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Does infinity exist?
I have been reading a lot about mathematics and astrophysics over my summer holidays. The question I have in my head right now is 'Does infinity exist?' or is it just a term to express what we cannot compute or understand yet?
Farrukh Yakubov 50+
Infinity is 'never ending'ness of a process, field, or sequence.
Nicoletta Strati
David Irvine
To make a perfect circle you can draw parallel lines and keeping the distance between them, move them through a centre position all the degree's and parts of a degree. for the circle to be perfect, the number of parallel lines has to be infinite!
Problem,
There is no perfect circle, just a notion.
There is no such thing as parallel lines, just a notion
Now if it were possible we would have an infinity.
If we then transpose the circle to a sphere we have infinite infinities !
In the circle example we assume 2d - i.e. lines have no width If we move up a dimension to 3d then infinity becomes infinity to the power of infinity, now add more dimensions and it gets weird. This I think is a problem with some advanced physics, we use these notions and then take them way to far out of context. Maybe an example of proper chaos theory where our initial assumptions are very poor, and immediately we move to N-Dimension thinking like string theory.
Huge subject that I find fascinating, great question, I do think there is an answer, but I believe we do not have the language (spoken, written and mathematical) to provide that answer just yet. We can live in the excitement that there are answers and there are so many we can all help find them, if we just think enough and accept current failings readily.
Great time to be alive!
David
Goran Malic
Think of it this way: a circle is a specific set of points contained in a plane, that is, it is a subset of the plane. A sphere is a specific subset of space. How many points are there in a plane? And how many in space? The answer is the same, both have an infinite number of points, so neither the circle nor the sphere can have more than an infinite number of points, i.e. they have exactly an infinite number of points, not infinity to the power of infinity.
Our intuition falls apart when dealing with infinity. A clear example is this one: consider the set of all positive integers 1, 2, 3, 4, 5 and so on. Now, cross out all the odd numbers in this set. You'll get the set consisting of all even integers 2, 4, 6, 8 and so on. The question is: which one is larger, the set of all positive integers or the set of both positive and even integers?
The usual answer is that the set of all positive integers is larger since we obtained the other set by crossing out odd numbers, but actually, they are of the same size, both are infinite. To clarify why this is so: well, we just rearrange the counting pattern of the even integers, we consider 2 as the first even integer, 4 as the second even integer, 6 as the third even integer and so on. In such a way we have established a correspondence in which 2 corresponds to 1, 4 corresponds to 2, 6 corresponds to 3, 8 corresponds to 4, 10 corresponds to 5 and so on, that is, to every even integer we can assign a corresponding integer. From this we conclude that there are as many even integers as there are all of the integers.
Goran Malic
As the name "countable infinity" suggests, there is, surprisingly, another kind of infinity called the uncountable infinity. That is the size of the set of all numbers and it is uncountable in the sense that we can no longer find the successor and the predecessor of any number. For example, if we choose 1 and try to find its successor, we could say that 1.00000001 is its successor - but that is not true because 1.000000001 or 1.0000000000000001 or 1.00000000000000000000000000001 (and so on) should be its successor.
As it turns out, the uncountable infinity is interestingly much larger than the countable infinity - although the term "larger" is not a good one; it should be substituted with "denser".
To answer the original question, as far as I know, there is no example of infinity in nature. Even the curved finite spaces such as the area of the Earth are finite in size, and one would eventually walk across every atom on the surface of the Earth.
As for the understanding of infinity, we cannot say that we understand it completely, but we can say that we have made significant progress ever since Georg Cantor inaugurated a branch of mathematics called "set theory" in the 1870s. There are still a lot of unanswered questions and some questions about infinity truly test the limits of mathematics as such - for example, the continuum hypothesis, which states that there is no infinity "more dense" than the countable infinity and "less dense" than the uncountable one, cannot be proved or disproved within the standard mathematical framework.
Sharon Turner 500+
Nino Dundua
I have come across web sites, and maybe you have also, that claim that atoms can be subdivided down into infinity, and that they contain tiny universes within them, and no doubt tiny people as well. Although science has not yet been able to prove we have reached the ultimate elementary particle from which all complexity is built, there is very strong theoretical and experimental evidence to show that quarks could be it. Smaller than quarks enters the realm of energy, not particles, as in string theory. As matter has been subdivided down from complex objects, to parts of the whole, to molecules, to atoms, to particles, to quarks, at each stage we see a simpler model, each stage is less complex than the previous level. All of which is in perfect agreement with the Big Bang model that describes how all matter is built up from simple to more complex elements, stage by stage. So when breaking down complex objects into smaller parts, it would come as a bit of a surprise if suddenly an entire universe popped up at even smaller scales than wave energy. Entire universes tend to be a bit complex!
However, if string theory is shown to be correct, then tiny loops, or strings, of vibrating wave energy may be the smallest, but they are not particles anyway, and strictly speaking quarks aren't either, as they can not exist independently outside of a particle.
Sharon Turner 500+
Goran Malic
We can, however, discuss the size of a number relative to another number (i.e. 7 is larger than -4 or 0 is greater than -1 etc.) or its absolute value (i.e. its distance on the real line (the x-axis) from the origin) which is usually called the magnitude of a number.
Christophe Cop 500+
http://www.ted.com/conversations/4380/beyond_just_science_and_religi.html
(http://www.ted.com/conversations/4380/beyond_just_science_and_religi.html?c=288429)
As for your math: http://www.khanacademy.org/#browse
Now to the question: That greatly depends on what you understand by infinity...
(We suppose that) there is no infinite amount of matter or energy in this Universe, but we suppose infinite time in the future.
"infinity" also exists as a concept. As the number pi does exist... though asking whether pi exists (or any number),... you need to know to what it refers...
pi exists in circles, and infinity too...
(To conclude: the question is void)
Sharon Turner 500+
Christophe Cop 500+
Sharon Turner 500+
I didn't think it was amateur. My maths knowledge is strange. I was weak at maths at school and quite honestly it terrified me until a year and a half ago when I realized that areas such as geometry, calculus and algebra made sense to me if I studied it by myself. There are gaps! As for Infinity, I am interested in the word and the concept within and beyond mathematics, from all areas. What does it mean to people? For example in your 1st comment you stated that outside of mathematics it is not useful. So is infinity for you only mathematical?
Sharon.)
J Ali
Sharon Turner 500+
Erwan Eriau
Chris Price
Goran Malic
We say that a is divisible by b if there exists c such that a=b*c. If such c exists, it is unique and we say that c is the result of the division of a by b. For example, take a=7 and b=7. We have to find c such that 7=7*c. Obviously, c=1, so the result of division of 7 by 7 is 1.
Now let a=infinity and b=infinity. We have to find c such that infinity=infinity * c.
Obviously c=1. But, c=2 will also do since infinity*2=infinity. And c=3, c=4, c=4392123249543 will also do. Even c=infinity will be OK since infinity*infinity=infinity. So far we have that infinity / infinity = 1 and infinity / infinity = infinity, and by combining this two equalities we conclude that 1=infinity. And that obviously isn't true.
Sahyadri Vibhu
Another great example i forgot to give last time is
"1/(x^n)" where "x" and "n" are two positive integers. Keeping the value of "x" fixed, go on increasing the value of "n". the value of "1/(x^n)" becomes zero only if the value of n becomes infinity.
There are loads of such examples in mathematics.
Sharon Turner 500+
Ed Schulte 30+
Yes I too have Collmen Bark's "Celebration of Mystical Love and Friendship" too indeed Rumi is the most quoted poet in the west thanks to Bark''s Bly and Hillmen.
You may wish to try out the knowledge the school children there have of Yunus Emre ( Rumi said ..wherever I went Yunus was there before me)
Also if you have time check out Henri Corbin's "Man of Light" a French soci-anthropoligist who spent the time period of ww2 in Istanbul being educated in Sufism. He and took it back to Europe ....lectured in Eranos / Switzerland to Jung and his colleges and from it Hillman began his Archetypical Psychology ......copies of 'Man of Light' can be found at the "Scribe" web site ...and I believe also on "Sacred Text" web site
Sharon Turner 500+
Joe Fletcher
I'm an anthropology major not a physicist, I just read on physics. You should cheak out A brief history of time (kinda outdated) the elegant universe, or many other qualatative based physics books for a MUCH deeper understanding of topics like this.
Sharon Turner 500+
Thanks for the reply and the book recommendations. I like you am also not a physicist and just read for pleasure. I have been reading a few other books you might be interested in:
-Parallel Worlds: The Science of Alternative Universes and Our Future in the Cosmos by Michio Kaku
-The Lightness of Being by Frank Wilczek
-Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time (Joseph Henry Book) by Marcia Bartusiak and National Academy of Sciences
I don't know if you wold be interested in sharing insights/ideas or questions as you read various books.
Joe Fletcher
Ed Schulte 30+
"Infinity" is a 'word' manifested by mind thought....turn the question inside out
"Exist" ence is INFINITE ( iow beyond mind thought generated 'words' )
Sharon Turner 500+
Ed Schulte 30+
Lucky You!!! you are in Istanbul sooooo why are you not in one of the Sufi Tekkia having this conversation ?? Well perhaps you are ...in which case ...they would discuss they around the subject "luminous black"
But ok over here in the west and putting up the limits of english and an allergy to the 'word' God ....lets give this a dervish spin ...as a "it can't be told by any mind" ( small m)
From Dr D. R. Hawkins latest
That which is ultimate and eternal transcends
both objectivity and subjectivity and is beyond
awareness. It is referred to in the ancient spiritual
literature as the Supreme Spirit. Out of the Supreme
arises all that is manifest and unmanifest ; all consciousness and awareness; all existence; All
That Is; either form or nonform; all that is linear
and all that is nonlinear; all that arises out of creation;
all possibility and actuality. The Supreme
is beyond existence or nonexistence; beyond beingness
or is-ness; beyond all Gods, heavens, or
spiritual forms; beyond all names or definitions;
beyond all divinities and spiritual denotations. It
is out of the Godhead that Divinity arises, and
out of the Supreme arises the Godhead."
Sharon Turner 500+
I also share an allergy to the word God and also religion. As for the Sufi, not yet. However one of my summer reads has been the RED BOOK by Rumi and I would also highly recommend Elif Shafak's book: The Forty Rules of Love based on the 40 Sufi tenants. I also loved this quote by Dr D. R. Dawkins when reading his latest. However I still feel the use of 'Supreme' in this quote has tones of religion even though he is not being religious. Reading your comments about the limits of English got me thinking about logographic scripts such as Chinese and how they view infinity beyond letters. Perhaps silence instead of words might be a better way to describe the infinite.
Joe Fletcher
Sharon Turner 500+
Carlin Covey
I think the simplest answer is "Yes, the mathematical concept of infinity does exist." It exists as a useful mathematical construct, just as imaginary and numbers exist as useful mathematical constructs. But you are never going to purchase an infinite number of apples (or an imaginary number of apples), so outside of mathematics these constructs are not as useful.
Sharon Turner 500+
Carlin Covey
Borrah Campbell
If you have two singularities that are next to each other, you can never make them touch no matter how close you push them together because they have no size... I know that doesn't make any sense. If you think it does it shouldn't because it's a paradox.
You take it for granted that you can touch your nose, but a room full of the smartest men who ever lived would not be able to tell you exactly how you did it... And they-have-tried.
In a nutshell, if you had a string of space you could keep cutting it in half... forever!
Sharon Turner 500+
Sahyadri Vibhu
"tan (90°)" check it out in Wikipedia. It is explained in the page http://en.wikipedia.org/wiki/Trigonometry.
Anything divided by zero [n/0] is also taken as infinity. But it actually should be "undefined". Think of it this way. when you have a fraction "3/4" you will say it is "3" parts out of "4". but when you have "n/0" it means "n" parts out of "nothing" which is undefined. But mathematicians like to take it as infinity
Sharon Turner 500+
Goran Malic
As for the division by zero example, I wouldn't say that mathematicians like to take it as infinity. They take it as infinity in terms of limits, i.e. when it is possible, "n/0" is replaced with "the limit of n/x as x approaches zero" which indeed is infinity.
Sahyadri Vibhu