Synthetic a priori, mathematics, and not-self

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Re: Synthetic a priori, mathematics, and not-self

Postby Pannapetar » Wed May 19, 2010 4:01 am

I'll address your points, but without quoting in order to make this easier to read.

Gabe, you are right about constructivism versus objectivism. These are the two opposing views that one might take. It is often the case that a scientist argues in favour of one of these views. Constructivism is also often juxtaposed with positivism. I remember having read the transcript of a conversation between Einstein and Heisenberg in which Heisenberg takes the positivist position and Einstein the constructivist point of view. Einstein argued that it is the theory that prescribes what physicists can observe, because experiments are always framed in terms of theory. This is a bit unusual for Einstein, because he was actually a realist at heart, and he never believed that Heisenberg's uncertainty principle was the last word on the matter. Anyway, I agree with you that it is wise to avoid the extremes of both positions.

JC, you are right, circles do not exist in nature, at least no perfect circles do. They are an abstraction. However, there are many things in nature that partake in "circleness", namely circle-like or spherical objects. Circles are different from mountains in that we can describe their essence by relatively simple formulas. This would be more difficult with mountains since mountains are large three-dimensional objects with a complex fractal topology. While all of these are of course "mental constructs", they do form a special class of statements, namely a non-arbitray, objective class of statements that can be validated by purely logical (non-empirical) means.

Kenshou, arguing for atman in mathematical formulas does not (at least no directly) end suffering. However, math and science are certainly helpful in the endeavour of ending ignorance and delusion. For example, thanks to Maxwell we can explain magnetism and electricity with hard cold formulas. We don't believe anymore that magnetism is a magical force, or that lightning is caused by the gods. The nature of many physical, statistical, or even social phenomena can be explained in terms of mathematics. In as far as mathematics leads to a better understanding of the nature of phenomena, it is instrumental in dispelling ignorance.

Dan, I agree with everything you say, especially about the platonic theory of forms. It might very well be that mathematics does not directly express atman, but that it instead expresses some sort of surrogate atman dependent on concepts. In other words, just as the Buddhadhamma points to nibbana using concepts, but cannot directly communicate the quality of nibbana, the dhamma of mathematics points to inherent existence, but cannot directly communicate its quality and relies on the use of symbols, operations, and algorithms instead.

Sobeh, is it possible that you are taking this a bit too far? I had not intention of bringing in the five aggregates and the sixth senses, as this would further complicate the discussion of an already complicated matter. Did I detect some aversion to metaphysics? For me, the point of getting acquainted with metaphysics is to learn the flaws of various metaphysical positions. Only then is it possible to avoid their trappings. Buddhism is, by the way, certainly not free of metaphysics. Although Buddhism wisely avoids extremes, I see it -especially in its Theravada form- leaning towards phenomenalism, which might explain why an objectivist understanding of science and math doesn't harmonise with it.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Postby Kenshou » Wed May 19, 2010 4:41 am

Kenshou, arguing for atman in mathematical formulas does not (at least no directly) end suffering. However, math and science are certainly helpful in the endeavour of ending ignorance and delusion.


I'm aware of the utility of math and science in those aspects. But, is it necessary for dispelling ignorance and delusion as they pertain to the four noble truths? I think the answer is no.

I think that the answer to the cessation of suffering and the answer to the true nature of reality, if there is one, are different subjects entirely. As you say, Buddhism leans toward phenomenalism, since it is experience that is relevant to dealing with the mind and suffering. For the purpose of ending dukkha, taking phenomena as not-self is a useful tool.

But as for the atman or anatman of "objective" reality? My impression is that Buddhism isn't concerned with it. The parable of the man shot by a poisoned arrow, for example. Therefore I think that trying to argue against the Buddhist doctrine of anatta using math, science and metaphysics is like trying to drive a screw with a hammer. Different things, different purposes, there's only conflict when you try to mash them together in ways they weren't meant to be.
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Re: Synthetic a priori, mathematics, and not-self

Postby Prasadachitta » Wed May 19, 2010 5:10 am

Pannapetar wrote: For me, the point of getting acquainted with metaphysics is to learn the flaws of various metaphysical positions. Only then is it possible to avoid their trappings.


Hi Thomas,

Im not so sure about this. I think that this idea might keep the wheels spinning right through till death without the benefit of much trappings avoidance.

The only valuable reason for philosophical inquiry is to pave the way for practice. If we use ideas to justify and or validate the cultivation and perpetuation of pain and suffering rather than do what we can to reduce it, then a bit of philosophical inquiry into those ideas is appropriate. Otherwise your just spinning your wheels. For those of us who have accepted a path of practice and have faith in it, what use is there in ruminating about ideas which have no bearing on that practice?

I must admit I do enjoy a bit of peeling out from time to time.


Metta

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Re: Synthetic a priori, mathematics, and not-self

Postby alan » Wed May 19, 2010 5:50 am

OK, I'm going to propose a boycott. No more responding to this nonsense.
Sobeh, good work. You have destroyed whatever remained of the argument. There isn't much left to say. So let's not say it. Agreed?
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Re: Synthetic a priori, mathematics, and not-self

Postby Dan74 » Wed May 19, 2010 5:58 am

alan wrote:OK, I'm going to propose a boycott. No more responding to this nonsense.
Sobeh, good work. You have destroyed whatever remained of the argument. There isn't much left to say. So let's not say it. Agreed?


Anyone is free to participate or not. Calling someone's contributions "nonsense" and calling for "a boycott" is poor online manners, I think. If you disagree, you are free to ignore or to make your point respectfully. These are the rules of engagement as I understand them.
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Re: Synthetic a priori, mathematics, and not-self

Postby alan » Wed May 19, 2010 6:16 am

The argument has been refuted so many times and in so many ways by so many people that I think it is fair at this juncture to say it is nonsense. That's not calling names. Calling for a boycott is just another way to say this thread has become useless, so please stop responding. I do that because it seems to me that anything we say will just give more fodder to needless proliferation. Nothing disrespectful about that.
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Re: Synthetic a priori, mathematics, and not-self

Postby Pannapetar » Wed May 19, 2010 6:55 am

Kenshou wrote:I'm aware of the utility of math and science in those aspects. But, is it necessary for dispelling ignorance and delusion as they pertain to the four noble truths?


Of course not, as you correctly stated. However, math and science dispel ignorance and delusion in other areas of life. There are many such areas about which Buddhism has nothing (or at least not very much) to say, for example medicine, science, ecology, and so on. Yet these are all things that affect the lifes of everyone directly. Some of us work in these fields and come into contact with them on a daily basis. Hence, it is more than justified to see how they fit in to the Buddhist world view.

gabrielbranbury wrote:For those of us who have accepted a path of practice and have faith in it, what use is there in ruminating about ideas which have no bearing on that practice?


Well, for one it helps to avoid "Buddhist tunnel view". You see, a regular problem for people becoming immersed into Buddhism is that they are keenly aware of clinging, yet often ignore clinging to views that their particular school endorses. They often do this even without realising it. Hence, an outside perspective is often useful to generate awareness for this particular problem.

alan wrote:OK, I'm going to propose a boycott.


Hilarious! :rofl: "To post or not to post... that is the question: Whether 'tis nobler in the mind to suffer..." Since discussion boards rely on voluntary participation, the proposal seems a little out of place. I suggest that you go ahead with your boycott, Alan.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Postby tiltbillings » Wed May 19, 2010 3:08 pm

Open for business.
This being is bound to samsara, kamma is his means for going beyond.
SN I, 38.

Ar scáth a chéile a mhaireas na daoine.
People live in one another’s shelter.

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Re: Synthetic a priori, mathematics, and not-self

Postby chownah » Wed May 19, 2010 4:01 pm

Pannapetar,
Sometimes a discussion goes awry because initial concepts are misunderstood. You have postulated that there exist a thing called a "mathematical law" and you talk as if it is widely understood that such a thing exists. I have a BA degree in mathematics from a major US university and while I do admit that it was a long time ago and that I have never worked in the field of mathematics (other than teaching and for engineering and personal use) I do not remember anyone ever talking about any "laws" of mathematics and I am reasonably sure that I have never been taught about any "mathematical laws"....axioms, postulates, groups, conjectures, proofs, and a host of other official sounding entities are discussed but never as far as I can remember is there a thing called a "law"....and this is for a good reason. Mathematics teaches that any system of mathematics (and there are thousands...or even one could say an unlimited number of them) and that the way these systems function is entirely dependent on initial assumptions...or in the Buddha's words they are dependent on conditions...

So....if the awe inspiring idea of "mathematical law" is dropped then you can perhaps develop a more approachable term such as "mathematical idea" which puts it squarely in the court as an object of the sense door called "mind"....and if you want to learn about that there are alot of reference in the Theravada Scriptures and Associated Commentaries which might benefit you in understanding its relationship to other stuff....I think....

Otherwise....can you please write down here a "mathematical law" and explain it to me...and why it is called a law....and the equation which indicates that pi is the ration between the circumfrence and diameter of a circle most assuredly does not count as a "law" because it is merely an equation which could be true or false...if you think it is true then please show me a proof...but even with a proof it should not be considered a "law".
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Re: Synthetic a priori, mathematics, and not-self

Postby nathan » Wed May 19, 2010 5:14 pm

Pannapetar wrote:mountains are large three-dimensional objects with a complex fractal topology. While all of these are of course "mental constructs", they do form a special class of statements, namely a non-arbitray, objective class of statements that can be validated by purely logical (non-empirical) means.
I have no idea what this discussion is about or what purpose it serves but I have a question since I live on a mountainside. How would I go about 'objectively validating by purely logical or non-empirical means' that the terrain surrounding me has a complex fractal topology? Would I need to borrow Tilt's tinfoil hat for this exercise or are you perhaps not finished with it yet?
But whoever walking, standing, sitting, or lying down overcomes thought, delighting in the stilling of thought: he's capable, a monk like this, of touching superlative self-awakening. § 110. {Iti 4.11; Iti 115}
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Re: Synthetic a priori, mathematics, and not-self

Postby David N. Snyder » Wed May 19, 2010 5:41 pm

chownah wrote:Otherwise....can you please write down here a "mathematical law" and explain it to me...and why it is called a law....and the equation which indicates that pi is the ration between the circumfrence and diameter of a circle most assuredly does not count as a "law" because it is merely an equation which could be true or false...if you think it is true then please show me a proof...but even with a proof it should not be considered a "law".
chownah


Exactly. As I understand it, mathematics deals with numbers and concepts, basically labels (nama). They are man-made concepts, with no intrinsic qualities.

They help us better understand the conventional world, but have no intrinsic nature.
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Re: Synthetic a priori, mathematics, and not-self

Postby nathan » Wed May 19, 2010 5:45 pm

chownah wrote:Otherwise....can you please write down here a "mathematical law" and explain it to me...and why it is called a law....

I'm thinking maybe... the law of "rent is due on the last day of the month". Mathematical because you will need to remit the numerically specified amount of money on the specific numerically indicated day and a law because you will be legally evicted in due course if you do not.
But whoever walking, standing, sitting, or lying down overcomes thought, delighting in the stilling of thought: he's capable, a monk like this, of touching superlative self-awakening. § 110. {Iti 4.11; Iti 115}
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Re: Synthetic a priori, mathematics, and not-self

Postby Sobeh » Wed May 19, 2010 6:11 pm

Pannapetar wrote:Sobeh, is it possible that you are taking this a bit too far? I had not intention of bringing in the five aggregates and the sixth senses, as this would further complicate the discussion of an already complicated matter.


We're talking about atta in this thread. That means, for a Buddhist practitioner, either the five aggregates or the six sense bases. Either way, if you're trying to talk about atta without recourse to the Dhamma on the subject, it's a non-starter.

Pannapetar wrote:Did I detect some aversion to metaphysics? For me, the point of getting acquainted with metaphysics is to learn the flaws of various metaphysical positions. Only then is it possible to avoid their trappings.


You didn't detect anything, I told you simply and clearly that they are ridiculous, mere idle speculation at best, intellectual masturbation at worst. Why? Because metaphysics has nothing to do with suffering or the cessation of suffering. Which brings us to:

Pannapetar wrote:Buddhism is, by the way, certainly not free of metaphysics. Although Buddhism wisely avoids extremes, I see it -especially in its Theravada form- leaning towards phenomenalism, which might explain why an objectivist understanding of science and math doesn't harmonise with it.


"In epistemology and the philosophy of perception, phenomenalism is the view that physical objects do not exist as things in themselves but only as perceptual phenomena or sensory stimuli (e.g. redness, hardness, softness, sweetness, etc.) situated in time and in space. In particular, phenomenalism reduces talk about physical objects in the external world to talk about bundles of sense-data."

Phenomenalism is epistemology, not metaphysics. The objectivism you refer to is otherwise known as philosophical realism, which is "the view that there is a reality or ontological realm of objects and facts that exists independent of the mind."

Phenomenalism, as shown here, is a metaphysical view, and as such it is bent to the task of posing questions and answers that have nothing to do with suffering or the cessation of suffering.

Once again, your proclivity to map the Dhamma onto a western philosophical tradition is flawed and results in a straw man.
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Re: Synthetic a priori, mathematics, and not-self

Postby Pannapetar » Thu May 20, 2010 3:23 am

Chownah, I had explained the motive for using the term "mathematical law" in post no. 5. Since I have also studied mathematics, I am aware that this is not a term that a mathematician would use. What you are saying is that an axiomatic system depends on its axioms. Well, yes. That is an important consideration which non-mathematicians often forget or overlook. In particular, much depends on fundamental axiomatic systems such as (Zermelo-Fränkel) set theory, the postulates of Euclidean geometry, or the inference rules of propositional calculus, just to name a few examples. So yes, these are idea systems. It doesn't really make a difference for my argument though. Here is why: A simple equation, such as C/2r=pi expression a relation of entities or -if you want- interdependence. Among other things, it implies that we know what the symbol "2" means; the symbol "2" implies natural numbers and for natural numbers we need the Zermelo-Fränkel set theory. Thus we find interdependence on a larger scale. Does this somehow constitute a deficiency? Does mathematics depend on conditions in any other way than the Buddhadhamma depends on conditions? That is to say, does the Buddhadhamma not depend on ideas, postulates, and theorems, some of which are simple, some of which complex, many of which are interdependent, all of which are expressed in symbolic language? Is the Buddhadhamma therefore deficient?

Nathan, there is a better way than doing this by hand: you can use computer software to generate mountains using fractal geometry. This is a run-off-the-mill feature in computer games, for example, for generating terrains. See here for example: http://scienceblogs.com/goodmath/2007/0 ... ntains.php

David, mathematics does indeed deal with nama, or perhaps better with "patterns" of nama. The interesting thing about these patterns is that they provide blueprints for constructing the universe. For example, you can (as mentioned) construct mountain- and plantlike shapes from the recursive application of fractal formulae. Or you can construct pine cones, snail shells, and other natural forms from the fibonacci sequence of numbers. You can use math to describe anything from force vectors and magnetic fields to the probability distribution in an electron cloud. Hence, wouldn't it be fair to say that math describes the "intrinsic nature" of these phenomena?

Sobeh, you are trying to press the term atta/atman into a very narrow mold which is, even from a Buddhist perspective, too limited. Apart from "soul", atta also means "inherent existence" which is the meaning I have used here. Furthermore, the terms "objectivism" and "philosophical realism" are often used synonymously in philosophy. I must also reject your objection that "phenomenalism is epistemology, not metaphysics". Such a broad claim would bring any philosophy professor to tears. Phenomenalism is firmly rooted in ontology. Actually, your very citation: "phenomenalism the view that physical objects do not exist as things in themselves" is a giveaway. It has ontology written all over it. Perhaps it would be wise to base your argumentation not entirely on Wikipedia verbatim snippets. Since your argument is based on questioning terminology, and since you haven't established a firm grasp of the same, I am afraid I have to reject your critique.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Postby retrofuturist » Thu May 20, 2010 3:51 am

Greetings,

Those who mistake the unessential to be essential
and the essential to be unessential,
dwelling in wrong thoughts,
never arrive at the essential.

Those who know the essential to be essential
and the unessential to be unessential,
dwelling in right thoughts,
do arrive at the essential.


The Buddha (Dhp. 11-12)
http://www.accesstoinsight.org/tipitaka ... .budd.html

:buddha2:

Metta,
Retro. :)
If you have asked me of the origination of unease, then I shall explain it to you in accordance with my understanding:
Whatever various forms of unease there are in the world, They originate founded in encumbering accumulation. (Pārāyanavagga)


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One who is such, calmed and ever mindful, He has no sorrows! -- Udana IV, 7


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Re: Synthetic a priori, mathematics, and not-self

Postby nathan » Thu May 20, 2010 3:51 am

Pannapetar wrote:Nathan, there is a better way than doing this by hand: you can use computer software to generate mountains using fractal geometry. This is a run-off-the-mill feature in computer games, for example, for generating terrains. See here for example: http://scienceblogs.com/goodmath/2007/0 ... ntains.php
Cheers, Thomas
No dude, I don't need a computer at all, I live on a real mountain. You suggested that in shapes in nature, specifically
mountains are large three-dimensional objects with a complex fractal topology
As I see nothing about the surrounding terrain to suggest a fractal geometry on any scale I asked for you to explain how a real mountain could possibly be correctly described in any way by employing fractal geometry.

This is why I will now go on to suggest that computer models, while they may frequently appear to indicate various realistic patterns are actually frequently suggesting false and illusory projections. Which is why I think that twice now it has been clearly shown that fractal geometry has no real relationship of any kind to any actual mountain in the natural world. I think this demonstrates however, an accurate example of many of your presentations in that they have many of the appearances of communicating something of great importance when in fact they are completely empty of actual useful significance. With the notable exception of considerable potential entertainment value, of course.
But whoever walking, standing, sitting, or lying down overcomes thought, delighting in the stilling of thought: he's capable, a monk like this, of touching superlative self-awakening. § 110. {Iti 4.11; Iti 115}
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Re: Synthetic a priori, mathematics, and not-self

Postby Ben » Thu May 20, 2010 4:13 am

nathan wrote:This is why I will now go on to suggest that computer models, while they may frequently appear to indicate various realistic patterns are actually frequently suggesting false and illusory projections.

I couldn't agree more, Nathan. Years ago I was managing vast project data libraries of an environmental engineering company and using a GIS system to map contaminated groundwater - amongst other things. I could produce visually impressive graphical representations of contamination plumes but the accuracy of the krigging algorythm was largely dependent on the number and placement of data points. It was very easy to believe that what you were looking at was the truth rather than, what was at times, an elegant speculation.
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Re: Synthetic a priori, mathematics, and not-self

Postby Pannapetar » Thu May 20, 2010 4:23 am

nathan wrote:As I see nothing about the surrounding terrain to suggest a fractal geometry on any scale I asked for you to explain how a real mountain could possibly be correctly described in any way by employing fractal geometry.


Well, maybe you can send me a picture of your mountain and then we can discucss whether it exhibits fractal geometry or not? Would that be acceptable? In the meantime, consider this example: http://wiki.tcl.tk/4560 written in tcl/tk. It shows an algorithm for constructing mountains and a visual example of the result. As you can see, the algorithm is already fairly complex while the resulting mountain is slightly cartoonish (though clearly recognisable). For more realism, more complex algorithms are required.

nathan wrote:Which is why I think that twice now it has been clearly shown that fractal geometry has no real relationship of any kind to any actual mountain in the natural world.


Why would you say that? Because the processes that shape actual real-world mountains, such as tectonics, mechanics, and erosion aren't there in the computer model? Well, in a sense they are. They are expressed by the variables, constants, and control structure nuances of the algorithm. Abstractions... that's what math is all about.

Ben wrote: I could produce visually impressive graphical representations of contamination plumes but the accuracy of the krigging algorythm was largely dependent on the number and placement of data points.


Accuracy is always dependent on initial data points and often on computational complexity, especially for nonlinear dynamic systems. What can we conclude? That you can lie with data? Sure. You can lie even with a simple bar graph. Misrepresentation is always possible. I don't see that this has any bearing on the question whether mathematics can model actual phenomena.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Postby Pannapetar » Thu May 20, 2010 4:42 am

retrofuturist wrote:Those who mistake the unessential to be essential...


Retro, your skill at quoting appropriate sutta is certainly unquestioned, but it comes across slightly condescending.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Postby retrofuturist » Thu May 20, 2010 4:50 am

Greetings Pannapetar,

Pannapetar wrote:
retrofuturist wrote:Those who mistake the unessential to be essential...

Retro, your skill at quoting appropriate sutta is certainly unquestioned, but it comes across slightly condescending.

It's not intended to be condescending... it's intended to give you the opportunity of seeing how the Buddha might guide you on such matters if he were here today.

It is for the individual to discern according to their own reason whether my selection of Buddhavacana is relevant to their situation, and in turn, if they wish to adopt it in their practice. All I do is join the dots and let people decide for themselves. If others did the same for me, I would be delighted.

Metta,
Retro. :)
If you have asked me of the origination of unease, then I shall explain it to you in accordance with my understanding:
Whatever various forms of unease there are in the world, They originate founded in encumbering accumulation. (Pārāyanavagga)


Exalted in mind, just open and clearly aware, the recluse trained in the ways of the sages:
One who is such, calmed and ever mindful, He has no sorrows! -- Udana IV, 7


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