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Friday, July 24, 2009

Infinity

We are a part of a circle
It’s like a Mobius strip
And it goes ‘round and ‘round
Until it loses a link


Sometime between the fifth and sixth centuries B.C., the Greeks discovered infinity. The concept was so overwhelming, so bizarre, so contrary to every human intuition, that it confounded the ancient philosophers and mathematicians who discovered it, causing pain, insanity, and at least one murder. The consequences of the discovery would have profound affects on the worlds of science, mathematics, philosophy, and religion two-and-a-half millennia later.

Infinity is today so well integrated into today's language that we can scarcely imagine many thoughts and expressions without it. However, despite its widespread use, infinity is one of those objects we scarcely understand. Most of us view time as infinite and space as infinitesimally decomposable and possibly infinite,, even though both involve unmeasurable, unfathomable dimensions that defy comprehension. Yet, infinities (yes, there are several) are very, very useful to "tie" things together, to provide comprehensible models, and for the mathematician to provide a completion of mathematical theories that actually simplifies statements, proofs, and applications.

But what is infinity? How can something infinite expand? Once and for all, how can we conclude that the universe is infinite? The fact that the universe is infinite may contradict Brane theory. Consequently, could it be tenable to suggest that this Brane is a sub-universe?

Anyhow, infinity is paradoxical because something infinite is not supposed to be able to expand,.since it already goes on forever and on top of that it supposedly never ends,.

There's a fundamental bit of foolishness that underlies all of the flames. Infinity is not a number. It's a mathematical concept related to numbers, but it is not, not a number.

The structure of a fractal object is reiterated in its magnifications. Fractals can be magnified indefinitely without losing their structure and becoming "smooth"; they have an infinite perimeter, an infinite surface area. An example for a fractal curve of infinite length is the Koch snowflake.

Achilles is in a footrace with a tortoise. He allows the tortoise a head start of 100 feet. If we suppose that each racer runs at a constant speed (the tortoise slower than Aquiles), then after some time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say,10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.

A Möebius strip is a two-dimensional surface with the puzzling property of having only one side. Despite this mind-bending characteristic, it's an easy object to make: just take a long strip of paper, give one end a half-twist, and tape the two ends together. Because of the half-twist, the front side of one end of the strip joins with the reverse side of the other end, so that the taped-together band has only one side. This is the symbol that represent infinity.

100 comments:

human being said...

hey my dearest Marianna...
see what you have done?!
just a few minutes ago on Tom's blog i wrote for you i'm too sleepy to put up those links... but writing for you made me eager to check your new post and there i am... not much sleepy and deciced to post the links... those works i told you about... the crow's understanding of non-Euclidean concepts... and really related to this post:

Moebius Ladder

Drinking from Klein Bottle



thanks for your always amazing posts... really enjoyed reading this one... especailly the paradox...

love and peace to you

Mariana Soffer said...

Human being and TC::
You make me feel so well human being, regarding what you say about how I transmit knowledge, and h that I have passion for doing it, wich it true, I love doing research, and I love communicating what I know to people who want to learn mo

So if you want to learn more you will, I can guide you trough it,
Check for example the moebious strip, what do you think it is euclidean geometry or nott?

I thik you are mistaken, I think you have much more things to tell share and teach to other peopoe,, I am sure about it, it is just your insecurity that does not let you take advatange of it,

Dp not force yourselfe to write or learn when you are to tired, it is conterproductive, just take your time till you fill you are ready and inspiired to transmite what you what to shae with others



In 1823, Janos Bolyai wrote to his father: "Out of nothing I have created a new universe." By which he meant that starting from the first 4 of Euclid's postulates and a modified fifth, he developed an expansive theory that, although quite unusual, did not seem to lead to any logical contradiction. Gauss expressed his conviction in consistency of the theory he had in mind in a letter in 1824. However, hesitant of the public reaction to the idea that, by the side of Euclidean, there is another geometry, he never published anything on the subject.

http://www.cut-the-knot.org/triangle/pythpar/Model.shtml

Euclid's geometrical thesis, "The Elements" (c. 300 B.C.E), proposed five basic postulates of geometry. Of these postulates, all were considered self-evident except for the fifth postulate. The fifth postulate asserted that two lines are parallel (i.e. non-intersecting) if a third line can intersect both lines perpendicularly. Consequently, in a Euclidean geometry every point has one and only one line parallel to any given line.

For centuries people questioned Euclid's fifth postulate. Even Euclid seemed suspicious of the fifth postulate because he avoided solving problems with it until his 29th example. Mathematicians stumbled with ways to prove the validity of the fifth postulate from the first four postulates, which we now call the postulates of absolute geometry. Those mathematicians who didn't fail were soon seen to have fallacious errors in their reasoning. These errors usually occurred because a mathematician had made self-fulfilling assumptions pertaining to parallel lines, rather than working with the other postulates. Essentially, they were forcing a result through the application of faulty logic.

http://www.essortment.com/all/noneuclideange_risc.htm



yPU HAVE SOME STUFF TO READ FOR NOW IF YOU FEEL LIKE, IT IS NOT VERY GOOODD, BUT i AM ALSO TIRED TO BE SEARCHING FOR THE EXACT THING i WANT TO SHOW YOU
taKE CARE GUYS

human being said...

WOW!
Mariana... first, accept my virtual hugs and kisses...
you are gem!
lots of good stuff to chew on...
and surely i shouldn't do it with a sleepy head... i want to take my time reading this and checking the links... then i'll come back with my crowings and questions...




this is for you (who know and love):



i know...
but it's not enough, i know
i love...
and it's not little, you know

i'm standing on a dot
but i can see
infinity
and
beyond
.
.
.

Mariana Soffer said...

Human being<
I am sorry Id did not wanted to keep you awake, but it seems we are syncronized and interested in each other stuff. Here I found the first tutorial with which I learn fuzzy logic
http://home.dei.polimi.it/matteucc/Clustering/tutorial_html/index.html
>http://home.dei.polimi.it/matteucc/Clustering/tutorial_html/cmeans.html


Regarding the emotion of the meaning you can experiment with
http://sentiwordnet.isti.cnr.it/browse/sentiwn.pl?word=good&show=position
This is the easiest to start with then there ae mudh more.
Hope you like the experimental soft

Jessie Carty said...

the idea of the paradox of the one point versus the many is actually something i am struggling with in a poem I'm writing so loved reading this, it just reinvigorates me to keep trying the poem even though my brain and science/math don't always mesh as well as i would like.

i love the way you make me think!

Mariana Soffer said...

Jessie Cart:
I am glad that it helps you to get more stregth reading my post, for writting something it is not easy for you to write.
Iy is like you say onee does not usually have the same level of hability in the different skills that are needed for a task.
Please let me know if I can help you with the math paart, I will be glad about that.
Mariana

ines.gato22@hotmail.com said...

Here is a paradox I like called the barber:

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

Asking this, however, we discover that the situation presented is in fact impossible:

* If the barber does not shave himself, he must abide by the rule and shave himself.
* If he does shave himself, according to the rule he will not shave himself.

Hope you like this one

Mariana Soffer said...

ines:
Thank you very much for the paradox, I really like that one in speciall, , when i discovered I stayed hours thinking whether the barber belongss to the self shavers or to the others.

pedro said...

Hi, I am fascinated with the moebious strip, can you tell me more facts or stories about it?
thank you for this fantastic post

Mariana Soffer said...

Pedro:
The Möbius strip has provided inspiration both for sculptures and for graphical art. The artist M. C. Escher was especially fond of it and based several of his lithographs on it. One famous example, Möbius Strip II, features ants crawling around the surface of a Möbius strip[1].

It is also a recurrent feature in science fiction stories, such as Arthur C. Clarke's The Wall of Darkness. Science fiction stories sometimes suggest that our universe might be some kind of generalised Möbius strip. In the short story A Subway Named Möbius, by A.J. Deutsch, the Boston subway authority builds a new line, but the system becomes so tangled that it turns into a Möbius strip, and trains start to disappear. Moreover, Martin Gardner's No-Sided Professor tells of a mathematician who invents a folding that goes one step beyond Möbius and creates an object with zero sides!

Hope you liked liked how the story of the symbol continued

TC said...

Dear Mariana,

We should have known it would be Ad Astra and Clear the Decks for Infinity with you one of these days, what other worlds are left to conquer?

Lovely turn of events, I'm still spinning meanwhile on the Meaning of Meaning. For you and David Lloyd I have found something beautifully

Meaningless

And perhaps this will be relevant, the infinite grains of sand on the paradisal playa:


To see the world in a grain of sand, hold infinity in the palm of your hand

"What the axiom of infinity is intended to say would express itself in language through the existence of infinitely many names with different meanings."--L.W.

TC said...

Excuse my infinite clownshow, it was Troy Lloyd I meant!

And Mariana, don't let Infinity spin you into the hospital. Take care of yourself, my dear, and ignore all of us if you must. We'll survive somehow.

Shubhajit said...

It is a wonderful post. very Very contemplative. Though I can't understand some of the theories.

I don't think time and space are infinite. For us yes. To me for human only infinite thing is perfection.

However, there is something beyond that infinite, else how this infinity concept comes? If we think deep about this universe then after certain part our minds can't go beyond because our minds can't go beyond the mind. What causes this infinity? Everything in this universe has some cause then only we can see the effect, else how we can see that infinity is this or that. Even time, space had some cause and it germinated from it and manifested.

And what is beyond that cause? What is beyond that space? What is beyond that time? even if we believe in popular theory of Black Hole then where that Black Hole stands on? Infinity is apparent because of the limitation of our finite mind. Through our finite abilities we can't find the infinite and that's proved that there is no infinity but must be stopped somewhere.

I thing I am not much clear with the concept because I only think of infinite from my finite mind. That's why I guess my inference about that subject become so complex.

Uncle Tree said...

O whither do I begin
and hither do you get off?
Lost between equations on the one side
and words on the side that doesn't exist

It's all pointless
with strings attached

Strip it naked
The Emperor's invisible
Mobius Dick swallowed him up
and down he went
He'd been spirally screwed
from the beginning
that has no end
and never will

Am I close?
Or already on it?
Can I get to Hell
through Heaven's back door?

Janus told me so
forgetting to tell me
which way to go

Turn At The Far Tree

the walking man said...

What happens to the concept of Infinite if you remove the property of time from the equation and substitute the property of light where time used to be?

Jason Gusmann said...

i'm going to look up those stories. thank you mariana! i often find that fiction assists me in comprehending concepts and theories that i otherwise have difficulty with.

Dave King said...

Interesting to compare the histories of the two concepts, infinity and zero, I think. Maybe they'll turn out to be two sides of the same coin. I find the case of fractals to be infinitely interesting! Seriously though, thanks for a great post.

Rick said...

In Alchemy, we have what we call the Ouroboros- the snake which devours its tale to constantly regenerate in cyclicality. Jung, who, in the end, became more of an alchemical theorist than a psychologist, perceived it as a symbol of the evolving self. So that, like infinity, the self's identity merges with the infinite by consuming itself in successive cycles only to re-emerge as a unified point the identity of which is infinite contraction and expansion- which is a symbol representation of your fractal example.

As always, Mariana, I enjoyed your post much and look forward to the next.

Jon said...

reminds me of the book, THE ELEGANT UNIVERSE by Brian Greene...

when you being up branes are you talking about superstrings?

LINK

Mark Reep said...

Enjoying the Moebius strip material. Neil Gaiman's short story 'Pages from a Journal Found in a Shoebox Left in a Greyhound Bus...' from his collection 'Fragile Things' is another nice example of an experience/account looping back on itself. A quick read, but one that's stayed with me.

Thanks for stopping by my blog- All the best!

Mark Reep said...

Did a quick Google- Here's the link to the Gaiman short.
http://www.hereinmyhead.com/neil/sw.html

Mariana Soffer said...

TC:
thanks for your kind words. Sadly I am far away to conquer infinity, although it would be nice, woudn't it? I do not know why we humans have the need to conquer things by putting names on it.

The meaning of meaning is smething difficult to comprehend to me as well. Maybe because it is an invention from humans covered with a bit of inference.

Neat video by the way. And also neat poem in your post I might say. And great and thougt provoking quote, that I am still thinkin off

Hugz

Mariana Soffer said...

TC:
Do not worry if you had not clarified the name of the other I would have never notice at all.

Thanks for your kind words. Do not worry that I am sure blogging is not going to take me to the hospital, actually it is doing me pretty well in my mind while I have nothing else to do with my life.
But I will give up blonging if I must, but for now I do not see the need of that.
Take care

Mariana Soffer said...

Shubhajit:
I am happy that you liked it, please feel free to ask anything you do not fully get, I will be more than happy to explain it in detail for you.

Very intereting thought about the no infinity of space and time, and that perfection is the only thing that it is endless. I think you might be right somehow right about the non excistence of infinity and our limited minds, I have to think about that again.

Infinity as you say it concepts, and concepts do not need to be tangible. But what you say makes sense, I always thought about that. You reminded me about this story:
Bertrand Russell once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!

I always thought as you do that our minds are limited and that they will never allow us to understand either infinity neither our own minds.
Thanks a lot for making me think a lot,

Mariana Soffer said...

Uncle Tree:
It looks as if our friendship is impossible,
as if the universe make us unble to understnd ech other

Poor guy spirling down forever and ever . Of course yoy are close I guess you just hit the point on the sente I put before.

This is fantastic:Can I get to Hell
through Heaven's back door?
I imagine that yes
Thank you so much for embelishing my post with your gorgeous poem, and also your interesting thoughts.
Hugz and more Hugz

Mariana Soffer said...

the walking man :

what an intersting question. Maybe nothing will happen, maybe it won't be possible, maybe everything wil change.But we will have to make the amount of light be able to increase only, it can not decrees neither diminish to a place where it was before, cause it has to be able to replce time, that goes one way (we suppose). Then our world will become brighter and brighter.
Thanks for the great comment man
M

Mariana Soffer said...

Jason Gusmann:
My pleasure Jason, of course fiction assist in understanding them, remember that sicence is also a kind of fiction (In a way). Just read borges, his short stories will help, specially the ones from fiction.
Take good care

Mariana Soffer said...

Dave King:
Very good idea the one you had.
Mathematcally they do not behave in all aperations as 2 sides of the same coin, if you add or substract them for exmple it does not work.
Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing be something?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero. So we can see that you are not wrong at all, they seem to be the 2 sides of the same coin.
About the fractals, it came to mind due to a congress I wen't where I was asked If I could do a program that reduced dimesionlities to a fractal one (The mandelbrot dimensionality is something like 2.4)

I am glad you liked the post and the fractal thought.
take care Dave

Mariana Soffer said...

Rick:
I like the idea of the serpent that eats itself a lot.
I had no idea Jung became an alchemist.. Glad you also found interesting the thing about fractals, but I do not understand why self identity emerges from something that consumes itself. I am going to find it nd read it.
hugs my friend

Mariana Soffer said...

Jon:
Interesting book inded:
There is an ill-concealed skeleton in the closet of physics: "As they are currently formulated, general relativity and quantum mechanics cannot both be right." Each is exceedingly accurate in its field: general relativity explains the behavior of the universe at large scales, while quantum mechanics describes the behavior of subatomic particles. Yet the theories collide horribly under extreme conditions such as black holes or times close to the big bang. Brian Greene, a specialist in quantum field theory, believes that the two pillars of physics can be reconciled in superstring theory, a theory of everything.

Brane theory: is the theory that the universe has four dimensions (not counting time as a dimension) instead of three. Imagine a bacterium on top of a smooth rock. He is aware of only two dimensions; he cannot sense the third dimension directly (though bacterial physicists theorize a third dimension, which is vigorously disputed by bacterial theologians). Likewise, we cannot directly sense the fourth dimension with our senses. The fourth dimension represents multiple "parallel" universes, which have come to be known as "branes.

txs for stepping by

Mariana Soffer said...

Mark Reep:
I am glad you enojoyed the moebious strip, I love it myself.
To tell you the truth I don t have a clue about the author or book you are talking about, can you please send me a link too it, cause it relly sounds interesting.

Thank you for your recomendation mark and a pleasure to stop at your blog

Mariana Soffer said...

Mark Reep:
Funny Y replied before reading the follwing post. Very interesting text, thanks! By the way I do not get what does Tori amos has to do with it, does she sing something from it? Isn't the text his?

Ok Sorry I will not bother you any more
M

TC said...

Mariana,

By the way--here's an interesting Infinity Link that's been right under (well, more like above) our noses in these in these
Islamic mosaic tile designs

"Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions..."

On the post I've left links to the recent discoveries of this infinitely-extending-pattern structure.

Abrazos

Tom

Mariana Soffer said...

TC:
tom, we seem to be so much in sink, that is amazing, here is some more interesting stuff I found about it (but it is better to see the pictures indeed)-
Lu is the guy who discovred the penrosse stuff was what the islam was made of

Lu suggests that Islamic architects used these shapes, which he calls girih tiles, to scribe the patterns onto the walls. That would explain how they tiled large surfaces with such precision.

Lu also figured out that the girih tiles could be broken up into the kites and darts of Penrose tiles. When he divided the tiles in this way, one building, the Darb-i Imam shrine, had a near-perfect Penrose tiling. The shrine was built in 1453, and it would be another 500 years before the mathematics behind Penrose tiles was developed.

Penrose says people ask him 'how do you know that that tiles when the problem is noncomputable?' but that's not the point. The point is that in a particular case you may have a way of seeing the solution, but there is no systematic procedure that could be put on a machine, which requires no more thinking."

Also escher figures where inspired by this shape, made by him, such as the famous "asciending and descending" where he draws an impossible building.

And also this guy focuses on the very interesting non euclidean gemoetry (that comes next)

geek said...

This reminds me of something I learned from my Mathematics for General Education class, which is the Hilbert's Hotel.

The Hilbert's Hotel has an infinite number of rooms which are filled with guests. However, since it is infinite, then there are vacancies. When an incoming guest arrives, someone from room 1 is moved to room 2, someone from room 2 is moved to room 3 and so on and so forth. Thus, leaving room 1 vacant for an incoming guest.

However, if there are more than one incoming visitors, guests who are already are staying in the hotels are moved twice of their original room number. Thus, room 1 is moved to 2, 2 is moved to 4, 3 is moved to 6, and so on and so forth.

My prof then said that if there's a finite set of numerals, we could easily say that there are more counting numbers than odd numbers. However, in the case of the Hilbert's Hotel where there are infinite number of rooms, the number of odd numbers are equal with the number of counting numbers.

http://mathematicianspictures.com/DAVID_HILBERT/Hilberts_Hotel_Paradox_explained_by_John_Derbyshire.htm

Math is indeed mind-boggling.

I hope you're feeling better now. Best wishes from across the world.

Mariana Soffer said...

geek:
I liked a lot the hilbert hotel story, is exactely the kind of thing I love to think about. Well my dear friend it turns out that I have been studying set theory by chance lately, so you have me here with an advantage.

One way to think it is the following: you have the set number 1 that is composed of all the integer numbers (all the rooms) and you have the set number 2 that has only the odd numbers, of course using your intuition you might say to me that the first set is bigger than the second one but you can also match each item from set 1 to an item from set 2, then you will have inifinite matching items cause set number 2 never ends, therefore the quantity of items in each set must be the same.

Thank you very much for your lovely colaboration my friend

Rob Bryanton said...

Hi Mariana, another brilliant entry, and you're right, another fascinating bit of synchronicity to my own blog published the same day. Entangled particles, entangled minds? No wonder Einstein called this stuff "spooky". :)

Fond regards,
Rob

Mariana Soffer said...

Rob:
Than you very much rob, it is nice to hear from you
I really appreciate your compliments to my entry. I guess you are right Einstein called it with the right name. Now that I think about it, all the coincidences our blog shared, it is a little scary. But I end up thinking more and more about entanglement and quantum physics stuff.

Harlequin said...

Mariana-- loved the frog and the meaning theories... I am at the end of a period of teaching some of these to students who just spark ( and sparkle ) once they realize how liberating theory can be... and how empowering!!

as for infinity... my calculus professor did his dissertation on Infinity and was quite the dude... and a damn fine teacher. Must be something to do with humility... nothing like infinity to remind me of my own finitude and my own dimensionality ... and my own responsibility... and my own... hey... this could go on and on ....

( I think that's the point!! )

thanks!

kj said...

mariana, i like and appreciate stretching my thinking this much. thank you for that once again.

i am not sufficiently skilled at higher math or science. thus my reaction to this, whose credibility i do not doubt, is that some things are simply to mysterious to understand. perhaps the mysterious is actually the divine.

but it was albert einstein i believe who said,not everything that can be counted matters, and not everything that matters can be counted.

xo
kj

Mariana Soffer said...

Harlequin:
my friend, I am glad you like that fable, I guess you must have read this, but I tell you just in case that is my favourite ever. And it is also cool you where into the meaning theories, I thought not many people would like that. I see your students are really lucky to have a teacher like you, that can encourage them to learn, and show them how usefull it is and the very important thing of why doing it. You are probably as a teacher really enlightening.

It is true and funny what you say about infinity, you need humility for sure to deal with the subject, and it also helps you be in persepctive of the magnitude of things.

Whenever you have time I would love to know what is it that you teach and to what age of people you do. Plain curiosity,
Thanks for stepping by H

Mariana Soffer said...

kj
Thanks to you, cause there are not that many people who like streaching their minds.

I tried to make this post as simple as I could, it might have a little bit of not that easy infinite math stuf, but my idea is to try and make people understand (except the paradoxes or puzzling stuff of course), so feel free to ask anything you want, it will be my pleasure to answer that.

I know that there are things that are not possible to be understood but I think that the curiosity keep us moving and learning stuff.

Great quote you mention by the way
Thanks a lot for stepping by

/t. said...

infinity:

ahh, the endless debate...

¤ ¤ ¤

/t.

Rayuela said...

Qué es el infinito?
No
es
unúmero*
(in)finitas
letras
compondrán
también
el
(in)
f
i
n
i
t
o?*
Seremos
(in)finitos
(re)tornantes
en
una
cinta
M
O
E
B
I
U
S?************************************


Besos*

Mariana Soffer said...

/t:


it certainly is endless, no questioning that.


I was thinking that you can draw with letters or signs a moebius strip that is chained with many moebius strips and the big picture looks like a moebious strip itselfs. So you will have a meta-strips, two levels of infinity. What do you think about that?

nice to see you my friend

Mariana Soffer said...

RAYUELA SAYS:
What is infinity?
is
Not
anumber*
(in)finit
letters
will compose
also
the
(in)
f
i
n
i
t
e?*
we'll be
(in)finit
(re)turners
in
a
strip
M
O
E
B
I
U
S?*************************

Mariana Soffer said...

Rayuela:
thank you very much for giving us your visual poetry, it is pretty cool and makes endless sense.

valbrussell said...

In this reality, we are confined in the prison of the concept of time and the walls surrounding this prison make it impossible to see the vastness of the truth that is infinite reality. Some leave through meditation but truly, most are caught in the sensual illusion of physical life on this planet. This is now my favourite post by you mariana. Well done my girl :) hugs

Mariana Soffer said...

Val:
It is excelent what you say about our prisions, we live such a limited life with no need of that. I wonder if it is because ignorance about something better or if it is due to something else, I guess time will tell the answer in myself. I think there are several ways we can escape, meditation, art, creation, human relations, drugs, and more. WE should fight to free ourself somehow.

I am really happy you like this post val, that 's great
hugs for you girl

Ruela said...

Now the Ruela ;) (Rayuela)
that's cool, very similar



fantastic post!

Chris H said...

In relation to the comment you left on my blog... what are you on about?
Diet coke has NOT been proven to cause cancer! If you believed everything you were told we would starve... because seemingly EVERYTHING can cause cancer.
I drink it. I love it. That's all there is to it. Have a nice day.

Mariana Soffer said...

Ruela:
it is simmilar but what does ruela mean? because rayuela is the name of a game that young kids play jumping arround.
Thanks for the compliment R

Mariana Soffer said...

Chris H: you are right that everybody is paranoid, I work in a company and I am in charge of monitoring social network and blogging people about their reactions to regular and light coke, and I can asure you people belive that and spend hour writting about that. Whatever society is sensacionalistic, people just want to be apalled

Shadow said...

i've always loved the infinity symbol. to comprehend it, however, not so easy to do.... it's like a really, really long time, heee heee heee

/t. said...

mariana,

i like your idea
&
i think that the dutch artist m.c.escher did interesting work with ideas about infinity and moebius strips that you would like

¤ ¤ ¤

/t.

Mark Reep said...

Yes, the short story is Neil Gaiman's. I don't remember reading that Tori was involved in its creation or any adaptation, but really dunno; they're friends, and it's possible they may have worked together on other projects. Glad you enjoyed the story- All the best!

Mariana Soffer said...

Shadow:
You are hilarious! I laughed out loud all by myself. Besides it is true what you say.
Thanks for stepping on this page

Mariana Soffer said...

/t_
I had posters all over my room when I was 12 from escher, I loved it, remember one that was over the 4 walls and was a strip that had the metamorphosis. If you look up this post you can see he was inspired by the Penrose tiles among other stuff.
Bye bye t

Mariana Soffer said...

mark reep: yes I use liked it, I just notice one interesting thing, I used to read sandman stories when I was younger, and I just saw them in my room and they are hi's, thats amazing.

Rakro said...

Infinity has always been a fascinating concept for me. I remember when I was a kid (five or six years old) to continuously ask about it to my teachers.

It was overwhelming to imagine something with no end. Maybe that’s why I like so much fractals. Time ago, I used a program to create my owns; and now, reading your post, I want to create some more.

Hugs

Joy said...

Fascinating blog! I plan to explore it often!

Anonymous said...

lack of knowledge, education, or awareness, definition of ignorance. Different perceptions are with knowledge. You have no perception of anything you do not know. I know nothing of embalming. THAT MAKES ME IGNORANT of it. Find another word to express what you are trying to say. God, Stuff, silly ass. An American God.. priceless.

Mariana Soffer said...

rakro:
hi, for me too it has always been an issue in my brain what I used to think most of all was how the universe could have now end, I thought it must stop at some point, but then if it stopped there should be something else after that, I could never real understand that in my mind.

I think I told you already that I did a program that draw a fractal, only one, the mandelbrot, that was when I was in highschool arround 16 years old, and I had to deal with understanding irrational numbers that was another complicated concept for my mind.

Then I draw several others I evented myself mostly in phyton that is a language I recomend you to lear, cause it is extremelly easy, you need to add the module to draw and you are all set. You can start by drawing the famous fractal triangle-like yourself
http://www.knowledgerush.com/kr/encyclopedia/Sphereflake_fractal/

Now what I am looking forward to understand at all is the fractal dimensionality they have, cause is not 2 or 3d is 2.xxx, how can that dimensionality exist in real life?

Mariana Soffer said...

Joy:
thank you very much for your compliment, I have been reeding your babble on blog and found it also really interesting. Do you know that the guy you talk about in your third post had an affair with a woman from my country? and that was what triggered all the press about him.
Do check my blog I think there are several entries you are going to like (not all of them)
Bye bye, an

Mariana Soffer said...

Anonymous:
what you say is pretty strange, there are things I do not understand, specially at the end.

You said:You have no perception of anything you do not know
that make me think of the idea of grabbing a real primitive human, an indian that lived always on the jungle putting it on a rocket and sending him to the moon. What do you think that guy would understand things are? would he see them? tell me what you think of that.
Another word for infinite I guess would be endless.bye

Buddha said...

Infinite is not a number but zero is?
I always thought of infinite as zero zero.
You know like; zero cows, zero cars, zero people, zero zeroes.
Think dividing 1 by 2,3,4,5,6, you get an infinite small amount but never a zero.
A zero is an infinitely small number, then a zero zero is infinite.

Mariana Soffer said...

Buddha:
Hello my new friend. It is very interesting to me what you said, never thought about it that way.

I can understand what you say graphically because 00 looks like the symbol representing inginity.

You are talking about things related to calculus and limits, which is an area of math. For example you can say that the function that divides by successive integers tends to cero when x tends to infinity. Be aware that it says tends but not is 0.

I understand that zero zeros would be zero if you think it in math terms, but you can also think about it as no nothings.

One think that might interest you is that if you dive something by zero the result tends to infinity.

There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all.
My brain is burning now, take care my friend.

AM said...

Infinte ignorance is what I feel the moment I read your log, Sofer. Congrats and keep marching in.

AM said...

Infinite ignorance is what I feel the moment I visit you log, Sofer.
Congrats and keep marching in.

foam said...

ick .. you made me think .. you bad girl .. lol ..
and here i am still on my summer break ..
but anyways, i was thinking about infinity and finite time ..

Buddha said...

I never thought of the mathematical aspect of Buddhism until I read your blog.
The Buddhist way is to see things as particulars to a general e.g
The western way to see a forest is a sum of all trees; the eastern view will be to see the tree as a part, fraction of the forest.
So the oneness is the only thing that there is and everything else would be parts or fractions of that.
So instead of saying that the universe is made of 250 billion galaxies we would say that a galaxy is 1/250billions of the oneness.
A solar system would be 1/250 billions/100billions and so one and so forth.
So basically everything would be a fraction of 1.
It might sound stupid but actually that is exactly how we measure when we add up things that can't be counted like , sugar and flour and water in a cake mix.
We turn them in tiny fractions of the universe we call grams!
So basically we have to numerical systems one that starts at zero and goes up and never ends and one that starts at 1 and goes down and never ends.
Logic dictates that one or both are wrong :)

Mariana Soffer said...

am:
my dear autor material, you have nothing to be ashamed about. I do not see lack of knowledge either in your blogs, your reflexions, or anythihng at all. If somebody comes and asks me about chemistry (for example), then I will have to say I am an ignorant as well, and I do not consider I am that myself, is just that I do not know stuff about that field, nobody knows it all anyway.
Besides you just get to know what you care about it is impossible to have knowledge of all that scientific stuff existing nowadays.
take care

Mariana Soffer said...

Foam:
I know I can be mean, even without wanting it sometines, but to me is a relief to think about science instead of about myself. Maybe it is upside down for you, everybody is different. But it is true what you say time is finite, so you have to choose in what to spend that anyway.
Take care

Mariana Soffer said...
This comment has been removed by the author.
~otto~ said...

You are really smart

Robb Todd said...

Thinking about this makes my brain hurt

Robb Todd said...

I forgot to mention that your post reminded me of this book, "Zero: The Biography of a Dangerous Idea."

http://www.amazon.com/Zero-Biography-Dangerous-Charles-Seife/dp/0140296476

Mariana Soffer said...

~otto~:
Thank you very much for your compliment otto, but I am going to disapoint you here, I am good in some stuff, such as math, and at other stuff, such as classical dancing, I stink.
take care dude

Mariana Soffer said...

robb todd:
Stop when it hurts too much, once the head ache is too strung it is much harder to l0wer the pain.
But I can infer that my post does not make you hurt too much cause you read the book you put the linked about.

Very interesting book you pointed at, it reminds me about my conversatiuons with Budha. It says "The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Line illustrations."

Do you have 10 mins to resume the main issues the book talks about?

thank you robb and take care
M

Mariana Soffer said...

Budha:
It does not sound stupid it sounded strange at the beginning, bug now I get what you say, because budhists see things as a hole, something complete.

Math invents measurments to be able to add things that you can not count, that is how it does it. But there are just conventions most people use.

I am not sure one is wrong, I think both can be used depending on the circunstances (although of course it is very hard for a person to do that). I do not belive in picking one system over another for good, I think all systems have something interesting to be used or to make us think about it.

Attain zero mind use zero mind says:
In Zen no meaning is great meaning, and great meaning is no meaning. We call this zero mind. I go around and ask, "Is zero a number?" One time in London I asked this, and somebody said, "Yes, it's a number."

So I said, "Yes, if you say zero is a number, you can do everything. Let's look at this. 9 x 0 = 0. Then, 9 = 0/0. O.K.? Then, if you say it's a number, then 0/0 = 1. So 9 = 0/0 = 1, and 9 = 1.

Then he said, "Ah, zero is not a number; that's not possible. 0/0 = 1 is not possible."

"O.K.; not possible is O.K. Then, 9 x 0 = 0. That means 9 = 0/0. 10,000 x 0 = 0. Then 10,000 = 0/0. 0/0 means 0/0 = 10,000 and 0/0 = 9. So 9 = 10,000.

"Zero mind can do anything. If you say zero is a number, that's O.K. If you say zero is not a number, that's O.K.; it doesn't matter. Zero is everything; everything is zero. This is Zen mathematics, O.K.? So zero mind is very interesting. If you keep zero mind, then you can do everything."

Then someone asked, "Soen Sa Nim, you talked about a child's mind as Buddha's mind, very simple, before memory. Before memory, all children's minds are correct mind, Buddha's mind, Enlightenment mind. Is this correct? Sleep time, sleep; eat time, eat. But a child only thinks of itself. Is this correct Buddha's mind?"

I said, "Before memory, a child's mind is no-Buddha, no-God mind. Someone once asked Ma Jo Zen Master, 'What is Buddha?' 'Mind is Buddha; Buddha is mind.' The next day someone asked, 'What is Buddha?' 'No mind, no Buddha.' Correct Buddha's mind is no Buddha, no mind. So a child's mind is correct Buddha's mind."

"Are they different, Buddha's mind and child's mind?"

"A child's mind is nothing at all; it is zero mind. It's like a clear mirror."

take care my friend just let me know and I will try to clarify what is not clear for you.

Buddha said...

Considering more of the mathematical significance of Buddhism metaphysical thought.
The universe is seen as binary universe where there are just ones and zeroes, a Boolean universe if you like.
Like in a computer program all is a combination of Yin and Yang - take a look at I Ching book, the similarities are just too great to be a coincidence IMO.
The "child mind" refers to a mind of no judgment. A "no mind" is a contemplative mind not an absent mind. In other words being enlightened doesn't mean being mentaly retarded. LOL!

Mariana Soffer said...

It is excelent what you are saying about one and zero, and its analogy with ying and yang.
I did never thought about it, and probabbly it would have never crossed my mind unless you
brough it up in this post.
You are right that being enlightened does not mean being metally retarted, but I think it means not forcing or trying to give it a rest to yout rational mind. Back to the ones and zeros, I thik you should write something about that, or create a new
theory perhaphs. You can think about how does binary numbers connects with the idea of a hole
number related to buddhist math.
Thank you very much for sharing those great ideas, they are really interesting to me, I will keep thinking about that
Take care my friend, hope you are all right

AM said...

But of course Ms Soffer. I can't but fully agree with you. I'm not ashamed of being an ignorant, quite the opposite, I'm proud of being aware that my ignorance is to my knowledge what a galaxy is to a single planet. Being aware of this astronomical ratio helps me to feel alive every day I get up in the mornings.

Ted Bagley said...

I see yin/yang as more accurately 0/-1. Man is empty and needs the illusion of one that is not him to be one. So yin/yang is nothing but a split subject, or $.
Buddhist math deals with 1/-1 where the split is revealed to be not there but is revealed through speech with another 1/-1. The no of "no-mind" is the bar between.
My experience seems to say that children are driven beings until they learn to contemplate, consider an other, so "child mind" has to signify something else.
Very cool site!!

Mariana Soffer said...

am:
I am really glad we agree about ignorance and it's related issues.
I liked the analogy you made by the way is really poetic, I also like it because you are adding the galaxy in the comment that is related to our talk about the universe that is going on here.

I am not sure why do you have to know it all to begin with, you seem to be departing from that point. Anyway I am glad that you are aware of the huge ratio between knowledges that helps you to feel better and to also get up.
Take care my smart friend, and do not be to harsh on yourself

Mariana Soffer said...

ted bagley:
Interesting idea about ying yang, it certainly is a split subject.

I loved the idea about the buddhist bar meaning no-mind, I think that is excelent.

I like a lot what you say about the child mind, I completelly agree with you, I think is pretty accurate, except that I am having trouble with what you mean with "child mind" has to signify someting else, to me it means the same untill it changes to the contemplative stage.

Thank you very much for your valuable thoghts my new friend

Ted Bagley said...

That something else is other than the way BOH was using it. More like Blake defines it.

Citizen of Earth said...

I don't believe the universe is infinite
Like everything else, the universe is a part of something bigger
And that may be...

Finite
Infinite
These are just concepts
That we carve out from relationships we don't fully understand

Mariana Soffer said...

ted bagley:
I guess you might be refering to WB saying
"To see a World in a grain of sand
And a Heaven in a Wild Flower,
Hold Infinity in the Palm of your hand
And Eternity in an Hour."

Which is fantastic, I take my hat of for this great verse. Hope you like it.
I did not understand well what do you mean by BOH, maybe is because I am a native speaker.
Thanks for visiting my friend

Mariana Soffer said...

citizen of Earth:
I agree that there are concepts that we do not understand, maybe they are to big for us. Maybe it is as if we where a small ant trying to understand what goes on when a human being passes walking near by.

Well the universe might be part of something bigger, but the question is if that something bigger is part of soemthing bigger itself, and so on till eternity, or not, or it stops somewhere.
Thanks for stepping by citizen

Ted Bagley said...

BOH was Buddha of Hollywood's comment before mine.

Uncle Tree said...

I am really happy for you, Mariana. You, and this site, have really taken off. The sky is the limit.
Wait...no it's not.

I'm always looking for win/win situations,
especially when we call them 'relatives'.
If it was lose/lose, we'd both find
someone else to blame.

Mariana Soffer said...

ted bagley:
Thanks for clarifying. I understood from the begining that you where talking about 2 different stuff, although both very interesting, I understand some people can confuse both, which was not my case, I understood what each one of you meant, and it is a very different concept in the end.
Take care ted, and I am sensing we aer going to be good thinking friends, and also have fun with our talks. I wnt to check your blog, the old parts, I will do it as soon as I have time.
Bye bye

Mariana Soffer said...

uncle tree:
thank you very much uncle, I know it is sincere your happiness for me.

Maybe if you do not mind you might be interested in help me out by telling me what you think about the subject of the next post, cause I might be sometimes to technical for people, and they get lost, also you can post sometihng in my blog whenever you want, just let me know if you feel like it and we ll talk about that
I loved your comment by the way
Love M

iarefreshtodeath said...

To say the least, infinity is an entertaining subject to ponder!

Mariana Soffer said...

iarefreshtodeath:
I like it too, as you can imagine, but I am glad that you like it, specially cause I have been checking your blog and I like what you say, i like what you right and I tihnk you have an interesting mind to open up

Uncle Tree said...

I'd be more than happy to help you out with that, Mariana. Just flash me an e-mail, and I'll get back with you tonight.

You're going to break one hundred with this one, babe. That is sooo cool! Your friends bring a wide range of knowledge to your discussions, and I enjoy reading along as we go. It's been fascinating. Cheerz, sweet niece! Big time!

Mariana Soffer said...

uncke tree:
Thank you very much for being willing to help me, it means a lot to me tp have someone
to share the writtings with. I think I already semt your yesterday a bunch of
possiblte post, so you could check and tell me what you think.But maybe it did not arri e,
I will check, or let me know if you have it.
By the way I am posting something in a short while, if you see something wrong
please let me know so I can correct it.

I have seen to become quite popular, which is somethig I like (I am not going to deny it)
because I can reach a higher amount of people like that. And I also do enjoy the
conversations with the visitors of the blog, who by the way you where the first one I get to know and liked.
Thanks a lot for your encouragment, talk to you real soon. Take care my hugable uncle
niece

Uncle Tree said...

I have received your e-mail, Mariana.
Sorry about not getting back to you last night. Spencer's birthday is tomorrow and I bought him a game to download (Sim's). It took two hours, and then he wanted to play it immediately, so I didn't kick him off of here.
I'm going to check out your new post first, and then I'll start checking out the subjects you've chosen for future discussions. Okay? See you shortly. ~Hugz~

Mariana Soffer said...

uncle tree:
Please uncle there is no hurry at all, I completelly trust you and I know you do things at your own time, same as I do, that is why I asked for, cause I know I won t be interfering too much with your life, otherwise it won t work.
Guau spenser s birthday, say Hi from myself (better not), can you send me his blog user cause I can not find him, and we talked to each other nicely a couple of time.
They say the sims it is quite an interesting game, actually I wanted to check out how it was eventually. Let s ask him after one or two weeks.
Talk to you soon my uncle
hugz