## Shapes

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.

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### Shapes

How can "circles" exist? How can any shape exist?

We think of a circle as perfectly "round" but how is this possible if you also have finite space?

There should be a "smallest" point so this would be the smallest possible point to start from for ANY shape. Once you then try and think of ANY shape that is just a little bit bigger than a point shapes essentially make no sense whatsoever.

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### Re: Shapes

I think you should see fractal issue : http://en.wikipedia.org/wiki/Fractal

You can consider a generic algorithm which build what we name a circle, each time smoother at each step of the algorithm...
Reality make the process stop after a finite number of step. So that's what you name "the smallest point".
Calculus limitation make this also.
Interesting question could be : does reality is the result of a calculus and it's precision reduce to universe's ability to solve calculus before a time quanta? And this time quanta, can it emerge from this own constraint?
PrayerReason
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### Re: Shapes

http://videos.howstuffworks.com/tlc/33733-understanding-fractals-video.htm

A video on Fractals.

There should be a "smallest" point so this would be the smallest possible point to start from for ANY shape. Once you then try and think of ANY shape that is just a little bit bigger than a point shapes essentially make no sense whatsoever.

"Smallest" is a subjective term, because someone else can make it smaller. The smallest possible point needed to make your point is what is required. Once you define the point, any "shape" is going to be different from dirrerent perspective. Looking down at a shape, may appear to be a circle. At 45 degree view, it would appear to be eye shaped and from the side it would be a line. It makes sense if you put it all in some context.

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### Re: Shapes

BadgerJelly wrote:How can "circles" exist? How can any shape exist?

We think of a circle as perfectly "round" but how is this possible if you also have finite space?

There should be a "smallest" point so this would be the smallest possible point to start from for ANY shape. Once you then try and think of ANY shape that is just a little bit bigger than a point shapes essentially make no sense whatsoever.

With respect to the question "how can circles exist", it seems first off that you believe they do and are seeking how it could be possible? One might suppose, then, that you have something in mind respecting the existence of the circle. You may be thinking it has some ideal existence, say one which we can imagine, an image of sorts, perhaps. It would then be reasonable to ask how such an existence could arise, or to be asking a question that a psychologist might tackle. If this is the path you are going down, how I would respond, not so much as a psychologist, but rather as someone who tries to make sense of things and have learned from others how such a thing could be approached, that the "circle inside us" isn't the image we make it out to be, rather it is merely a particular concept (or rule) from (or out of) which our mind constructs its familiar image, one in which we can mimic by a certain schematic, one which is performed over a space in a period of time, though in doing so, the rule cannot be performed with the exactitude required of it (on the basis not only our being limited creatures, but also because the circle as it is defined by the rule can't be actualized in the physical world).

With respect to the second question regarding shapes, generally, however, if what is intended by it is that which is defined by rules as I've done in the above, the answer would be the same. However, such answers aren't going to be all that interesting if you have something else in mind. What is needed is to get over the idea of a circle and a shape having some absolute and universally pure character. It seems perfectly reasonable to say the earth isn't flat on the basis of circumnavigation. Moreover, even if you are a flat-earther, this doesn't mean that you would regard evidence of mountains and valleys as evidence that negates your thesis.

Despite this, however, respecting the physical world, there does seem to be an element of perfection respecting the laws of nature under the assumption that its mathematical representations correspond to the rules by which the universe constitutes itself. If these rules are in fact true of the universe, one could argue that such a perfection exists, and given that, circles or other shapes might exist.

On the other hand, I suspect there's a better way of thinking about (physically) existing things, at least on the scale in which humanity can make much sense of things. And it is here that existence, of things in space which have some shape to them, over some period of time, can be understood not as something permanent and unchanging, but rather something which derives from being under the control of forces. Controls aren't something that require perfection. Controls exist only so long as conditions support them. They give rise to such ideas that would support dynamic equilibrium of more or less random variables, of systems and of subsystems.

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### Re: Shapes

With respect to the question "how can circles exist", it seems first off that you believe they do and are seeking how it could be possible? One might suppose, then, that you have something in mind respecting the existence of the circle

I do believe they exist in a pure sense. I think the idea is an illusion.

I am asking this question with the idea to reinvent mathematics. As you note nature eludes to this form over and over and number such as Pi and the Golden ratio puzzle us and so does the macro and micro world. I am looking for a way to forget about the idea of shapes and bring a new idea to the table (if no one else has already?).

I'm no mathematician so it may take me a few years to see where mathematics has pushed out its reach but I am just suggesting that maybe it started off on the wrong foot considering we have based so much on Greek theorem.

Basically I think Pi is either wrong or needs to be thought of in a different light. I think circles are one of natures biggest clues to what makes the universe the universe.

My thinking is to start off with this idea by assuming there is a smallest point and giving this a conceptual measurement and then seeing where I can take it from there.

Up to now I have this series of numbers :

1, 5, 4, 8, 9, 13, 21, 25, 16, 24, 32, 25, 29, 37 .... ??

Need to sort out another two series and then combine all three and see what happens ... if anything!?!?

Also need to study some serious high mathematics to help me :P

I am basing this on expanding symmetry from a square base and then I'll do hexagon and then triangles. I'm sure this must have been looked into before so if anyone can point me in the right direction I would greatly appreciate it.

Thank you

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### Re: Shapes

"I do believe they exist in a pure sense. I think the idea is an illusion."
What do you want to say... Only idea, concept can be understood, manipulated, have an existence in real world. They exist "in a pure sense"...what do you mean? That circles could exist but they are not in real world?

You want to reinvent Mathematics... are you crazy? Moreover you are not a mathematicien...
The only thing you could do is to open a new way in Mathematics field... add your view to the mathematics collection.
If you are not mathematician, how could you know about the recent principle and theroem. Greek theorme is Greek theorem...Maths are not old school, they are living one and you should learn what exist before to say you will reinvente them!! I am not saying you don't have to think by your own...this way is nice. Be carefull on what you say or intent..., that's all.

"I think circles are one of natures biggest clues to what makes the universe the universe."
...ok, an intuition...is that all?
universe from circle is the clue you are trying to unify your understanding.
If you had use a line, you would have been trying to go ahead, in future etc.
You can mix circle and line to make what you want...

Then, a series and a plan to mix 2 or 3 another... and expect. You look like a alchimist.
What do you expect? That universe grace will fall in you and give you a wonderfull explaination of the universe?!!

I can understand, it's fun to make this... but of course, you won't find any super-theory. Be honest.
People who find theory on the world understand it and try to express their understanding to other men, with the language they are familiar (more or less). It can be music, art, mathematics...
You could try to give us little mathematics games if you want... For exemple, try to find the next element in your serie... Of course, if it's done with a huge function, noone could find and the game has no interest...
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### Re: Shapes

Yeah I may be crazy then again everyone else may be crazy.

Do you think its crazy that an electron can be fired through one slit and go through two?
Does Quantum "make sense"?

Trust me I know how nuts I sound and I have a lot of mathematics to learn. Alchemy? NOPE! You hav eno idea what I am actually talking about because I have barely explained it in full and have no idea IF its a plausible route to take yet or not.

What I am eluding too is something like a step from Newtonian gravity to Einsteins theory of gravity. I think something could have been missed by the Greeks because today with have MUCH more at our disposal then they did back then.

I think "reinvent" was too string a word to be honest. I've got an idea and its logical.

I think circles are one of natures biggest clues to what makes the universe the universe."
...ok, an intuition...is that all?

Well no. Why are you being so hostile? May be that is not your intention but that is what it comes across like to me in case you did not realise?

As said above by another :

Despite this, however, respecting the physical world, there does seem to be an element of perfection respecting the laws of nature under the assumption that its mathematical representations correspond to the rules by which the universe constitutes itself. If these rules are in fact true of the universe, one could argue that such a perfection exists, and given that, circles or other shapes might exist.

Circular shapes appear in nature EVERYWHERE. The Earth is vaguely round as is the Sun as are many things. I may be wrong in my assumption but you may be wrong in yours.

I'm not expecting to understand the universe at all. ITS IMPOSSIBLE!!! Its like trying to eat yourself. Like you said its fun and I'll check it out. I only posted here to see if anyone has taken this line before?

My idea is simple and based on an ever increasing square that is symmetrical in 90 degree rotations and then adding up the total number of squares to get an answer. The smaller you go the more frequent the "jumps" but the bigger and bigger it gets the fewer the jumps. I see this vague pattern in nature over time and thought maybe it could mean something or maybe not ... either way it gives me an excuse to take up mathematics again because I used to love it before I got frustrated with the entire teaching system which only cares about text results and not the ability to think.

If you want to check out the origin of Alchemy you'll find its based on basic psychology that got twisted over time ... that is a completely different topic altogether though. I'd be happy to discuss that too if you wanted on another thread or by PM, e-mail or whatever? The placebo effect fools some ... even me or you sometimes but I am more than aware of it.

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### Re: Shapes

I am not sure you are coherent but I will make abstract.

"Circular shapes appear in nature EVERYWHERE."...hum, probably my calendar is a circle and I never notice it... Again, be honest, there are many circular shapes in nature but that's not enough.
Compare Cubism, Impressionism ... and Reality.

"My idea is simple and based on an ever increasing square that is symmetrical in 90 degree rotations and then adding up the total number of squares to get an answer. The smaller you go the more frequent the "jumps" but the bigger and bigger it gets the fewer the jumps. I see this vague pattern in nature over time and thought maybe it could mean something or maybe not ... "
That 's probably interessting. It's your pattern, You watch the world through this. You could notice, that have nothing to do with your first post...no circle indeed.
I don't understand clearly your algorithm... I can imagine you take a square and make a rotation of 90 degree from one corner... you get 2 squares linked by an edge... If you make the rotation from center, you keep 1 square, so not interesting. Then addind the number of square to get an answer... ok 1, 2.... you make a serie.... but then I can't see what you want the process go on and what about your jumps?

"either way it gives me an excuse to take up mathematics again because I used to love it before I got frustrated with the entire teaching system which only cares about text results and not the ability to think."
You are frustated... ok. And you want to demonstrate yourself you like or are good with Mathematics... We try first to be human... Humility is one of its attributes. Dignity is another one.
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### Re: Shapes

BadgerJelly wrote:How can "circles" exist? How can any shape exist?

We think of a circle as perfectly "round" but how is this possible if you also have finite space?

There should be a "smallest" point so this would be the smallest possible point to start from for ANY shape. Once you then try and think of ANY shape that is just a little bit bigger than a point shapes essentially make no sense whatsoever.

As I understand it, we don't yet know whether space breaks down any smaller than the Planck-space. So, space is either infinitely divisible or not; if not, then I think you're right; no image of a perfect circle can exist.

There are a few spanners in the works:

1. Geometry can be done, by mathematicians, without drawing anything.
2. A straight line is just a circle with an infinite gradient.
3. As I understand it: where there's energy, space-time is Non-Euclidean. The fastest route between two points is technically a geodisic, not a straight line.

With regard to (1) we might choose to distinguish between a circle (as some kind of perfect, Platonic object), and an image of a circle (as a physical representation of the former). With this in mind it's possible to contend that a perfect circle exists, even if it is not to be found in the universe. With regard to (2) we might contend that we can prove the existence of a circle if only we can prove the existence of a straight line. With regard to (3) it might be worth noting that any discussion of whether circles exist in the real world may have to proceed from Non-Euclidean presuppositions (but you already half-acknowledged this with your point about quantum physics).

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### Re: Shapes

BadgerJelly wrote:Up to now I have this series of numbers :

1, 5, 4, 8, 9, 13, 21, 25, 16, 24, 32, 25, 29, 37 .... ??

Need to sort out another two series and then combine all three and see what happens ... if anything!?!?

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### Re: Shapes

With respect to the question "how can circles exist", it seems first off that you believe they do and are seeking how it could be possible? One might suppose, then, that you have something in mind respecting the existence of the circle

I do believe they exist in a pure sense. I think the idea is an illusion.

You might want to re-read this, with a critical eye.

When one uses the term 'pure', it can be compared with 'ideal', so one might conclude that circles have an ideal existence, which if you aren't an idealist, respecting reality, they exist in our mind. But then you go on suggesting that they are an illusion. To be an illusion would ordinarily mean that we are being fooled into thinking it is something that it isn't. This would then imply that the pure circles that exist in our mind don't actually exist in our mind. So, as this doesn't make a lot of sense, I suppose I should conclude that you are only trying to reinforce your view that such ideal circles aren't real and in turn this more or less indicates that you hold reality to be material or physical and that physical circles cannot really exist. The use of 'illusion' then suggests that it may be possible that we observe circles, for example the halo around the moon that is sometimes seen under certain conditions, but that were we able to observe it at a closer range there would be gaps or other distortions (impurities). But what of the forces themselves that cause the shape that appears to us to exist? Do they exist? Wouldn't they be physical if they did? Gravitational forces are such that they could be said to emanate or originate from masses along three dimensions of space from some origin upon other masses? (Similarly for electromagnetic forces.) On the basis of such ideal physical forces, one defines the orbits and orbitals of material objects in motion.

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### Re: Shapes

As I understand it, we don't yet know whether space breaks down any smaller than the Planck-space. So, space is either infinitely divisible or not; if not, then I think you're right; no image of a perfect circle can exist.

Correct. This is the assumption I am working with but it could be false.

I do believe they exist in a pure sense. I think the idea is an illusion.

You've caught me out again! :)
By pure sense I meant in the universe of mathematics. And in reality I think the situation is different just like was referred to on another topic about the bales of hay being added together to make one bale of hay.

In reference to circular motions and patterns in nature such as through gravity and magnetism this is what made me think that the micro world could not have circular motions if there is only so far down you can go as Lomax referred to.

For a visual reference this is what I am talking about although I have not put too much thought into it yet:

It is just a little puzzle at the moment and I would be surprised if it has not been considered already. Obviously trying to work out how this would figure out for the visual of circle is going to be a bit tricky considering my math ability is slight and VERY rusty.

Just thought I'd share the idea anyway and if someone was interested that would be good and if someone could point me to something similar that would be better. If not I'll just have to wait until I can order some maths books in.

Anyway looking at it in this very simplistic manner anything other than a square causes problems except maybe triangles? It's a stab in the dark but the idea interests me.

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### Re: Shapes

Your figure are similar to cellular automata... if you don't know, you could see http://en.wikipedia.org/wiki/Cellular_automaton and find a "game of life" on the net...
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### Re: Shapes

PrayerReason wrote:Your figure are similar to cellular automata... if you don't know, you could see http://en.wikipedia.org/wiki/Cellular_automaton and find a "game of life" on the net...

Very interesting stuff!

I'll put a better visual together that has some "order" to it when I have time and post here to see what you guys think.

The idea is to basic start with 1x1 square in the middle and expand out until I have to revert to a 2x2 and then start the process again.

Then to formulate this for a circular pattern if possible and to start to consider different shapes and then work into 3 dimensional space ...

Baby steps for me first though. I have many irons in many fires so any interest/information/feedback is greatly appreciated.

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### Re: Shapes

you might be interested in comparing your geometry with taxicab geometry

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### Re: Shapes

you might be interested in comparing your geometry with taxicab geometry

SEXY!!

Thank you :)

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### Re: Shapes

One of things you should think about, respecting the granularity of the universe, is that if space is discrete, there are issues with isometry. I'm assured by Lincoln that this has been considered and the issues have been overcome, but I have not yet satisfied myself of this conclusion. Moreover, a space that is taxi-cab in nature will not be isometric (at least that's my intuition).

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### Re: Shapes

taxicab thing looked good at a glance but is not :(

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### Re: Shapes

BadgerJelly wrote:taxicab thing looked good at a glance but is not :(

If I were to be sincere, I should tell you that this was the reason why I posted that suggestion: to let you wonder whether somebody else had not been proceeding along those same lines (and corners :°), but ending up with something which has quite limited use and a series of problems in general theoretical analysis.

In the end, old Euclide was not so bad, and his definition of distance quite useful - note that the most direct way to address the question of circles is by considering distance, which in itself is a quite relevant physical aspect (I believe owleye referred to this in relating circles to forces and interactions). And though he might have been fooled by parallel lines, still orthogonality, whatever geometry and space manyfold you like, actually is quite a useful concept, in relativity as well.

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### Re: Shapes

I think I know where I am going with this ... sort of!?!?

I was thinking along the lines of a mathematical relation to quantum with a absolute constant in an absolute dimension.

Not sure if I am using the correct terminology here though but if you are familiar with mathematical quantum mechanics (Which I am not yet!) then maybe you see my line of thought?

From what little I know I think this is pushing towards what I believe is Topology? Anyway if there are any mathematicians out there a shove in the right direction may be useful for this theoretical puzzle of avoiding infinities.

NOTE : The image posted above is not particularly clear. The idea is to work from 1 square "pixel" and add on "pixels" until I can add no more then go onto a square of 2x2 and repeat, then 3x3 and repeat and so on ... Eventually to replicate the form of a circle (each "pixel" being a finite quanta).

Thank you

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### Re: Shapes

You're heading in the wrong direction. Look up anti-aliasing, with respect to pixels, and you should get a feel of the problem (and its possible solution path in graphical representations) in your form of quantizing space. Your methodology works in general only when space is continuous, as only then can the size of the pixel approach zero. In raster scan devices, anti-aliasing works because the device space is limited. I doubt that the algorithm would work when the circle is on the scale of even the visible universe. Small deviations at a local level would be magnified at that scale and would result in easily detectable differences in some directions over others, making it impossible to obtain the same distance measurement of distant objects with nearby telescopes.

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### Re: Shapes

I am looking at this as a mathematical puzzle first and foremost set within my own definitions.

The "pixel" is just an expression not the reality of my made up universe.

only then can the size of the pixel approach zero

I am saying the "zero" is one "pixel" in this world and that there are not shades of colour. The "pixel" is either "on or "off". If there is a pattern I hope to resolve it mathematically and if its beyond me I'll have fun trying and learn. Would be better if I can see how someone else has done this because someone must have at some point.

You're heading in the wrong direction

Not sure how this is relevant as I don't believe in "wrong"? I am playing and hope to learn. Thanks for the suggestion of looking at anti-aliasing there may be something there I can use once I delve deeper into this puzzle I have made up.

Thank you

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### Re: Shapes

BadgerJelly wrote:I am looking at this as a mathematical puzzle first and foremost set within my own definitions.

The "pixel" is just an expression not the reality of my made up universe.

only then can the size of the pixel approach zero

I am saying the "zero" is one "pixel" in this world and that there are not shades of colour. The "pixel" is either "on or "off". If there is a pattern I hope to resolve it mathematically and if its beyond me I'll have fun trying and learn. Would be better if I can see how someone else has done this because someone must have at some point.

You're heading in the wrong direction

Not sure how this is relevant as I don't believe in "wrong"? I am playing and hope to learn. Thanks for the suggestion of looking at anti-aliasing there may be something there I can use once I delve deeper into this puzzle I have made up.

Thank you

Play around all you like. Don't expect me to join in. I now plan to put your messages on my do not respond list. You asked me in an earlier posting to remain in contact with you and I did. However, based on how you treat my responses, and the frustration I have with your replies in general (and what it causes in me that makes me so hateful), I am forced to withdraw. You are too much for me to engage. Find someone else.

James
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### Re: Shapes

I can be gentle if you want. Don't think that is what you mean though.

I'm always here though I stone wall no one.

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### Re: Shapes

Hello, Shape exist because perception exist.
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