Two and two the mathematician continues to make four,in spite of the whine of the amateur for three,or the cry of the critic for five... James Mc Neill Whistler

asked 26 Jun '10, 03:13

Robert's gravatar image


edited 26 Jun '10, 12:04

The quote seems to express that the inherent logic of numbers and their relationships to each other are unchangeable, fundamental truths.

It could very well be that numbers are the actual building blocks of everything in nature.


In the "beginning", which really means beyond our concept of time and space, there was only void. Zero. But because there was no time, it was only a matter of chance that something would happen. Something different. Something new.


The void suddenly woke up and realized "I am! I exist!". One. The concept of existence was born. Consciousness, awareness. God.


But now that initial consciousness, or God, asked itself how it was/is like to not exist. Non-existence vs existence. Hence, the concept of duality was born. Two. Separation.


The two long to be together as one again. They strive for their differences to be unified in a higher principle. They create a child. Trinity. Three.

And so on... Thoughts like these also touch the field of Numerology I guess.

Furthermore, when we look at computers today, we know that we merely need the symbols 0 and 1 to create amazing, seemingly endless virtual worlds. But I believe that as programmers we haven't reached the perfection of nature yet.

The Fibonacci numbers that @DMin mentioned are a very simple concept that any child can apply.

1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13

This principle is also at the base of the famous Golden ratio.

Golden spiral

All that nature seems to do is to repeat that principle over and over again.

Golden leaves Golden shell Golden sunflower Golden broccoli

Nature is complex, not complicated. The complexity in nature is based on simplicity. Simplicity is beauty.

I actually believe that we have already found the Theory of everything in these patterns. We will eventually find that everything we observe in the micro- and macroscopic universe will fit into this, and that all formulas in science and physics will be deducable from these principles.


answered 26 Jun '10, 09:12

herzmeister's gravatar image



Very recently,IBM mathematician Clifford A.Pickover wrote>I do not know if God is a mathematician,but mathematics is the loom upon which God weaves the fabric of the universe.The fact that reality can be described or approximated by simple math expressions suggests to me that nature has maths at its core.I think the same.

(26 Jun '10, 12:29) Robert

Great answer and illustrations.

(26 Jun '10, 12:56) Michaela

Dont know if god exists but nature sure does have some close link to numbers.

Fibonachi Numbers :

The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.

The number of petals found on flowers, more often then not are one of the following numbers: 3, 5, 8, 13, 21, 34 or 55 -- which are all Fibonachi Numbers.

Golden Ratio :

The Golden Ratio is a universal law in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form.

More Here

The Golden Ratio is also linked to what is generally perceived by humans beautiful design : eg. The standard iPod is actually a Golden Rectangle.

More Here

A deeper understanding of Science Mathematics & a scientific approach does not take away the beauty of nature. It give the beauty of nature an even greater depth & meaning.


answered 26 Jun '10, 05:13

xyz's gravatar image


your last sentence is completely true....

(26 Jun '10, 16:44) Robert

I too always felt like there was something unusual in mathematics. Like it was magical. It was very complex and in the same time every part of it was matching each other. It seemed almost impossible that mathematics was something random. I got the impression that is must have been a perfect law of the world, universe.


answered 26 Jun '10, 10:21

Asklepios's gravatar image


I have no idea what your quote means, but math is woven deeply into the fabric of the universe.

That's what makes math so beautiful.


answered 26 Jun '10, 05:20

Vesuvius's gravatar image


I do not have an answer to this question; but I do have a story which some of you might like. Once there was a lazy (and somewhat incompetent and sadistic) schoolmaster teaching fifth graders and to get the students off his back for one day, he gave them the following problem. Add all numbers from 1 to 457 and give the result. I must say that 457 might not be the actual number he asked; it might have got changed in retelling; but it does not really matter to the main thrust of the story as you will see.

There was one brilliant student in the class. He noted the following. First write the series and then write the reversed series below it and add:

001 + 002 + 003 + ........ + 455 + 456 + 457

457 + 456 + 455 + ........ + 003 + 002 + 001


458 + 458 + 458 + ........ + 458 + 458 + 458

Therefore, twice the sum we need is 458*457, and so the sum we need is (458 *457) divided by two, which can be computed much easier.

The student who found this easy solution thus outwitting the teacher, later became known as the prince of mathematicians.

The purpose the story above was to argue that there are interesting things in mathematics even without looking for pictorial illustrations, etc..


answered 26 Jun '10, 15:07

A%20G's gravatar image


edited 26 Jun '10, 15:20

You are right, there are lots of interesting things hidden in mathematics, for example Kaprekar number, it's worth to take a look on the web.

(26 Jun '10, 16:38) Robert

@Robert: If you are interested in serious number theory, I suggest that you take a look at things like the quadratic reciprocity theorem, or the Dirichlet theorem on arithmetic progressions.

(26 Jun '10, 17:12) A G

I will...thanks

(26 Jun '10, 19:52) Robert
showing 2 of 3 show 1 more comments

I do not know whether the quote implies that mathematics is completely rigid. If that was the meaning, then I must say that it is not strictly true, and that there is a certain freedom allowed. Let me illustrated with an example.

Let us consider two-dimensional geometries, ie a geometry in which we can draw lines, triangles, etc.. We assume the following properties. Our geometry has a notion of distance between points. A "line segment" between two points is the shortest path connecting the two points. A line is a path in the space with the property that for any two given points one segment of our path between these two points, is the shortest among all connecting them. You form triangles between three points as usual, etc..

Now let me give two models for the above notion of "geometry".

Model 1 -- plane geometry: This is our usual plane. Here the lines are usual straight lines. We have studied triangles in this geometry in school. Some properties: 1. There is a unique line passing through any two points. 2. Any two lines meet at the most at one point. 3. Given a line and a point outside it, there is exactly one line through that point, which does not meet the first line anywhere. 4. The sum of the three angles in a triangle is always 180 degrees.

Model 2 -- spherical geometry: Here we consider the surface of a sphere as our space. For example you might visualize the surface of the earth to be a sphere. The "lines" in this geometry give the shortest paths you would take if you were to fly from one point to the other. For example all the latitude circles and longitude circles you study in geography, are such "lines". Let us see whether the four properties for model 1 are true for this model. It turns out that: 1. There is indeed one unique "line" passing through any two points. 2. Any two "lines" meet at the most at two points. 3. Given a "line" and a point outside it, it is possible that there can be infinitely many "lines" through that point, none of which touches the first "line". 4. The sum of angles in a "triangle" is always going to be less than 180 degrees.

So we have two models of a "geometry" with the notion of points, lines and triangles. But in the second model, some things are very different from the first model. So depending upon the model of a mathematical theory, some properties which are not included in the definition of the theory might differ. So there is after all a certain amount of choice in forming a mathematical theory.


answered 26 Jun '10, 16:09

A%20G's gravatar image


No, the quote implies that while mathematics is a precise science, the results are always interpreted according to the individual mental function of each person. In other words, you interpret it according to your vision of the world.

(27 Jun '10, 00:13) Robert

It is for this reason that the explanation of the reality of the world, based on mathematics, can be caused by a particular vision as scientific, or religious. That's why I asked the question. Can a religious thinking that God ordered all without using mathematical laws? Or can a scientist believe that God alone blow job heaven to create the universe?

(27 Jun '10, 00:19) Robert

I do not know what most religious persons think. But I have seen mathematicians who are devout believers in their specific creed, and also mathematicians who were stone-ass atheists. So it would seem that there is not too much correlation.

(27 Jun '10, 16:17) A G

The point is that despite your personal beliefs, whoever you are, according to the Platonic view, mathematics have always been there. in some kind of abstract world, and our duty is merely discovered. Even if we ignored the existence of God, Euclediana geometry, Fibonacci sequence, the golden section and the Einstein equations would remain part of our reality that transcends human minds.

(28 Jun '10, 00:40) Robert

Yes, yes. That is true. The theorems of mathematics would be valid even if the earth or the sun did not exist, for example. But this platonic view was debated sometimes. For example, see my answer about the two kinds of geometry, in which the second example was non-Euclidean. It turns out that some non-Euclidean geometries are more suited for physics, in relativity theory and other things. So some people argue that mathematics is simply the abstract creation of our thought.

(28 Jun '10, 12:39) A G
showing 2 of 5 show 3 more comments

There is an old saying when God created the universe "God Geometrized"


answered 26 Jun '10, 15:29

RPuls's gravatar image


I had always heard an architect! The architect of the universe...


answered 26 Jun '10, 15:33

LeeAnn%201's gravatar image

LeeAnn 1

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Asked: 26 Jun '10, 03:13

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Last updated: 26 Jun '10, 16:09

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