Saturday, 5 April 2008

Quote of the Day: 1 + 1 = ?

What's your theology of maths? Would you say that ultimately 1 + 1 = 2 if you were a Hindu? How can we derive plurality from unity? Is one ultimate?

Vern Poythress has an excellent paper on a Biblical View of Mathematics, on If you thought that mathematics is theologically neutral, think again.

"In saying, "1 + 1 = 2" we are thus stating a truth about the Trinity: a truth about the Wisdom of God, and then, secondarily, a truth about the world that he governs. (Note, however, that since the Trinity and the Wisdom of God are incomprehensible, God's own "mathematics", as it were, is not accessible to us in all its fullness. ...) How far this is from a "neutralist" view of mathematics, which supposes that mathematics has nothing to do with God!

"... Not all men are called to be specialists in mathematics. For the one who does so specialise, using the gifts that God has given him (Luke 19.11-26, 1 Peter 4:10), how does Christian ethics come to bear? How should the Biblical motive, standard and goal affect him?
a) The mathematician should be motivated by the love of God to understand the mathematical truths which God has ordained for this world (and so understand something of God's mathematical nature); love of neighbour should also motivate him to apply mathematics to physics, economics, etc.
b) The mathematician should find his standard in the command of God, the programme which God has given man to fulfill: "Be fruitful and multiply, and fill the earth and subdue it; and have dominion..." (Gen 1:28). Part of this programme is that man should understand God's works (Gen.2:18-23).
c) The mathematician should work for the glory of God. He should praise God for the beauty and usefulness that he finds in mathematics, for the incomprehensible nature of God which it displays, for the human mind which God has enabled to understand mathematics (Ps. 145; 148). And he should endeavour to exhibit ever more fully and clearly to others that "from him and through him and to him are all things. To him be glory for ever. Amen." (Rom 11:36). ...

"If a man is working for the glory of God, he won't be a "secret" believer; he will say so as he talks mathematics. How far this is from a "neutralist" stance! The man who ignores God as he does his mathematical task is not neutral, but rebellious and ungrateful towards the Giver of all his knowledge."

- Vern Poythress, A Biblical View of Mathematics. An excellent paper!


Andrew Millard said...

"In saying, "1 + 1 = 2" we are thus stating a truth about the Trinity: a truth about the Wisdom of God, and then, secondarily, a truth about the world that he governs."

I think this statement summarises how the article has too limited a view of God and too high a view of mathematics. If He is omnipotent then surely He could create a universe where 1+1=3? I cannot conceive how such a universe would function, but I can conceive that God is able to do it. If mathematics is an essential part of God's nature then he could not do things which contradict equations such as 2+3=5, yet creatio ex nihilo, or on a smaller scale the miracle of the feeding of the 5000, seem to do just this. In Jesus' hands, 2 loaves plus 3 loaves became much more than 5 loaves. More fundamentally, the very idea of the Trinity as three-in-one is mathematically incongruous, for 1+1+1=3 and 1+1+1=1 are equally good attempts at an arithmetic description of the Godhead. But both equations are only metaphors, because God created mathematics and is beyond it just as he is beyond physics or biology.

Ben Stevenson said...


I am not why God being able to create a world in which 1+1=3 makes God any bigger than saying that 1+1+1=3 express truths about God that are unchanging.

The Doctrine of the Trinity means (amongst other things) that God exists as three persons.

One person (The Father)
+ One person (The Son)
+ One person (The Holy Spirit)
Total: 3 persons

Wouldn't saying that 1 person + 1 person could equal 3 persons if God had made the unvierse in a different way also change the nature of God.

I don't think it changes God's omnipotence to say that God cannot do things that contradict his nature - so, for example, we can say that "it is impossible for God to lie" (Hebrews 6:18).

I also don't think miracles like the feeding of the 5,000 contradict mathematics. We are not told in Matthew 14 (or any of the other places that record this miracle), that 5 loaves is equal to 500 loaves - but that God has such control over matter that he can change 5 loaves into enough food to feed 5,000+ people.

Ben Stevenson said...

If mathematics is theological, do you think that makes it in any way preferable for a Christian student to learn mathematics in a Christian school or university where a mathematics is taught within a consistent Christian framework?
In America, Christian students have the opportunity to study not just theology in Christian universities/seminaries, but also subjects like engineering (e.g. Union University)

Andrew Millard said...


I was probably unclear in what I wrote.

If we assert that mathematics is an integral part of God's nature, including 1+1=2, then we are asserting that he cannot make a universe where 1+1=3. I think that the article is wrong at this point and mathematics is part of the created order, not an essential part of God. The article's view of God is therefore limited, and its view of mathematics too high. Our understanding of God's omnipotence is not changed by asserting that he cannot contradict his nature; our understanding of God's omnipotence is limited if we wrongly assert that something created is part of God's nature.

With regard to the Trinity:
1. You mention the Three Persons, but it is equally true to talk of the One God: as such our limited, human expression of the One God as Three Persons does not make mathematical sense, which suggests to me that God is beyond mathematics, rather than that mathematics is an essential part of his nature.
2. I cannot conceive how a universe with 1+1=3 would function, so I cannot sensibly discuss how the Triune nature of God would be represented to finite beings in such a universe.

The miracle of the multiplication of the loaves is called that of a good reason: 12 baskets of left overs came from 5 loaves. Whatever way one counts the matter involved, as loaves or atoms or meals, the total at the end is more than at the start. Counting amounts of matter is a piece of very simple mathematics, usually expressed in physical terms as the law of conservation of matter, but we can see here that mathematics is unable to account for what happened. I think this also illustrates that God can do what is impossible in mathematics (and in this case also in physics) because he is not constrained by maths as he would be if it were part of his character.

étrangère said...

Interesting discussion, guys - I want to think more about this before joining in, but I'm off to New Word Alive so although the thinking will be ongoing, the joining in will have to wait. Look forward to it.

Takis Konstantopoulos said...

Hm... very strange views. First of all, what you write here or what V Pythress talks about has nothing to do with mathematics. I can ASSURE you that one can do mathematics without interpreting


as a "truth about the trinity".

1. It is DANGEROUS to urge mathematicians to do something in the name of god. It is also DANGEROUS for a mathematician to preach about god simply because he or she appears as an authority figure to people (who are not mathematicians).

2. You are not referring to an arbitrary god, but to the specific god of your specific religion. Other religions have other god or gods. So what about them?

3. The concept of trinity was not invented by christianity, but by an older religion, the zoroastrinism.
Number 1 in Trinity: Ahura Mazda
Number 2 in Trinity: Mithra
Number 3 in Trinity: Apam Napat
Christians, simply, borrowed their beliefs and rituals from older practices (e.g. from orphism!) For example, Dionysus (a.k.a. Bacchus) descended into hades and returned to life. (Does this ring a bell?)
4. You are referring to god as "he". Are you sure god is male?

5. But, more to the point, I can write any number of nonsensical postmodern-looking collections of sentences about arithmetic and religion and make them appealing to some "naive" people. I don't think you'll find too many mathematicians (you will, but not too many) who will not smile (or laugh) at these writings...

6. Mathematics was considered dangerous, especially by christians, for hundreds of years. Around the 4th century, they made sure to terminate every intellectual/scientific achievement of classical greece (e.g. they stoned Hypatia, they destroyed Pythagorean basilicas) and declared:
"There is another form of temptation, even more fraught with danger. This is the disease of curiosity... It is this which drives us to try and discover the secrets of nature, those secrets which are beyond our understanding, which can avail us nothing and which man should not wish to learn."
"The good Christian should beware of mathematicians and all those
who make empty prophecies. The danger already exists that mathematicians
have made a covenant with the devil to darken the spirit and confine man
in the bonds of Hell."
(Saint Augustine)

7. It took at least 1000 years for christianity to come to terms with rationality and mathematics. Thankfully, they now do not despise maths and, like you, try to compromise it to religion (the particular religion whose rituals you follow).

8. There is something good about christianity: it recognises its mistakes (e.g. the burning of idolaters, the condemning of Galileo, etc.) and re-shapes its beliefs. The only problem is that it takes this religion a few hundred years to recognise its mistakes. Can you and other religious people do something to speed up this process? It would be a great service to humanity!