Dukkha and pure mathematics.

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workbalance
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Dukkha and pure mathematics.

Post by workbalance »

How does Buddhism view the power of mathematical reasoning and its high status
in the philosophy of Pythagoras and Plato, as a training method that provides
great assistance in the gradual transformation of human consciousness
from painfully subjective to joyfully objective perception of reality?

Over the years, this accumulated power has been exploited
towards construction of machines & models of reality in a distinctively
quantitative sense, so I would like some guidance on my search for what
buddhist texts say or imply on its mystical side.

After all, arithmetic and geometry seem to be simple, universal and
objective starting-points for examining the inner workings of our minds
and gradually build a perception of reality based on "objective analogies":
a balance between quantification and wishful dreaming.

tkp67
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Re: Dukkha and pure mathematics.

Post by tkp67 »

I see analogs both in flat linear math and geometry.

A simple illustration follows.

I will say this much about math and the mind since it can be used to describe the nature of some conversations here and from the buddha himself as well.

We can state the same absolute fact through a variety of number systems.

Let us take use the decimal expression of 100 as the fact.

1100100 is the binary expression for 100

100 is the decimal expression for 100

64 is the hex base 16 expression for 100

At face value without translation they look intensely different but in proper context they are all the same.

The capacity to see value from different perspectives (or not) is the nature of the mind as expressed.
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Malcolm
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Re: Dukkha and pure mathematics.

Post by Malcolm »

workbalance wrote:
Sun Mar 08, 2020 12:04 pm
How does Buddhism view the power of mathematical reasoning and its high status
in the philosophy of Pythagoras and Plato, as a training method that provides
great assistance in the gradual transformation of human consciousness
from painfully subjective to joyfully objective perception of reality?
Math, logic, has no role in awakening. But they are useful for science and disciplining ones thinking, respectively.

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Dan74
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Re: Dukkha and pure mathematics.

Post by Dan74 »

I largely agree with Malcolm. Perhaps not 'no role', but not a major role. Logic can be helpful and clear thinking, concentration and devotion to truth are important, IMO, and they are arguably qualities that mathematical training helps develop.

FWIW, I am a trained mathematician, phd, publications, etc.. but I don't find it is of any central significance to Buddhist practice. The Buddha and teachers who came after him did not emphasize mathematics, nor even intellect. The Dharma is open to all sincere seekers, even to those of low intellect for whom pure mathematical concepts are out of reach.

In fact, an overly intellectual, thought-focused disposition can be a huge hindrance to Dharma practice, I believe. It is an embodied attention-driven practice, not a thought-driven intellectual one, IME.

muni
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Re: Dukkha and pure mathematics.

Post by muni »

I largely agree with Malcolm.
Dito.

The creativity can be used in investigations, for example in the medical, technical research for welfare of all.

It will not have direct value on purifying view/awakening, since knowledge is not to know all things but the nature of all things. Then counting What?
The presence of space makes it possible for the whole universe to be set out within it, and yet this does not alter or condition space in any way. Although rainbows appear in the sky, they do not make any difference to the sky; it is simply that the sky makes the appearance of rainbows possible.
Phenomena adorn emptiness, but never corrupt it. Dilgo Khyentse Rinpoche.
All dharma abide in mind mind abide in space space abides nowhere. Master La.
https://samyeinstitute.org/philosophy/w ... -concepts/

workbalance
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Re: Dukkha and pure mathematics.

Post by workbalance »

Dan74 wrote:
Sun Mar 08, 2020 4:09 pm
an overly intellectual, thought-focused disposition can be a huge hindrance to Dharma practice
I totally agree, that's exactly my problem with mathematics as is taught today,
i.e., without the mystical side which by all evidence the Pythagoreans did emphasize.
Perharps it was a peculiar development in a specific society and thereafter suited only to a peculiar
type of personality.
But it has an appeal, that crystal-clear clarity of deep results and that no-cheating, earnest progress
in learning. Where else can these qualities be found? So as to appeal not only to the intellectual faculty.
That's what I'm trying to answer..

tkp67
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Re: Dukkha and pure mathematics.

Post by tkp67 »

I think ever generation of buddhists is presented with evolving extraneous but necessary products of mind (science, math, philosophy, etc).

Keeping these changes in context with the human condition and experience without engagement of self in a world where information like this is exponentially increasing seems difficult. Emphasis on seems.

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Dan74
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Re: Dukkha and pure mathematics.

Post by Dan74 »

workbalance wrote:
Sun Mar 08, 2020 5:30 pm
Dan74 wrote:
Sun Mar 08, 2020 4:09 pm
an overly intellectual, thought-focused disposition can be a huge hindrance to Dharma practice
I totally agree, that's exactly my problem with mathematics as is taught today,
i.e., without the mystical side which by all evidence the Pythagoreans did emphasize.
Perharps it was a peculiar development in a specific society and thereafter suited only to a peculiar
type of personality.
But it has an appeal, that crystal-clear clarity of deep results and that no-cheating, earnest progress
in learning. Where else can these qualities be found? So as to appeal not only to the intellectual faculty.
That's what I'm trying to answer..
How do you propose maths should be taught 'with the mystical side'? Can you provide a concrete example?

workbalance
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Re: Dukkha and pure mathematics.

Post by workbalance »

Dan74 wrote:
Sun Mar 08, 2020 7:54 pm
workbalance wrote:
Sun Mar 08, 2020 5:30 pm
Dan74 wrote:
Sun Mar 08, 2020 4:09 pm
an overly intellectual, thought-focused disposition can be a huge hindrance to Dharma practice
I totally agree, that's exactly my problem with mathematics as is taught today,
i.e., without the mystical side which by all evidence the Pythagoreans did emphasize.
Perharps it was a peculiar development in a specific society and thereafter suited only to a peculiar
type of personality.
But it has an appeal, that crystal-clear clarity of deep results and that no-cheating, earnest progress
in learning. Where else can these qualities be found? So as to appeal not only to the intellectual faculty.
That's what I'm trying to answer..
How do you propose maths should be taught 'with the mystical side'? Can you provide a concrete example?

Plato's dialogue Meno is a nice elementary example, where a boy is led to double the area of a square;
which is then viewed as innate knowledge revealed.

An example of a pythagorean concept:
https://en.wikipedia.org/wiki/Tetractys

A old book on pythagorean arithmetic:
http://djm.cc/library/Theoretic_Arithme ... Taylor.pdf

Many other contemporary writers, e.g. Leonid Zhmud.

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Aemilius
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Re: Dukkha and pure mathematics.

Post by Aemilius »

Abhisamaya-alamkara-vritti of Vimuktisena:
" Now with his very words the Lord responds, Therefore the Tathagata does not derive his name from the fact that he has acquired this physical personality but from the fact that he has acquired all-knowledge. ..,this all-knowledge has come forth from the perfection of wisdom and this acquisition of the physical personality of the Tathagata is the result of skill in means in the perfection of wisdom and becomes a sure foundation for the cognition of all-knowing, i.e. serves as a cause for completion of all-knowing knowledge in others."
Last edited by Aemilius on Sun Mar 08, 2020 10:32 pm, edited 1 time in total.
svaha
"All human beings are born free and equal in dignity and rights.
They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
Sarvē mānavāḥ svatantrāḥ samutpannāḥ vartantē api ca, gauravadr̥śā adhikāradr̥śā ca samānāḥ ēva vartantē. Ētē sarvē cētanā-tarka-śaktibhyāṁ susampannāḥ santi. Api ca, sarvē’pi bandhutva-bhāvanayā parasparaṁ vyavaharantu."
Universal Declaration of Human Rights, Article 1. (in english and sanskrit)

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Wayfarer
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Re: Dukkha and pure mathematics.

Post by Wayfarer »

I became aware of the power of the idea of Platonic mathematics through a kind of accidental epiphany many, many years ago.

I was like this: every object in the material domain (in Buddhist terminology 'all compound things') is composed of parts and has a beginning and an end in time.

But numbers don't come into or go out of existence. 7 always equals 7, and is not composed of parts. It is 7 for any mind capable of counting. You might say, well isn't 7 a material object? The material object is the symbol, the sign - and that can be many things, whether it's 7, VII or 'seven', or made from all kinds of materials. But 'what is signified' is always the same. That is an 'intelligible reality'.

When I had that thought, I suddenly felt I understood why ancient philosophy esteemed mathematics: it is nearer in nature to the Uncreated, as it pertains to the realm of pure ideas or forms (which is also known as the Formal Realm). In Pythagorean and Platonist thought, there is an hierarchy of being, with intelligence at the top (later identified with God by Christianity) and matter at the bottom, with humans, the 'rational animal', in the middle. So intelligible objects, like number, were of a higher nature to the objects of sense, as they can be perceived only through the eye of reason.

I never studied Plato at school or university, except for in passing in units in history of philosophy but nevertheless I am sure that this intuition is fundamental to the Western intellectual tradition. But I discovered through studying the subject that Platonic realism has generally fallen out of favour in Western thinking, due to the influence of nominalism and, later, empiricism. For the empiricists, only compound things are real, and the idea of ' the intelligible object' is not intelligible to them (irony of ironies). This has had many profound consequences, which we're generally not able to be aware of, because it's 'in the air we breathe'. Discussing this topic for a long while on philosophy forums I have found that generally it is not understood and usually maligned.

All of this is outside the scope of Buddhist philosophy, generally; I don't think any of the classical Buddhist logicians had much to say about it. But I don't think it means that Buddhism negates this kind of understanding - it simply doesn't need to pursue it for its purposes. (It probably also means that the subject is strictly speaking out of scope for a Buddhist forum, but it doesn't hurt to be aware of it.)

See also Buddhism and Nominalism.
Last edited by Wayfarer on Sun Mar 08, 2020 10:42 pm, edited 1 time in total.
'Only practice with no gaining idea' ~ Suzuki Roshi

narhwal90
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Re: Dukkha and pure mathematics.

Post by narhwal90 »

workbalance wrote:
Sun Mar 08, 2020 10:12 pm
Dan74 wrote:
Sun Mar 08, 2020 7:54 pm
workbalance wrote:
Sun Mar 08, 2020 5:30 pm

I totally agree, that's exactly my problem with mathematics as is taught today,
i.e., without the mystical side which by all evidence the Pythagoreans did emphasize.
Perharps it was a peculiar development in a specific society and thereafter suited only to a peculiar
type of personality.
But it has an appeal, that crystal-clear clarity of deep results and that no-cheating, earnest progress
in learning. Where else can these qualities be found? So as to appeal not only to the intellectual faculty.
That's what I'm trying to answer..
How do you propose maths should be taught 'with the mystical side'? Can you provide a concrete example?

Plato's dialogue Meno is a nice elementary example, where a boy is led to double the area of a square;
which is then viewed as innate knowledge revealed.

An example of a pythagorean concept:
https://en.wikipedia.org/wiki/Tetractys

A old book on pythagorean arithmetic:
http://djm.cc/library/Theoretic_Arithme ... Taylor.pdf

Many other contemporary writers, e.g. Leonid Zhmud.
Don't see the point of mysticism here- any elementary school I've happened to be in (and similarly montessori) have sets of blocks showing how numbers may be compounded in 2 and 3 dimensions. Effective and useful. The 10-hole triangle-peg-jumping game is also a handy exercise found all over the place... When younger I found the latter a an interesting exercise for learning programming languages; brute-forcing solutions for that problem are tractable and a good way to work out simple recursion in an unfamiliar language.

For my part I've found my own mathmatics/engineering predisposition to be a continual risk of impediment in practice. The Lotus sutra for example goes on at length about major world systems counted by the dust obtained by hypothetically grinding others- an easy trap for the mind used to counting in exponents and approximations to refine estimates.

workbalance
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Re: Dukkha and pure mathematics.

Post by workbalance »

Wayfarer wrote:
Sun Mar 08, 2020 10:23 pm


All of this is outside the scope of Buddhist philosophy, generally; I don't think any of the classical Buddhist logicians had much to say about it. But I don't think it means that Buddhism negates this kind of understanding - it simply doesn't need to pursue it for its purposes.

See also Buddhism and Nominalism.
You just gave me a nice research project!

workbalance
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Re: Dukkha and pure mathematics.

Post by workbalance »

narhwal90 wrote:
Sun Mar 08, 2020 10:41 pm
workbalance wrote:
Sun Mar 08, 2020 10:12 pm
Dan74 wrote:
Sun Mar 08, 2020 7:54 pm


How do you propose maths should be taught 'with the mystical side'? Can you provide a concrete example?

Plato's dialogue Meno is a nice elementary example, where a boy is led to double the area of a square;
which is then viewed as innate knowledge revealed.

An example of a pythagorean concept:
https://en.wikipedia.org/wiki/Tetractys

A old book on pythagorean arithmetic:
http://djm.cc/library/Theoretic_Arithme ... Taylor.pdf

Many other contemporary writers, e.g. Leonid Zhmud.
Don't see the point of mysticism here
Tetraktys is a basic mystic symbol. The link provides many clues: https://en.wikipedia.org/wiki/Tetractys

narhwal90
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Re: Dukkha and pure mathematics.

Post by narhwal90 »

Not personally interested in mystic symbols.. but I guess it takes all kinds to make a world.

tkp67
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Re: Dukkha and pure mathematics.

Post by tkp67 »

narhwal90 wrote:
Sun Mar 08, 2020 11:52 pm
Not personally interested in mystic symbols.. but I guess it takes all kinds to make a world.
math has been influential in creationism
Chazal say that Hashem looked in the Torah and created the world. Thus to the Jew, mathematics and science are not cold facts but facets of Heavenly wisdom; numbers down here are rooted in spiritual sources.
https://www.storyofmathematics.com/islamic.html

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Wayfarer
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Re: Dukkha and pure mathematics.

Post by Wayfarer »

workbalance wrote:
Sun Mar 08, 2020 10:51 pm
You just gave me a nice research project!
One that I might be interested in, so keep us posted.

By the way, you might be interested in a not-very-well-known book called The Shape of Ancient Thought, by Thomas McEvilly. He was an art historian; this book was published around 2006 or so, the culmination of a 30-year project of his (he has died since). It does a very deep dive into comparative studies between ancient Greek and Indian philosophies, which, he claims, interacted far more closely along the ancient silk routes and through the Alexandrian empire, than mainstream scholarship allows.
'Only practice with no gaining idea' ~ Suzuki Roshi

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Aemilius
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Re: Dukkha and pure mathematics.

Post by Aemilius »

There is some mathematics in several Mahayana sutras, here for example from the Lalitavistara sutra:

Alex Bellos in his book Alex's Adventures in Numberland in Chapter three, Something about Nothing, quotes from the Lalitavistara Sutra:

"Not only was the Buddha able to fathom the impossibly large, he was also proficient in the realm of the impossibly tiny, explaining how many atoms there were in the yojana, an ancient unit of length around 10km. A yojana, he said, was equivalent to: Four krosha, each of which was the length of One thousand arcs, each of which was the length of Four cubits, each of which was the length of Two spans, each of which was the length of Twelve phalanges of fingers, each of which was the length of Seven grains of barley, each of which was the length of Seven mustard seeds, each of which was the length of Seven poppy seeds, each of which was the length of
Seven particles of dust stirred up by a cow, each of which was the length of Seven specks of dust disturbed by a ram, each of which was the length of Seven specks of dust stirred up by a hare, each of which was the length of Seven specks of dust carried away by the wind, each of which was the length of Seven tiny specks of dust, each of which was the length of Seven minute specks of dust, each of which was the length of Seven particles of the first atoms. This was, in fact, a pretty good estimate. Just say that a finger is 4cm long. The Buddha’s ‘first atoms’ are, therefore, 4cm divided by seven ten times, which is 0.04m×7–10 or 0.000000- 0001416m, which is more or less the size of a carbon atom.

Not only was the Buddha able to fathom the impossibly large, he was also proficient in the realm of the impossibly tiny, explaining how many atoms there were in the yojana, an ancient unit of length around 10km. A yojana, he said, was equivalent to:

Four krosha, each of which was the length of

One thousand arcs, each of which was the length of

Four cubits, each of which was the length of

Two spans, each of which was the length of

Twelve phalanges of fingers, each of which was the length of

Seven grains of barley, each of which was the length of

Seven mustard seeds, each of which was the length of

Seven poppy seeds, each of which was the length of

Seven particles of dust stirred up by a cow, each of which was the length of

Seven specks of dust disturbed by a ram, each of which was the length of

Seven specks of dust stirred up by a hare, each of which was the length of

Seven specks of dust carried away by the wind, each of which was the length of

Seven tiny specks of dust, each of which was the length of

Seven minute specks of dust, each of which was the length of

Seven particles of the first atoms.

This was, in fact, a pretty good estimate. Just say that a finger is 4cm long. The Buddha’s ‘first atoms’ are, therefore, 4cm divided by seven ten times, which is 0.04m×7–10 or 0.0000000001416m, which is more or less the size of a carbon atom."


Re: Atoms in the Abhidharma and the Element Stupa
svaha
"All human beings are born free and equal in dignity and rights.
They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
Sarvē mānavāḥ svatantrāḥ samutpannāḥ vartantē api ca, gauravadr̥śā adhikāradr̥śā ca samānāḥ ēva vartantē. Ētē sarvē cētanā-tarka-śaktibhyāṁ susampannāḥ santi. Api ca, sarvē’pi bandhutva-bhāvanayā parasparaṁ vyavaharantu."
Universal Declaration of Human Rights, Article 1. (in english and sanskrit)

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Aemilius
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Re: Dukkha and pure mathematics.

Post by Aemilius »

In the Diamond sutra, transl. of Edward Conze, Buddha says in chapter 7b The Buddha's Superknowledge of others' thoughts:
"What do you think, Subhuti, if there were as many Ganges rivers as there are grains of sand in the great river Ganges, and if there were as many world systems as there are grains of sand in them, would those world systems be many?"

Note: One world system (trichiliocosm, trisahasralokadhatu) is a system of thousand million worlds.
Bhagavan Shakyamuni uses this mathematical device or its variation several times in the Diamond sutra.
svaha
"All human beings are born free and equal in dignity and rights.
They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
Sarvē mānavāḥ svatantrāḥ samutpannāḥ vartantē api ca, gauravadr̥śā adhikāradr̥śā ca samānāḥ ēva vartantē. Ētē sarvē cētanā-tarka-śaktibhyāṁ susampannāḥ santi. Api ca, sarvē’pi bandhutva-bhāvanayā parasparaṁ vyavaharantu."
Universal Declaration of Human Rights, Article 1. (in english and sanskrit)

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Aemilius
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Re: Dukkha and pure mathematics.

Post by Aemilius »

The Flower Ornament Scripture, Chapter 30, The Incalculable:
The Buddha said,"Ten to the tenth power times ten to the tenth power equals ten to the twentieth power;
ten to the twentieth power times ten to the twentieth power equals ten to the fortieth power;
ten to the fortieth power times ten to the fortieth power equals ten to the eightieth power;
ten to the eightieth power times ten to the eightieth power equals ten to the power of 160;
ten to the power of 160 squared equals ten to the power of 320;
and so on... it continues for three pages!!!

A nice little article about the Incalculable (Asamkheya in sanskrit) http://www.drbachinese.org/vbs/publish/ ... 62p042.pdf

In Entry into the Realm of Reality, which is part of the Flower Ornament Scripture, in the chapter of Indriyeshvara:
Indriyeshvara said, " I have been taught writing and mathematics by Mañjushri, and have been led into the door of knowledge encompassing higher knowledge of all practical arts. So I know all the various arts and crafts and sciences in the world dealiong with writing, mathematics and symbols, physiology, rhetoric, physical and mental health, cityplanning, architecture and construction, mechanics and engineering, divination, agriculture and commerce, conduct and manners, good and bad actions, good and bad principles, what makes for felicity and what fro misery,
svaha
"All human beings are born free and equal in dignity and rights.
They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
Sarvē mānavāḥ svatantrāḥ samutpannāḥ vartantē api ca, gauravadr̥śā adhikāradr̥śā ca samānāḥ ēva vartantē. Ētē sarvē cētanā-tarka-śaktibhyāṁ susampannāḥ santi. Api ca, sarvē’pi bandhutva-bhāvanayā parasparaṁ vyavaharantu."
Universal Declaration of Human Rights, Article 1. (in english and sanskrit)

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