 2nd of February. The church also celebrates the memorial of the presentation of Mary, on this day, 21st November. This memorial has been kept in the church since at least the eight century. It commemorates the consecration of Mary’s life to God. In the first reading today, God calls on the city of Jerusalem, the daughter of Zion, to sing and rejoice because he is coming to dwell in the midst of them. These are words that could easily be addressed to Mary. She too can sing and rejoice because the Lord came to dwell in the midst of her, in her womb. Indeed, according to Luke’s gospel, she did sing and rejoice in response to this good news, in her prayer that has come to be known as the Magnificat. We too can sing and rejoice that the Lord has come to dwell within Mary, because through the Lord’s dwelling within her, he has come to dwell in the midst of us all. It is through Mary that God became Emmanuel, God with us. The Lord was able to dwell within Mary because, in the words of the gospel reading, she was someone who did the will of God the Father in heaven. She was completely given over to doing God’s will, to allowing God to do his will in and through her. This is the aspect of Mary’s life we are celebrating today, her giving over of herself to God and to God’s purposes. Through Mary, God has come to dwell among us in the person of Jesus, now risen Lord. Mary shows us how to respond to that wonderful initiative of God towards us. Like her, we are to give ourselves over to doing God our Father’s will, as that will has been revealed to us by Jesus.

And/Or

(vi) Feast of the Presentation of the Blessed Virgin Mary

There is no scene in the gospels corresponding to today’s memorial. Yet, there is a presumption that Mary’s parents would have presented her to the Lord in the Temple of Jerusalem when she was a child. Christian tradition has understood that Mary’s presentation to the Lord by her parents symbolized the consecration of her life to the Lord. As her parents presented her to the Lord, Mary as an adult presented herself to the Lord, made herself available for God’s purpose, as expressed in her response to the angel Gabriel, ‘Let what you have said be done to me’. In a similar way, our parents presented us to the Lord on the day of our baptism. As we grow towards adulthood, we then confirm for ourselves what happened for us on the day of our baptism. Our confirmation is our personal confirming of our baptism, which we try to live out every day. Mary’s giving of herself over to God’s purpose for her life did not always come easy to her, because God’s ways are not our ways. In today’s gospel she and other members of her family approached where Jesus was teaching and stood outside anxious to have a word with him. However, rather than just going out to his mother, Jesus sent back word to her that he now had a new family. His disciples, those who did the will of God as Jesus revealed it, were now his brother and sister and mother. Mary had to learn to let go of her son to God’s purpose for his life. When we enter into a personal relationship with God, it is always God who does the leading and we who try to follow. God’s purposes are always greater and more mysterious than ours, and so there is always a letting go to God on our part. That doesn’t come easy to us, no more than it came easy to Mary, but if we allow God to have God’s way in our life, we can be assured that it will be the way of life for us and for all we influence.

And/Or

(vii) Feast of the Presentation of the Blessed Virgin Mary

This feast originated in the East. It commemorates the presentation of Mary to God by her parents in the Temple of Jerusalem, when she was a child. It reflected the church’s understanding of Mary’s subsequent grace-filled life, wholly given over to God’s purpose for her life. Today’s gospel reading suggests that there were times when she struggled to understand what was God’s purpose for her life, especially in relation to her son Jesus. She sets out from Nazareth with other members of Jesus’ family to Capernaum where Jesus was ministering. Perhaps, they wanted him to come home and rest. However, Mary subsequently discovered that this was not God’s purpose for Jesus or for her. Jesus sent word out to Mary and his relatives that they no longer had any claim on him because he was starting a new family of his disciples and from now on they would be his mother and brothers and sisters. There was much here for Mary to ponder. What she wanted for Jesus was not necessarily what God wanted for him. In that sense, Mary’s experience can be very close to our own. Like her, we may want to give ourselves over to God’s purpose, we may want to do God’s will, but, like her, we can struggle to discern what God’s purpose for our lives is. We sometimes have to come to the painful recognition that what we want for ourselves and others isn’t always what God wants. We can’t allow ourselves to become too sure of God’s desire for our lives and the lives of others. Like Mary, we have to keep ourselves open to where the Lord is leading us. Like her, we need to keep prayerfully pondering on our life experience, trusting in the Lord’s promise that those who seek will find.

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Monday, Thirty Fourth Week in Ordinary Time

Gospel (Except USA)

Luke 21:1-4

The widow's mite.

As Jesus looked up, he saw rich people putting their offerings into the treasury; then he happened to notice a poverty-stricken widow putting in two small coins, and he said, ‘I tell you truly, this poor widow has put in more than any of them; for these have all contributed money they had over, but she from the little she had has put in all she had to live on.’

Gospel (USA)

Luke 21:1-4

He noticed a poor widow putting in two small coins.

When Jesus looked up he saw some wealthy people putting their offerings into the treasury and he noticed a poor widow putting in two small coins. He said, “I tell you truly, this poor widow put in more than all the rest; for those others have all made offerings from their surplus wealth, but she, from her poverty, has offered her whole livelihood.”

Reflections (12)

(i) Monday, Thirty Fourth Week in Ordinary Time

The term ‘the widow’s mite’ has made its way into our daily speech. It is inspired by today’s gospel reading. It is generally used to refer to someone who makes a small contribution that is generously given and that is all the person can afford. Jesus noticed the widow’s very small contribution to the Temple treasury, two small coins. Yet, he saw in that small contribution a tremendous generosity of heart, because in giving a little, she was giving her all. Others were giving far more money to the Temple treasury but, having given their contribution, they had plenty more to spare. When the widow gave her little contribution, she had nothing left. Generosity can be hard for us to measure. Someone who is making a small contribution to something, not just financial, can be displaying enormous generosity, because in giving that little they are giving their all. It is only the Lord who can judge how generous someone is, because only he can see into the heart of others. In the gospel reading, the widow would probably have been invisible to most people; her tiny contribution to the Temple would have gone unnoticed. However, the Lord noticed the selfless generosity that her small contribution expressed and he drew the attention of others to her. There can come a time in all our lives when we feel we have very little to give, and not just financially. Our energies may be low; the state of our physical or mental health may be holding us back. Today’s gospel reading reminds us that the little we give in those moments of weakness can reveal a greater generosity of heart and spirit than the great deal we might give when we are in moments of strength.

And/Or

(ii) Monday, Thirty Fourth Week in Ordinary Time

The widow who gives all she had to live on to the temple treasury could be understood as an image of Jesus who gave all he had, his life, for others. Although she gave very little in monetary terms, her giving was more generous than the larger contributions of others, because she gave her all. She reminds us that generosity is not always easy to measure. Those who appear to be giving little may, in reality, be more generous than those who appear to be giving a lot. At the end of the day, it is really only the Lord who can measure generosity, because he alone knows what we are capable of giving. The Lord’s assessment of generosity will often be very different to how we access it. Whereas we tend to look at what is visible, the Lord looks deeper; he looks at the heart. The widow would not have made much of a visible impression on those who saw her, but she made a big impression on Jesus and he pointed her out to his disciples. The gospel reading reminds us that there is often more to people than meets the eye and more to their giving than we might think. We might pray this morning for the gift of seeing others as the Lord sees them.

And/Or

(iii) Monday, Thirty Fourth Week in Ordinary Time

The term ‘the widow’s mite’ has come into our language from the gospel passage that we have just heard. The gospel reading brings home the paradox that, sometime, in giving a lot, some people are actually giving a little, whereas other people, in giving a little, are actually giving a lot. The widow gave less than anybody else to the temple treasury, but, in reality, she gave an enormous amount, because she gave everything she had. That paradox is true even of our own individual lives. There are times when we may appear to be giving very little but, in reality, we are giving a lot, because we are giving as much as we can give. For various reasons, we can be below par. Our health may be troubling us; our energy level may be low because of some personal issue we are struggling with. What we have within ourselves to give is much less than it usually is. In those circumstances, even to give a little of ourselves can be giving a great deal, can, in fact, be giving everything, because all we have to give is a little. The widow in today’s gospel reminds us that, even when we have little to give, we can still be extremely generous.

And/Or

(iv) Monday, Thirty Fourth Week in Ordinary Time

The widow who gives all she had to live on to the temple treasury could be understood as an image of Jesus who gave all he had, his life, to God and to God’s people. Although she gave very little in monetary terms, two small coins, her giving was more generous than the larger contributions of others, because she gave her all, as Jesus would give his all. She reminds us that generosity is not always easy to measure. Those who appear to be giving little may, in reality, be more generous than those who appear to be giving a lot. At the end of the day, it is really only the Lord who can measure generosity, because he alone knows what we are capable of giving. The Lord’s assessment of generosity will often be very different to our assessment of it. Whereas we tend to look at what is visible, the Lord looks deeper; he looks at the heart. The widow would not have made much of a visible impression on those who saw her, but she made a big impression on Jesus and he deliberately drew other people’s attention to her. The gospel reading reminds us that it is in those times when we feel very impoverished, when we sense that we have nothing to give, we can be at our most generous. The little we give in those difficult circumstances can in fact display greater generosity than the more we might give in more favourable circumstances.

And/Or

(v) Monday, Thirty Fourth Week in Ordinary Time

Widows in the time of Jesus could be very vulnerable to poverty. Without a husband to support them they were at risk unless they had other family members, in particular sons, who could provide for them. The widow in today’s gospel reading is identified as a poor widow; she had very little to live on. Yet, she gave what little she had, two copper coins, to the Temple treasury. Jesus was very critical of how the Temple was being run and of those who were in charge of it. Yet, he recognizes the extraordinary piety and generosity of this widow towards the Temple and drew the attention of others to it. As far as she was concerned she was giving to God, and Jesus appreciated her readiness to leave herself even more vulnerable in her service of God. There are times when we may feel that we have very little to give. Our personal resources seem to be very low. Our health may not be great, our energy levels may be poor. Yet, in drawing attention to the widow’s tiny financial contribution to the Temple Jesus is reminding us that it is not how much we give that is important, but rather how generous we are with what we have. We give what we can out of what we have. It may seem very little to others, but in the eyes of the Lord it can have enormous value.

And/Or

(vi) Monday, Thirty Fourth Week in Ordinary Time

The term ‘the widow’s mite’ has made its way into the English language. It often refers to something small which, nonetheless, displays a tremendous generosity of spirit. The widow gave a very small amount of money to the temple treasure, but in giving that very little, she was giving everything she had to live on. Jesus identifies her to his own disciples as an example of a wonderful generosity of spirit. Jesus often encouraged his disciples to learn from people who were not his disciples. At this point in the gospel Jesus is in the Jerusalem, about to face into his passion. This woman who gave everything was a figure of Jesus who was soon to give everything on the cross. This seemingly insignificant widow who seemed to give next to nothing was, in reality, a living witness of divine generosity. The widow reminds us that there are saints in our midst that we don’t often notice. A wonderful generosity of spirit can reveal itself in gestures that appear very ordinary and even insignificant to those observing. There can be times in our lives when we appear to have very little, in all kinds of ways, but if we give generously out of the little we have, we are rich in the eyes of the Lord.

And/Or

(vii) Monday, Thirty Fourth Week in Ordinary Time

The gospels suggest that Jesus was very observant, especially when it came to the behaviour of people. He not only noticed the behaviour of other people but he saw more deeply into that behaviour than others saw. The behaviour of others spoke to him of God and of God’s relationship with us and our relationship with God. He went on to share with others what he saw, what he noticed; he did not keep it to himself. His observations became a teaching opportunity. We find this happening in this morning’s gospel reading. Jesus noticed people putting money into the Temple treasury. The rich put their offerings into the treasury. Then a widow put in two small coins, much less than the rich had put in. Yet, Jesus saw that in putting those two small coins into the temple treasury, the widow had put in more than the rich people because she was putting in all she had to live on. She gave everything to God, even though it seemed very little in comparison to what others were giving. Jesus draws attention to her because he sees that she has a great deal to teach people about generosity of spirit towards God. Jesus is teaching us that when it comes to our relationship with God, and with each other, a little can be everything, if all we have is a little. We can get discouraged that we are not doing as much as we used to do or giving as much as we used to give. Yet, the reality may be that we may not have much to give, be it for reasons of health or whatever. In those circumstances the little we give can be greatly valued in the eyes of the Lord. Generosity is not always measured by observable, external performance. It is ultimately a matter of the heart and it is the heart that the Lord sees.

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(viii) Monday, Thirty Fourth Week in Ordinary Time

It is striking how many terms and phrases from the gospels and from the Scriptures as a whole have made their way into the English language. When a person is described as a good Samaritan, for example, we know exactly what is meant. Based on today’s gospel reading, we sometimes hear reference to the widow’s mite. We understand that to mean something small but truly valuable. The widow in today’s gospel reading gave very little, but in relation to what she possessed she gave an enormous amount. Jesus declares that she put in all she had to live on. In giving a little, she, in reality, gave her all. That could not be said of the rich people who put much more into the temple treasury than she did. They gave out of their abundance; she gave out of her poverty. Most people looking at what was happening would have said that those who gave the most were the most generous but Jesus knew that the poor widow was the most generous. If all we have to give is a little and yet we give that little than we are being truly generous. That is the case not just in the matter of giving money. Our physical condition can mean that our ability to give of ourselves can be very limited but we can still be extraordinarily generous. In giving a little we can be giving our all. Sometimes we can be hard on ourselves and say, ‘I am not doing as much as I used to do or I am not giving as much as I used to give’. Yet the little we give now can mean more in the Lord’s eyes than the great deal we used to give because that little may be our all. No one would have taken any notice of the widow if Jesus had not drawn attention to her. It is often the way that great generosity goes largely unnoticed because it is so ordinary, so seemingly small. The gospel reading suggests that the Lord notices.

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(ix) Monday, Thirty Fourth Week in Ordinary Time

The gospels suggest that Jesus was very observant of life, and, in particular, of people. In today’s gospel reading he notices someone that would have gone unnoticed by others. In the midst of rich people putting offerings into the Temple treasury, Jesus notices a poor widow putting in two small coins. Socially speaking, she was insignificant, and her contribution was insignificant compared to that of others. Yet, Jesus noticed a quality of generosity in her that was truly praiseworthy. In giving her little, she was, in reality, giving everything, all she had to live on. I am reminded of a verse in the Jewish Scriptures, ‘Humans look at appearances, but God looks at the heart’. In her tiny contribution to the Temple treasury, Jesus recognized an extraordinary generosity of heart. Perhaps Jesus recognized something of himself in her. She gave her all, and Jesus was about to give his all as he faced into his passion and death. There are times in all our lives when we are very aware that we have very little to give, for whatever reason. It might be due to ill health or advancing years or some personal circumstance which is taking its toll on us. We may feel that we are contributing little to others. Yet, the little we give in those circumstances can reveal a great generosity of spirit. We may not always recognise that in ourselves; others may not recognize it. Yet, today’s gospel reading suggests that the Lord certainly does. The Lord always notices the little we give, when a little is all we have.

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(x) Monday, Thirty Fourth Week in Ordinary Time

In Luke’s gospel Jesus tells a story of a rich man who had a bumper crop. He had so much grain that he didn’t know what to do with it. It certainly never occurred to him to share his surplus with the less fortunate. Instead, he build bigger barns to store it all. Possessing and protecting his surplus was what mattered to him. Not only was there no room for others in his life, there seems to have been no room for God either. In the story Jesus tells he dies suddenly and too late he discovers that he is poor in the eyes of God. The widow in today’s gospel reading is the polar opposite of that man. Unlike him, she was poverty-stricken. Unlike him, she was very aware of God. Unlike him, even though she had little, she was extraordinarily generous with the little she had, putting into the Temple treasury all she had to live on. She wanted to use the little she had to serve the worship of God that went on in the Temple. Most of us probably find ourselves somewhere between the extremities represented by these two very different people. In calling our attention to this widow and praising her, Jesus is inviting us to move closer towards her attitude of heart. The tendency to find our security in what we own, what we possess, is present in all of us. We struggle to entrust ourselves to the Lord as our ultimate security. The culture we live in encourages us to acquire more and more, and especially to get the best and latest of everything, if we can afford to do so. The gospel encourages us to have something of the widow’s freedom to give generously from what we have, even if it is only a little. Such a freedom is rooted in a conviction that the Lord alone is the firm foundation of our lives.

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(xi) Monday, Thirty Fourth Week in Ordinary Time

A number of phrases and images from the Bible have made their way into the English language, such as Job’s comforters, salt of the earth, wisdom of Solomon. Today’s gospel reading has given rise to the expression ‘the widow’s mite’. We understand the meaning of the expression when it is used, don’t we? We recognize that what seems like a small contribution, in reality, is worth a great deal, because of the generosity of spirit which lies behind it. The widow’s contribution to the Temple treasury was tiny. The ‘two copper coins’ that she put into the treasury were the smallest coins then in circulation. They might be equivalent to our penny cent coins. She seems to have given very little, almost nothing, in comparison to the contributions of the well-to-do. Yet, Jesus recognizes that, in reality, she was being more generous than anyone else, because the little she gave was ‘all she had to live on’. In giving these two small coins, she was giving her all. Jesus understood that the quantity of her giving, which was meagre, bore no relationship to the quality of her giving, which was exemplary. The widow was a type of Jesus himself because, like her, he gave his all. We tend to measure generosity in quantitative terms. We often fail to see the quality of people’s generosity if quantity, output, measurable results, is missing. There can be times in our lives when we have very little to give, and not just in monetary terms. Our human resources can be at rock bottom. Yet, at such times, we can be more generous than we might have been when our human resources were at their height, if we give generously from the little we have.

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(xii) Monday, Thirty Fourth Week in Ordinary Time

November is a month when we remember those who have died. There are many widows and widowers who are remembering their deceased spouses. Several widows are mentioned in the gospels, especially in the gospel of Luke from which we are reading today. They are always portrayed in a very positive light. There is Anna, the eighty four year old widow, who worshipped in the temple with prayer and fasting night and day. There is the widow in the parable Jesus spoke who wore down an unjust judge until she eventually got what she was entitled to. In today’s gospel reading we have another widow who is singled out by Jesus for her extraordinary generosity. She was poor, with little in the way of financial resources. What she contributed to the Temple treasury seemed very little indeed, just two small coins. We could thing of two 10 cent coins today. Nobody would have paid any attention to her. Yet, Jesus noticed her and made sure his disciples noticed her as well. He saw that the little she gave was all she had to live on. Even though she gave little, in reality she gave everything. The quality of her giving was extraordinary, even though the quantity she gave was tiny. Quantity isn’t always a good indicator of quality. That is true in a more general sense, not just a monetary sense. As we get older and frailer, we will have less to give. Our health can be poorer, our energy level can be lower. Yet, if we give generously out of the little we have, the Lord will recognize something of the quality of his own spirit in us. On the cross, Jesus had nothing to give; everything had been taken from him. Yet, it was at that very moment that he was giving everything.

Fr. Martin Hogan.

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