wandelaar

The perfect square has no corners?

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One sentence in the Tao Te Ching chapter 41 reads:

 

Quote

The perfect square has no corners

 

I find this paradox very hard to understand. Any suggestions?

 

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Two possibilities come to mind , geometrical shapes are sometimes obtained as positions within a spectrum of possibilities. 

Transecting a circle in various ways can yield a square, and at either end of the progression one ends up with a single dot or the entirety of the unbounded manifest , neither of which can be said to have corners.

The other , is that the abstract specifies the lengths of the sides, and the corners are dependent and unspecified... they fill the role rather than initiate a square specifically , ( four 90 degree angles could make for a rectangle ) 

So , if you were 'doing' the non-initiative participation of wei wu wei, you could be likened more to a corner,  than a side. 

But that's just guessing , to fit the answer,  to the shape of the question.  

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I think Paradox Is the theme. 

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The straightness of the Way seems curved.

The highest virtue seems as low as a valley.

The purest white seems stained.

The grandest virtue seems deficient.

The sturdiest virtue seems fragile.

..

The perfect square lacks corners.

 

Perhaps a wake up call to see the world in a different way.  To appreciate the low, the stained, the deficient, fragile..

 

 

 

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3 minutes ago, thelerner said:

I think Paradox Is the theme. 

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The straightness of the Way seems curved.

The highest virtue seems as low as a valley.

The purest white seems stained.

The grandest virtue seems deficient.

The sturdiest virtue seems fragile.

..

The perfect square lacks corners.

 

Perhaps a wake up call to see the world in a different way.  To appreciate the low, the stained, the deficient, fragile..

 

That's a nice explanation that works for the other paradoxes, but the problem with the perfect square without corners as a geometrical object is that it would be extremely difficult to work with such an inconsistent concept. Is it certain that a geometrical square is meant, and not an urban location such as in our day's Times Square? 

 

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Interesting to see this translated as perfect square. 

The characters are  大方 which is literally 'large' or 'great' square. 

 方 can also mean direction.

There are other, more specific characters for perfect.

I'm not a native speaker but like to play with translations sometimes.

 

I wonder if the intention here is perfect square vs great or greatest square.

Still not certain about the intention of corner-less.

Could it have something to do with expansion?

It's a tricky line.

 

If you google "a perfect square has no corners" you'll come across a variety of pages with some interesting theories.

 

I invoke my teacher's advice with something like this - don't focus too much on what you don't understand.

There is plenty that you do understand to work with.

Over time it might make more sense.

That's my approach.

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Perhaps  the idea is that a square made by for instance a carpenter can never be geometrically perfect because its corners will always be of non-zero dimensions, whereas a geometrically perfect square has corners that are mere zero-sized points. And so there would be two meanings in one:

 

1. A geometrically perfect square has corners that are mere zero-sized points.

 

2. Any practically useful square lacks corners in the geometrical sense. 

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For me, it's like a koan... presenting one's mind paradox with the intent to drop incessant story identification, projection, evaluation, comparison and judgement through the presentation of an irreconcilable concept.  It's like an interrupt signal to bring brief pause to the incessant monkey telling stories about how understandable every aspect of phenomena and noumena are...

 

The Way is beingness, not a thing to be understood.  The Way is a fluid verb that encompasses all phenomena, emptiness, concepts and the non-conceptual.  One does not logic The Way.  One lives it.  It encompasses all the senses, and all that which is beyond sensory interaction. 

 

 

Many experiences of my life remain beyond my mind's ability to analyze and compartmentalize into neat logical concepts, in spite of them being repeated experiences dozens and hundreds of times over decades. 

 

The logical mind is a small tool, useful within certain parameters, but is not capable of encompassing The Way. 

Release.  Be here now. 

 

 

it's purposefully paradoxical.

the Way cannot be intellectualized logic'ed and spoken of concisely. 

it can be lived.  

 

being.  presence.  awareness

 

 

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10 minutes ago, Kar3n said:

Given any thought to other translations of the original text for a better understanding?

 

大象無形

 

Thanks. Looked at some others too, and the translation "great(est) square" seems to be the preferred translation. That kind of nullifies my above interpretation as it is based on a "perfect square". :(

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Posted (edited)

A "greatest square" would have to be infinitely great and in that case the supposed corners cannot be surrounded by a space of the common sort we know of because then we could push the corners still further away. So the corners of the greatest square - if they exists  - lie beyond our common sense comprehension.

Edited by wandelaar
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I took a quick look around to see how the word square is used in other works and translations. There seems to be a couple of different usages.

  • Square often seems to be used for Earth and Circle in reference to Heaven, or
  • Square can refer to a tool, as in a compass and square, or
  • Square can mean ccan also mean firm, correct, rectitude.

Perhaps some one (not me) able to analyze the chinese character can help distinguish the meaning here.  Otherwise, look to the context for some guidance. None of these seems to quite open the paradox for understanding.

 

One passage I found in Lin Yutang's translation of zhuang zi seems intreaguing:

 

Those who rely upon the arc, the line, compasses, and the square to make correct forms injure the natural constitution of things. ... Things in their original nature are curved without the help of arcs, straight without lines, round without compasses, and rectangular without squares...

 

and again later

 

The potter says, 'I am good at managing clay. If 1 want it round, 1 use compasses; if rectangular, a square ... But on what grounds can we think that the nature of clay and wood desires this application of compasses and square, and arc and line?

 

So, combining a couple of these notions, perhaps the idea being conveyed here in DDJ 41 is that the great square (Earth) as an expression of Dao cannot be defined using corners. 

 

... or maybe not. Seems like kind of a stretch ... and then, what about the remaining paradoxical lines in 41. Just fodder for discussion. : )

 

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16 minutes ago, OldDog said:

So, combining a couple of these notions, perhaps the idea being conveyed here in DDJ 41 is that the great square (Earth) as an expression of Dao cannot be defined using corners. 

 

That would be an explanation...

 

Quote

... or maybe not. Seems like kind of a stretch ... and then, what about the remaining paradoxical lines in 41. Just fodder for discussion. : )

 

See:

 

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Posted (edited)
20 hours ago, Kar3n said:

Given any thought to other translations of the original text for a better understanding?

大象無形

1. Its firmest virtue seems but poor and low; Its solid truth seems change to undergo; Its largest square doth yet no corner show

 

 

Interesting how both versions rhymes.  The greatest square will rightness desert.  I wonder if square has other meanings in the ancient tongue. 

 

Addon> I see this was answered well above by OldDog, Square in the past referred to Earth.

2. "The solidest virtue seems not alert, The purest chastity seems pervert, The greatest square will rightness desert.

 

 

 

 

 

Edited by thelerner

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19 minutes ago, thelerner said:

1. Its firmest virtue seems but poor and low; Its solid truth seems change to undergo; Its largest square doth yet no corner show

 

 

Interesting how the second version (Goddards) rhymes.  The greatest square will rightness desert.  I wonder if square has other meanings in the ancient tongue. 

 

 

2. "The solidest virtue seems not alert, The purest chastity seems pervert, The greatest square will rightness desert.

 

 

 

 

 

The character translated as square in the text has various meanings, none of them literally a square.

象- 

shape, form, appearance, to imitate or be like, elephant

 

It could be translated as the greatest form is invisible

 

The characters for square are very different from the above.

Hyphenation square
Part of Speech (名) noun, (形) adjective, (动) verb, (副) adverb

https://www.yellowbridge.com/chinese/dictionary.php

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Is there such a thing as a perfect square in nature?  I suggest that there is not.  Therefore the perfect square is an altered state of nature.  That can't be perfect.

 

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Posted (edited)

I`m reminded of Tyra Bank`s advice to contestants on America`s Next Top Model who often worry about perceived flaws in the structure of their faces: Perfect is boring, human is beautiful.  Put another way, it`s our imperfections that perfect us.  Pushed to it`s limit, yin gives rise to yang and vice versa.  One hundred percent yin isn`t yin any more at all -- it`s the beginning of yang.  This is a truth that can be divined gazing at the Tai Chi symbol, though I prefer to watch reality TV. 

 

Everything is fluid and constantly turning into something else, often it`s very opposite.  This is especially true at the extremes, whenever something is the perfected or "greatest" version of itself.  These extreme points are topsy-turvy transition areas where rational definitions cease to hold.  Ugliness flips over into beauty;  Squares lose their corners;  Nothing is as it seems. 

Edited by liminal_luke
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Posted (edited)

Thank you all. :) I understand the general idea of not overdoing things, and thus of the rejection of perfectionism (in the psychological sense of the word).

 

But why I started this topic is because I am interested in how this applies to the specific paradox of the perfect or greatest square.

Edited by wandelaar

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It boils down to what it means to you and how you apply it to your existence.

 

Looking for perfection or greatness that does not exist is a trap. ;)

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12 minutes ago, wandelaar said:

But why I started this topic is because I am interested in how this applies to the specific paradox of the perfect or greatest square.

 

The perfect square is no-square: it does not exist.

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5 hours ago, wandelaar said:

One sentence in the Tao Te Ching chapter 41 reads:

 

 

I find this paradox very hard to understand. Any suggestions?

 

 

I suggest that you PM @Eric Woon

 

☮️

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4 minutes ago, Lost in Translation said:

The perfect square is no-square: it does not exist.


I agree that all concrete square's we find in nature are imperfect. And that the greatest square if it exists at all is a problematic concept. So that could be an explanation of the paradox. But I find it hard to believe that that's all there is to it. But maybe it is, I don't know.

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Posted (edited)

The French philosopher Descartes, famous for the axiom "I think therefore I am", after proving the existence of the self found that after that proof, the next thing he could prove existed was shapes. He reasoned that shapes could be proven to exist because shapes only existed as a mental construct, a concept within his own mind. Ergo the act of mentally creating the concept of a square proved the existence of that mental construct.

There is no square. There is no thing that exists only in two dimensions with four equal-length sides joined at right angles.

But there is a square, since we can and do use the idea of a square in mathematics. So there is a square that exists as concept, but not physical reality.

A perfect square is a concept, not a physical thing. Ergo, could it be said the perfect square has no corners??

Edited by Alchemical Walrus
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6 minutes ago, Alchemical Walrus said:

The French philosopher Descartes, famous for the axiom "I think therefore I am"

 

That's a wrong translation imo, and as a quick google search shows, other philosophs come to the same conclusion like I did independantly concerning what the correct translation must be...

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5 hours ago, wandelaar said:
6 hours ago, thelerner said:

I think Paradox Is the theme. 

like

The straightness of the Way seems curved.

The highest virtue seems as low as a valley.

The purest white seems stained.

The grandest virtue seems deficient.

The sturdiest virtue seems fragile.

..

The perfect square lacks corners.

 

Perhaps a wake up call to see the world in a different way.  To appreciate the low, the stained, the deficient, fragile..

 

That's a nice explanation that works for the other paradoxes, but the problem with the perfect square without corners as a geometrical object is that it would be extremely difficult to work with such an inconsistent concept. Is it certain that a geometrical square is meant, and not an urban location such as in our day's Times Square? 

 

Those are my views too.  I can see how the first statements can make sense but that last one just does not compute.  I never could accept that last one so I just ignored it.  Possibly I will learn something as I read on.

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