Mathematics : How far is infinity?

in steemstem •  6 years ago  (edited)

As a kid and even as a grownups, we wonder about many things. Science is a discipline that is bent on satisfying man's curiosity. Just as my friend believed he could lift a glass of water with his mind after watching the movie series, Merlin, I also believed that infinity can be reached.


The symbol of infinity. credit: wikimedia. Creative commons license. Contributed by the US Department of Veteran's Affairs

The concept of infinity came to me as a kid when I went to have a haircut, the barbing saloon had two mirrors facing each other, one meant to be used by the person who is having a haircut and another hanging on the wall just opposite the first one. As I was having a haircut one day, I decided to checkout the back of my hair by looking at the mirror hanging just a little distance from my back from the mirror situated before me.


source: wikimedia CC0 license. Author: pcdazero

I got more than I bargained for cause I saw both my face and back of my head many times with each view becoming smaller and smaller. I became interested in what I saw and when I went home, I brought two smaller mirrors, placed their shiny sides to face each other and leaving small space between them. I placed a pencil in between the two mirrors and I got the same effect as before; same image appearing countless times with each preceding image becoming smaller than the image before it. This was my first encounter with infinity.

Infinity is a very common word, both in science and in mathematics (especially in calculus) and simply means limitless size and or length. As kids we all learnt how to count the natural numbers which is usually in the sequence of 1, 2, 3, 4, and so on but up till now, we're still counting. Mathematics simply described Real numbers as a set consisting of positive infinity and negative infinity making the set of a natural numbers a subset of real numbers.

Irrespective of how go in the infinity, we would still find out there's more. The new internet protocol version 6 contains addresses that have the size of 2 to the power of 128, our solar system contains stars with the number of about 10 to the power of 23, the universe contains atoms with number up to 10 to the power of 87 while scientists estimated the lifespan of the universe to be about 100 to the power of 100, yet there's still more!

Lets consider a set of natural numbers consisting of only the even natural numbers which is usually of the form {2, 4, 6, 8, 10, ....}, if we match this set of numbers to the set of natural number, we could say that the even natural number has size that is twice that of the natural numbers but this is wrong. This is because for every value of the natural number, there exist a positive even number that can match the natural numbers as illustrated below.

blood_sample_lab_laboratory_medical_drop_glass_research-.jpg
designed by me @yandot using windows paint

But this is not the same for all instances of infinity cause there are some infinity that are actually bigger. This brings us to the two types of and as you might have already guessed it, they are:

  • Uncountable infinity and
  • Countable infinity
  • The set of natural numbers which was described earlier perfectly describes a countable infinity but we cannot say the same for the set of real numbers which the set of integers, natural numbers and fractions. Take for instance, the gap between 0 and 1, is actually an infinity! This is because whatever fraction you think exists between 0 and 1 can always get smaller and or bigger, hence you can add as many zeros as possible in the decimal point between 0 and 1 inexhaustibly. Hence the number 0.000000000000001 and 0.9999999999999 exists between 0 and 1 and can get bigger without equating to a 1 or get smaller without equating to a zero. This is of the type uncountable infinity.

    Irrespective of the fact that both type of infinity cannot be attained, the countable infinity is lesser both in size and length when compared to the uncountable infinity. As an example, the number existing between 0 and 1 can be said to be as the whole natural numbers because we can match the whole natural number with a number between zero and one!

    Phenomenon Of Infinity in Reality


    The concept of infinity as we have seen is very weird and at this point, I want us to see infinity in its full manifestation.

    1. The Paradox of Omnipotent Being

    They say that religion is the opium of the masses and I dare any christian to come forward and debunk this claim. This very paradox comes in the form of a question and the question is, is it possible for an almighty being with a limitless or infinite power create something so big and mighty that he, the creator cannot carry it?


    image source: wikimedia. Creative commons license. Contributed by Shaahin

    For instance an omnipotent god who can infinitely do "all" things, should also be able to create something he cannot displace. If he creates something he cannot displace or move, then he is not infinitely powerful after all.

    2. Banach-tarski Paradox

    When I was in the high school, the seniors (bullies) do give us $5 to buy $10 worth of edibles, funny right? This is very similar to what Banach-tarski paradox has to say. It is a theorem and it states that it is possible to obtain two balls from a single ball with the resulting two balls having the same geometric properties as the original ball.


    image source: wikimedia. Creative commons license. Contributed by Benjamin D. Esham

    This very complicated theorem bases its claim from the fact that a ball which has spherical shape contains an unlimited amount of points in

    3. Zeno's Paradox

    The popular saying that a journey of one thousand miles begins with a step but what about a journey of one step? Zeno of Elea who is a Greek philosopher who believes that motion is nothing but an illusion because for a specified distance to be covered, an infinite amount of distance needs to be covered first.

    To understand this paradox, suppose Mr. Blockchain is told to cover a distance of say 10 meters, obviously he needs to cross half of the distance which is 5 meters before reaching the said destination and before he reaches half of the distance, he needs to reach half of half of the distance (2.5 meters) and before he reaches half of half of the distance, he needs to cross half of half of half of the distance (1.25 meters) and the sequence continues like this infinitely.


    image source: wikimedia. CC4.0 license. Contributed by Martin Grandjean

    This simply implies that for one to move from one place to the order he needs to complete an infinite number of tasks and this, Mr. Zeno believes is impossible. This is because apart from the initial problem of completing infinite task, the said movement contains no initial distance since any given distance can be continually divided into two and hence contains no initial point. The implication of this is that the motion cannot even begin in the first place.
    Conclusively, Zeno’s paradox implies that any movement over a stipulated distance can neither be started nor finished, hence, motion is nothing but an illusion. Hence to move from one place to another, no motion is required in the first place!

    4. The Hyperwebster Dictionary

    The paradoxes that proves how boundless infinity is are many but I’ll stop in this one. Have you ever imagined a dictionary that is uncountable? Have you also imagined a dictionary that contains all possible words obtainable using the English alphabets? Well, I present to you, the Hyperwebster dictionary.


    source: wikimedia CC4.0 license.

    The idea of Hyperwebster dictionary was put forth by Dr. Stewart Ian in a bid to describe how boundless the points on a real number line are. The idea of the Hyperwebster dictionary is to combine the letters A to Z in every possible way giving rise to all English word both said and unsaid with no definite length.

    The Hyperwebster dictionary of course contains both meaningful words and meaningless words. Words like SRRWTBQ, WTRIPVMXQESTYT, QUIDPROQUO, HELLO, WHAT, HOWAREYOU, WHATISYOURNAME, etc. Because of the fact that some letter combinations has no meaning, the company that published the uncountable dictionary decided to do so without associating a meaning to any combination. Hence, in the Hyperwebster dictionary, words are written in the form A, AA, AAA, AAAA, AAAAA, AAAAAA, …, AB, AAB, AAAB, AAAAB, …, ABA, ABAA, ABAAA, ABAAAA, …, B, BB, BBB, BBBB, BBBBB, …, and continues till, ZZZZZZZZZZZZZZZ…..

    With this, the best way to punish a troublesome kid is to give him the hyperwebster dictionary and tell him to find the word, Abracadabra, lol.

    Summary


    The concept of infinity has been a very old and fascinating one. From the symbol of infinity, it could be noted that infinity has no open ends, hence infinity describes things that are boundless. This concept is applied vastly in the field of mathematics and physics and many philosophers have put forward some paradoxes to explain the concept of infinity and some were described in this post in a very subtle manner.


    Thanks for your time.

    References


    1. Infinity ~wikipedia
    2. Mackie & The Paradox of Omnipotence ~withalliamgod
    3. Banach-Tarski Paradox ~mathfunfact
    4. Zeno's Paradox ~wikipedia
    5. Hyperwebster - an uncountable dictionary ~ravi-bhide

    U5duDDZt6vnm3d35Bkh45vQGfEy7yoi.gif

    Authors get paid when people like you upvote their post.
    If you enjoyed what you read here, create your account today and start earning FREE STEEM!
    Sort Order:  

    sang can ret steemstem

    Haha pane na :D

    hai neubi link disqord steemstem ile

    Mantap bang @yandot,sangat bermanfaat. Terimaksih bang. Salam.

    Terimakasih bang

    Great post professor @yandot
    Thanks for sharing this science post

    Thanks for read it brother!

    High quality post.
    Well done, @yandot.
    uvote.png

    Thank you very much sir! @elgeko i am really appreciate it :))

    Thanks for sharing this @yandot! Very interesting to think about. I too had the same experience in a barbers chair. Mind blowing as a child haha

    Thank you for reading! It was a funny experience :D

    My first taste of the concept was after my Grandma tucked me in for the night. I was pondering what she had told me in our bedtime chat about infinity.

    Well, I have always had the overactive imagination so my mind started running away from me. Plus this happened after having watched one of the Superman movies where I cried because he let the bad guys float out into space forever...

    The thought of infinity and eternity and forever kept me up into the night, and I had a few nightmares after that!

    Great article!

    the barbing saloon had two mirrors facing each other

    I had a similar experience when I was little.

    But it was in my own home. It is crazy to see this representation of infinity when little, and even to this day I remember it, so it clearly had an impact in my younger self.

      ·  6 years ago (edited)

    Thank you for you reading man!

    . It is crazy to see this representation of infinity when little,

    a forgotten un experience!

    For me, infinity was always interesting concept. I viewed it through the fact that there is always something infinitely smaller and something infinitely bigger than myself. Based on that I concluded that difference in size and importance between me, the universe and a single atom is negligible ;)

    Thanks for you reading!

    . I viewed it through the fact that there is always something infinitely smaller and something infinitely bigger than myself

    Thats correct point!
    very interested Infinity does have the concept of a nice to learn.

    This post has been rewarded with 30% upvote from @indiaunited-bot account. We are happy to have you as one of the valuable member of the community.

    If you would like to delegate to @IndiaUnited you can do so by clicking on the following links: 5SP, 10SP, 15SP, 20SP 25SP, 50SP, 100SP, 250SP. Be sure to leave at least 50SP undelegated on your account.

    If you are from India, follow @indiaunited and Join us in

    to get community support and guidance

    Please contribute to the community by upvoting this comment and posts made by @indiaunited.

    Dizzying and perplexing... I love this stuff! Keep it coming.

    Thank you for reading!

    Excellent write-up. I also used to wonder a lot about infinity. From my childhood, I have always feet that the concept of infinity should closely be associated with infinity and God concept as well. Your relative reference to infinity and god is very nice. 🙂

    For instance an omnipotent god who can infinitely do "all" things, should also be able to create something he cannot displace. If he creates something he cannot displace or move, then he is not infinitely powerful after all.

    Thank you for you reading!

    I have always feet that the concept of infinity should closely be associated with infinity and Good concept as well.

    Thats right, infinity is good concept

    The paradoxes that proves how boundless infinity is are many but I’ll stop in this one. Have you ever imagined a dictionary that is uncountable? Have you also imagined a dictionary that contains all possible words obtainable using the English alphabets? Well, I present to you, the Hyperwebster dictionary.

    It would then also include the words of any language using the same alphabet, isn't it?

      ·  6 years ago (edited)

    Thank you for reading sir!

    It would then also include the words of any language using the same alphabet, isn't it?

    Yes include the words of any language have the same alphabet but english very important!

    Well, if you can have language like German, Spanish, Italian, French, etc... for free, it is more powerful ^^

    Lawd! He is a brainiac!

    Thank you for reading!

    You just received a Tier 0 upvote! Looking for bigger rewards? Click here and learn how to get them or visit us on Discord

    Hi @yandat.I am a student of mathematics department.I know the importance and also the contradiction of infinty very much.Thank you for sharing your valuable information with us.

    So far i just know the word "infinity". used it , write it in exam paper for marks only.

    What is it, what is the limit, why we use this word!!! i don't have Clear concept.
    Reading this article i am bit clear about it.
    Hope to get much more article from you in future.

    Thank you for reading!