Final fishy fun for Friday

Apologies to those with no interest in mathematics. Normal service will be resumed next week, with more insights into God's word.

Just a couple more observations on 153 before I leave the subject.

153 is also rather rare in that it is divisible by the sum of its digits:

153 / (1 + 5 + 3) = 17

Now, if I receive 1 fish on day 1, and 2 fish on day 2, 3 fish on day 3, and so on. How many fish will I have after 17 days?

No need to reply. You should know the answer by now! ;-)

God is the greatest mathematician!

Fish Cubes

Here's an interesting number game for you to try when you have a few spare minutes (and a calculator!):

1) Think of a number, any number, pick one at random. Can be as big or small as you like.

2) Multiply this number by 3

3) Split the number into its digits (e.g. 27 would give you 2 and 7)

4) Calculate the cube of each of these digits (the "cube" is calculated by multiplying the number by itself three times. e.g. 2 cubed = 2x2x2 = 8. 7 cubed = 7x7x7 = 343)

5) Add the cubes together to form a new number

6) Repeat steps 3->5; splitting the number into its digits, and summing the cubes. Stop when the number doesn't change.


What do you get? Post your answer in the comments.

153 - a fishy play on numbers

So Simon Peter went aboard and hauled the net ashore, full of large fish, 153 of them. And although there were so many, the net was not torn. (Jn 21:11)

WARNING: What follows is not a rigorous exegesis of this passage. In fact it's not intended to be an exegesis at all. It's just an amusing play on numbers that will (a) serve as a mnemonic for this number (b) draw out some truth easily exegeted elsewhere.

Let's start with some maths that is indisputable:

153 = 70 + 72 + 11

Now I'm just going to use these numbers as a "hook" without inferring this significance is implied in the passage.

In Matthew 4, Jesus calls the disciples to leave their jobs as fishermen and to follow him to become "fishers of men". In Luke 9 Jesus sends out the 12 (of whom 11 were left at this post-resurrection appearing), and in Luke 10 he sends out the seventy-two, which some texts render as the seventy.

Jesus said he would make them fishers of men, and in this miraculous catch of fish there is a connection to the numbers of men who were sent by Jesus: the 70/72 and the 11. A link between the catch in and the commission.

What I would like to draw out is that Jesus did not just draw men to himself, but fishers of men. Those who would themselves be sent to draw men after him. In turn the disciples were not just fishers of men, but fishers of fishers-of-men. The disciples were not just told to go out and make converts, but more disciples. Those who are drawn are also sent. They are sent to draw men who in turn are also sent, and so on. To switch analogies, the harvest is not just bread for the eater, but seed for the sower. That is, the harvest itself is intended to produce a still greater harvest.


Here's some more maths:

153 + 40 = 193

Now this is definitely not inferred in the passage, but 193 is the number of nations currently recognised by the United Nations. Forty is significant for many things, but in the context the hook I'd like to use is that it is the number of days during which the risen Christ presenced himself among his disciples before he was taken up into heaven.

As fishers of men, the disciples were called to go into all the world; to reach every nation tribe and tongue. But despite all their natural resource they were warned that this is a job they would be unable to do without the empowering presence of God with them - the Holy Spirit poured out by the risen ascended Christ.

Since the number of nations changes year to year, I appreciate this is a hook with a limited lifespan! But for me, and those in related churches it is one that will stick in the mind, as we have recently committed to go into all 193 nations over the next two years. [See www.mission193.com]


This number study is just a bit of fun, but I hope it has blessed you. At least you'll never forget how many fish were caught now! For any School of the Word Students (any of you reading this year?) this is a question, as I recall, in your end of year Bible-knowledge exam, so here's one extra mark on me! ;-)

Divine Symmetry: 110

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Today's post is brought to you by the number 110.

I have posted on this before, but as it was back in the early days when I averaged about 1 hit a fortnight, there's no harm in revisiting it. Anyone who can remember it from the first time round gets extra brownie-points!

Joseph lived 110 years, as did Joshua. I am struck by this symmetry in the Word, between the man who led the people of Israel into Egypt, and the man who led them back into Canaan.

Both Joseph and Joshua are types of Christ. I have already mentioned about the typology of Joseph, but the typology of Joshua is just as strong. Joshua was the conquering commander of God's people who led them in victory after victory to take hold of their inheritance. In fact even his name is identical to Jesus. It is only because Joshua is transliterated directly from the Hebrew Old Testament, and Jesus is transliterated via the Greek of the New Testament that the names are different. In the Septuagint (the Greek translation of the Hebrew Old Testament) Joshua is called Jesus too!

The early church historian Eusebius makes much of this. In a great insight he points out that the two men that Moses had with him in the tent of God's presence, both had their names changed prophetically. Aaron became the high priest, the anointed one; and Hoshea son of Nun, had his name changed to Joshua. Thus in the Greek, these two men with Moses before the Lord were "Christ" and "Jesus"; just one more way the whole testimony of Scripture points forwards to our Lord.

This symmetry then becomes highly significant. Egypt was a time of sorrow and trial for God's people. Yet God wants it to be clear, that the same Lord who led them in would also lead them out! This is something we see repeated many times in Scripture, in particular in the book of Daniel. God does not always spare his people from the time of trial, but he is always with them in it, they only last an allotted time, and he always leads them out stronger than when they went in. The people of Israel went into Egypt as 70 individuals, but emerged as a mighty nation of over half a million!

So apart from this symmetry, is 110 in itself significant as a number? Maybe! I'd like to put forward that 110 is significant, in terms of times of trial for God's people, as being 40 + 70. We see this pattern in the very last chapter of Genesis. In the same passage where we are told that Joseph lived 110 years, we are also told the times of preparation and mourning for Israel (Jacob): 40 days, and 70 days respectively. Just like the flood, this period of 40 days reoccurs in Scripture as a time of preparation and testing; and both 40 years and 70 years represent times of mourning for Israel (the people) as the time in the wilderness, and the exile in Babylon.

By placing these two types of Christ, like book ends, either side of the time of trial in Egypt, and linking them with a number also representative of trials, God is revealing himself as the God who is there for us in every fiery-furnace of life. Trials may come, but God is always faithful. He is always with you, his strength is always available to you. You can and will overcome all that life can throw at you, and in the end, God will lead you out with increased strength to a place of greater blessing. In the 24 years of my walk with the Lord, I can testify this is always true.

Enough of the shadows and types, let us come out into the light, and see what the reality himself has to say on this matter:

"I have told you these things, so that in me you may have peace. In this world you will have trouble. But take heart! I have overcome the world." (Jn 16:33)

Threefold Authority

This post is brought to you by the number three.


I mentioned in a previous post that the number three is very significant in scripture. The problem is, though, that it is significant for more than one thing.

Three days is a prophetic time in scripture that points forwards to Christ's death and resurrection. Examples are Jonah's three days in the belly of the fish, and Moses' declaration that the people should take a three day journey into the wilderness in order to offer sacrifices. (Mt 12:40, Ex 5:3)

Three is also significant in that is one of the numbers of established witness: by the testimony of two or three witnesses a thing is firmly established. An example would be Abraham's three visitors who testified against Sodom. Most other examples of witnesses tend to be twos rather than threes: Joshua and Caleb who gave a good witness after spying out the land, Moses and Elijah who witnessed Christ's transfiguration, and the two witnesses in Revelation. But it is still worth bearing in mind that three can be used in this way too. (Dt 19:15, Mt 18:15)

But the threes that have been jumping out at me lately are the threes of God's delegated authority. Within the Godhead of course we have Father, Son and Spirit who set the example for all the others. In the heavens God established Sun, Moon and Stars. In the created order he established Man, Woman and all the animals. In the family his order is husband, wife, children. And in the church we have the pattern of Apostles, Elders, and all God's people.

It is interesting to speculate about a possible link between the final two uses of three. Three is the number of the community of God. Two is the number of the community of man (husband and wife). Either of these two numbers can be used to establish something, which reflects the fact that God has delegated his governmental authority to man.

Though one may be overpowered, two can defend themselves. A cord of three strands is not quickly broken. (Ecc 4:12)

For three, and for four

OK, here is what I've got on Amos' use of numbers in the first two chapters of his book.

Tetrads

First, the structure has been carefully chosen to be very close to the tetrad forms of the kind found in Proverbs 30.

Three things are never satisfied; four never say, "Enough" (v15)
Three things are too wonderful for me; four I do not understand (v18)
Under three things the earth trembles; under four it cannot bear up (v21)
Three things are stately in their tread; four are stately in their stride (v29)

These tetrad forms were apparently a popular Jewish teaching device of the time. The introduction of the elements as three, and then four, was to give emphasis to the fourth item. I guess they are an ultra-micro version of a three-point sermon with a conclusion — no wonder they were popular! ;-) The fact that Amos chose to use a form (very similar) to these tetrads, perhaps implies that he was a prophet who also had a teaching ministry, or maybe a prophetic teacher — I like that! This might also explain his reticence to include himself among the mainstream prophets of his day. (pure speculation of course!)

But I stressed, that his words are very close to this kind of tetrad, because although they are crafted to have the same form as this device, Amos' words are not tetrads! If they had been they would have been subtly different. If Amos had said:

"For three sins of Damascus I will not revoke the punishment; for four my wrath will not be turned away."

This would have been a true tetrad. But he didn't; the structure of the sentence is very close, but subtly and deliberately different. Also note that unlike the tetrads in proverbs, no list of four sins or transgressions is listed - just one! What Amos is actually saying is "For three sins and for four", in other words in a roundabout way he is saying: "For seven sins of Damascus...."

Sevens

This leads on to the second point. The symbolic use of the number seven in scripture is clear and unambiguous. It represents fullness or completeness, because on the seventh day God rested from all his work of creation. Seven transgressions would thus correspond to a full measure of sinfulness.

Compare this with the following scriptures:

In the fourth generation your descendants will come back here, for the sin of the Amorites has not yet reached its full measure. (Ge 15:16)

In this way they always heap up their sins to the limit. The wrath of God has come upon them at last. (1Th 2:16)

God is the creator of emotions, and he is an emotional God. He feels anger, love, zeal, even hatred and jealousy. But unlike human emotions, the emotions of God are never from wrong motives or out of control. God is never in an out of control rage, but he does decide to get angry. In his mercy and his forbearance he does not respond immediately to sin, but allows time for repentance and restoration, but there comes a point when sinfulness reaches its limit, and God decides, enough is enough; I'm going to get angry now.

Amos was prophesying that the sins of the neighbouring nations, and of Judah and Israel themselves, had reached that limit; God's judgement was imminent.

And something else I can't quite put my finger on....

The third layer of symbolism is one that I have not quite pinned down yet! I just have a gut instinct that there must be more here. I'm not trying to force the scriptures to say anything that is contrary to the plain reading of the text; I'm not looking for any "hidden coded messages". I believe, despite what some may think after reading the latter part of Daniel, that the purpose of prophetic symbolism, and all prophetic communication for that matter, is always to illuminate never to obfuscate! And it is for this reason that I feel there is more here.

The main message of Amos is clearest understood as "For seven sins of....", so why would he split it into 3 / 4 unless there was some more significant symbolism to be communicated by doing so. Although the tetrad device is clever, I do not for one minute think that the prophet communicated this way just to show off how clever or educated he was. "I may be a farm boy, but get a load of this..." No, just doesn't sit right. The prophet is bringing the symbolism of the number 3 and/or the number 4 into play.

My first reaction was to link this and contrast it with the three righteous men mentioned by Ezekiel in his judgements of the nations: Noah, Daniel and Job could save only themselves if they were present (Eze 14:16,18). But on closer inspection it didn't seem to stick.

Something to chew over, and come back to another day, I think. My good friend Matthew has already suggested a possible significance of the 3 / 4 split in a comment on my previous post, that I think has some mileage.

A way with numbers

“For three transgressions of Damascus,
and for four, I will not revoke the punishment..." (Amos 1:3)

It seems I'm not the only one who is intrigued by numbers. The more I read in the prophetic writings, the more I am struck by the significance and prophetic symbolism in the numbers they chose. This is particularly true with the books of Daniel and Revelation which I have studied in some depth, but I believe it is also true of some of the other prophets.

Take the above quote from the beginning of Amos, repeated throughout chapters 1 and 2. If you are like me, you have probably skipped over the numbers here without giving them much thought. But I suddenly have a new found respect and admiration for this "rustic" prophet. Far from being a simple farm lad, he had an ingenious grip on the prophetic symbolism of numbers. I believe there are at least three layers of meaning carefully chosen and crafted together in this phrase....

....Unfortunately I don't have enough time to fully expound them today, so you'll have to come back tomorrow if you want to know what I've discovered. ;-) If you can't wait here are some clues: Abraham. Proverbs. Completeness / Fullness.


Update

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Sorry! This is what happens when you post in a hurry! The link to Abraham is tenuous at best! What I had in mind was actually Eze 14:16,18. And as Ezekiel was some 200 years after Amos, he could not really have been building on this revelation. In my haste I misrecalled the number of righteous men for which God would spare the city when Abraham pleaded for Sodom. Although Abraham had three visitors the number which he "bargained" down to was 10 not 3. Kinda takes the wind out of my sails on this one. But hey, you don't get fresh revelation if you're not prepared to explore some new avenues... but some turn out to be blind alleys.

Three is still a significant number in the scriptures even without this link. So I may still post on it anyway.

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Perfect Numbers

I took a number of books on holiday to read. Apart from the Bible I took a book on Church history that I still have to finish, a collection of early Christian writings, and a good paperback novel which I bought in the airport.

The paperback I bought this time was "Fermat's Last theorem" by Simon Singh. I had already read his follow up book "The Code Book" and found it fascinating. Despite this book being about mathematics, I found it a rivetting read.

As part of the background to the theorem, Singh provides some background to some mathematical theories in the dramatic historical context in which they were first formulated. One such concept that particularly caught my imagination was the idea of "Perfect Numbers"

Every number has a set of divisors: numbers that can divide the original number into another whole number. If the only whole number (apart from itself) that can be a divisor is 1, then the number is said to be "Prime". Examples of prime numbers are: 1, 2, 3, 5, 7, 11 etc. If the sum of the divisors is more than the number itself, that number is said to be "excessive". If the sum of the divisors is less than the number it is "deficient". But if the sum of the divisors is exactly equal to the number itself then it is said to be a "perfect" number. The first 2 perfect numbers are 6 (1 + 2 + 3) and 28 (1 + 2 + 4 + 7 + 14).

Why this caught my interest is that some early Christian writers, like Augustine, noticed a link between these perfect numbers and the numbers involved with God's creation: God created the world in 6 days, and the moon which was created to mark the months has a 28 day cycle. This, they say, points to the initial perfection in all God made.

Now, I'm still unconvinced on the merits of this link. One has to be very wary of imposing modern scientific understanding upon the text of the scriptures, which neither knows, nor cares about such ways of viewing the world. The language of Genesis is one of description, not mechanics, and it holds true regardless of what the current scientific theories might be (I don't include Darwinism as a scientific theory!). Also the term "perfect" is a happy accident; if Pythagoras had named them "balanced" numbers instead, I wonder if the connection would have been so apparent. Finally the third "perfect" number is 496 which has no scriptural references whatsoever.

Never the less, I can't help but like elegant connections and details like this. God's creation was indeed perfect in every way before sin marred it. Who knows if God chose these numbers to reveal this perfection or not? One thing that I particularly like is the restoration of the number 6. This number has often been associated with evil or demons, but even Revelation 13 is very clear: it is man's number. Man was the pinnacle of God's perfect creation, created on the sixth day. To me the fact that 6 is a perfect number is a fitting reminder that man was created perfect, and is destined to return to perfection. Man does not belong to the devil nor to demons, but to his perfect Creator.