Galileo described the universe thus: "This grand book is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures." WHY does gravity work by the principle of inverse squares ? WHY do simple geometries pervade nature - from the hexagons of the honeycomb, to the complex architecture of crystals ? So was the architect of the universe a mathmetician ? If so, why didn't he give the year a nice even number of days? WHY 365 days and almost, but not quite, an extra quarter ? Musings from one of my favourite books, 'Dinosaur in a Haystack' by Stephen Jay Gould

All mathematics is subjective. It is a construct of the human mind trying to make sense of the material universe around it. If there was an object in existance which we could all agree is equal in all ways to another, then we would call that object the 'universal 1' and all things could be added, subtracted and multiplied according to that standard. However, I propose that there is no single thing which exists outside of our minds by which we could standardize completeness in and of itself. Therefore X=1 means that it is an idea...a construct of the mind and thereby open to debate. We are also of the false notion that the universe is infinite...another act of faith. As well, we are pleased to think the material universe is inalterable...an act of faith as well. The most powerful force in existance is that which binds atoms...and we have no idea what that is. The most plentiful stuff in the universe (dark matter) has an unknown quality as well. Mathematics therefore are an act of faith, as much as the belief in God. We will never be able to prove it, but it serves us beneficially in most things. Imho, if the God we believe in IS all of matter, then we could say that faith holds the universe together, the binding glue by which all atoms are formed. The fact that we can see uniformity through mathematics is always open to changes. They are a useful tool only through generalities, falling apart as we look closer and deeper into what matter is. ie...if you give me an apple and then someone else gives me another, then it is plausable that I have 2 apples. The problem lies in the fact that no two apples are identical...thereby making it only true that I have 2 objects called apples. One is a Granny Smith and the other a MacIntosh. They are not equal to each other in actuality, only in the subjective name we have for them. I have heard potatoes called 'ground apples' and a woman called 'the apple of my eye'...are these then 'apples' as well?

The strong nuclear force is described by QCD, quantum chromo-dynamics. I agree that mathematics requires axioms. assumptions that are simply posited, to work. According to Gödel's incompleteness theorem that internally consistent mathematical systems can't be complete if they have a finite numbers of axioms. There are always 'good' (correct and relevant) questions that the systems can't answer. I think that logic and mathematics are required to understand and describe the world. We can't exist in a illogical world and mathematics is built on logic.

I have to aggree that the Universe appears to be created on the same basic scheme. How everything from seashells to galaxyz spiral. From how galaxy superclusters interact to the way atoms combine. To the orbitals of electrons to the orbitals of planets. Squares, triangles, rectangles, hexagons, and octogons ever so present in many forms of nature. Maybe its just the fact that the human brain is a pattern finding device and we have the tendyncy to see bueaty and paterns in everything. But to me it appears its all the same basic model.

I am the farthest thing from a mathmatician however, I fancy myself a thinker and have thunk the following thinks. Maybe mathematics is not subjective or a leap of faith. Maybe it is a blueprint to the universe that we have not constructed but rather discovered. And maybe we just have not yet come to fully understand it thus it appears subjective to us. Maybe we still have a great deal to learn. Maybe that is the key – there is no one thing which can standardize completeness, it is only in the combination of things and patterns that we find completeness. Possibly a false notion. However, that begs the argument that if the universe is not infinite then what lies beyond it and is that part of the universe and further what lies beyond that? Can your mind really grasp the concept of nothingness – true and utter nothing? More fine examples of our lack of understanding our ourselves and our universe.

Great posts and thoughts ! what I have learned about mathematics is that it is not a science of numbers , but a study of patterns . Although we may have arbitrarily given values to the things we describe , an amazing amount of things relate to each other from these base definitions . We need a frame of reference to pose our individual ideas from , and mathematics suits those needs . As stated above , the patterns of a spiral are evident all around us , the golden ratio PHI (pronounced FEE) is an excellent topic on its own . The spirals in the face of a sunflower , the shells we find on the beach , and even our anatomy have ratios in their design that are described by mathematics . Is this evidence of inteligent design ? The fibonacci sequence where a number is added to the previous number is a good example (1,1,2,3,5,8,13......) is evident in nature , and would not be apprent without the advent of mathematics . I would like all who read this post to take the time to measure thier height (no shoes , to the top of the head) and devide that amount by the height o0f your bellybuttons . You may be amazed to find out that the result is , or is very close to , 1.618 (the golden ratio) . This holds tru for many other bodily relations and My ex is EXTREMLY devine in her proportions compared to me, but more importantly , WHY do these figures hold true for so many examples in life and nature ? The patterns in nature are evident with our respect to our form of quantity and measurement , I personaly believe that mankind has mutated through the eons as a result of our sun and the radioctivity of the earth (remember that when you see a representration of a light wave or radioacrtive decay that you are only seeing it in 2 dimensions , it is most likely similar to a spring and travels in 3 dimentions like a snail shell) The spiral seems to be a key to many unanswered questions , and the recognition and mathematical similarities that we all share is simply amazing ! these patterns that we all share could not have been evident without mathematics , and the simplest recognition of these patterns and thier associations make the world a wonderful place to learn and explore ! I feel like I am 4 again , and the only word I know is : why ?

I believe you hit on a key point here - "recognition". Meaning, humankind did not invent these principles of mathmatics, we simply have begun to recongnize and identify them. We may think we have gained so much wisdome and are so superior to other creatures of this earth but I think the reality is, we've only just begun to discover all the wonderous things of life.