Dear Francesco, the yuga-theory from ancient Hinduism in which cycles of increasing social and moral deterioration follow each other repeatedly may be of interest here, especially because it connects cosmological and metaphysical considerations with the theory of rebirth and questions about the problem of identity within the cycle of rebirths.

How the Hindu views differ from influential Christian and European reflections on eternity can (for example) be seen against the background of Kierkegaard's treatment of the topic in his "Concept of anxiety."

A rich source for the broader picture of European thoughts on the topic is the book "Measuring eternity: The search for the beginning of time" by Martin Gorst (2001).

If you are interested in time then you may well have read some Heidegger, how about Carol White's Time and Death: Heidegger's Analysis of Finitude (Intersections: Continental and Analytic Philosophy)

I'd be interested to learn if you find any substantial texts on the anthropology of infinite. Brian Butterworth's 'The Mathematical Brain' is a really enjoyable read on the history of counting and mathematics. Thomas Crump's 'The Anthropology of Numbers' makes mention of infinite here and there. I also remember reading some material on Australian aboriginal counting as an undergraduate student, but I can't recall the title, journal or author...

The text Paul is thinking of might be one of Helen Verran's investigations into the topic, especially her "Science and an African Logic" (University of Chicago Press, 2001).

Basic nonwestern notions of time and space has been analyzed by Gillermo Páramo, from the perspective of paraconsistent logic.

http://www.youtube.com/watch?v=PWmaRiyv2Ks

http://www.bdigital.unal.edu.co/24576/1/21765-74532-1-PB.pdf

Thank you very much Pradeep, Norman, Paul, Franz Rolando, Cecilia and Lorenzo for your important suggestions. I am travelling through Hinduism at the moment, following the distinction between "infinite" and "indefinite" René Guénon recommended [additional question: what do you think about Guénon?]. So, mathematical concepts are a little peripheral - but I am an estimator of Jadran Mimica and surely will read that article: a special thanks to Lorenzo for this reference. 

Infinity and zero are relative terms and mathematically inverse of each other. Therefore from my point view one does not make any sense without the other. Similarly there is no such thing as absolute zero or absolute infinity. You can say that zero is an infinitely small quantity or infinity is some very very large quantity. In Advaita Vedanta philosophy, there is a concept of formless God, which is the underlying reality of the entire universe and is called Brahm(a). But this Brahm is not described as infinite. It is described as one without a second. The word Advaita means non-dual. Advaita is a state of mind of the person who has reached perfection and acquired immediate knowledge of Brahm. In this state of mind the individuality of the mind gets dissolved in Brahm and the distinction between the observer and the observed gets lost. This is

when the perfected man is able to say "I and my father in heaven are one.' Or "Those who have seen me has seen the father." Therefore the concept of one without a second is more realistic and accurate compared to infinite.

Hi Francesco. Probably you're already familiar with Max Müller's work on 'Natural Religion' - a cornerstone in the anthropology of religion written in the late 1800's. He argues that the 'Infinite' is what 'begins where our finite knowledge seems to end' and religion came to existence when man started to sense the Infinite. He says 'religion is the language or interpretation of the Infinite': Infinite is the divine quality in nature that evolves into, or is revealed as, successive manifestations of the Supreme Being, the prime object of all religion. He shows the evolution of religion through Vedic tradition, Greek classical religion, etc arriving at Christianity. Not a recent study but it's really worth reading and gives you a great view on how Western thought and European anthropology started to research the question of Infinite. You can find more about this in the 'Gifford Lectures of 1888-92'. I'm pretty sure that many recent anthropological studies on the infinite are affected by this primeval work.

Really interesting, Susan, thank you very much

I will second Lorenzo Bottos's suggestion of Jadran Mimica's book, intimations of Infinity, as this is probably the only ethnography that has looked, in depth, at how the concepts of number are perceived in a small scale society (the Iqwaye of  New Guinea), not just as instruments for the numeration of things, but as being deeply embedded in their ideas about kinship and their cosmology.  As part of his argument regarding the Iqwaye, Mimica refers to Cantor's ideas about transfinite number and Brouwer's mystical ideas about mathematics.  However, it should be noted that Mimica's book has been heavily criticized in a review appearing in the American Ethnologist by Thomas Crump (reference provided in Bottos's Answer): "This book may well be the first anthropological monograph devoted to the use and understanding of numbers by a single population. ... allowances must be made for the shortcomings inherent in almost any pioneering work.  unfortunately ... these are so numerous as to cast serious doubt on the value of the book as a work of anthropological scholarship" (p. 608).  Nonetheless, it is worth reading through Mimica's book, keeping in mind the nature of the criticisms raised by Crump. As he points out, this is the only anthropological monograph on how numbers are conceived in a small scale society, and the fact that Mimica turns to Cantor and Brouwer as part of his argument underscores his perception that their notion of numbers and their cosmology cannot be understood without considering their notion of the infinite.

Francesco:

Please read up on the sanskrit word "Ananta". It is infinity concept from a Indian perspective.

Regards

Thank you very much, Dwight, for your precise review about Mimica's work.

That Infinite in the Hindu tradition means "beatitude", Ravendra, is what  fascinates me the most.

Yes, it exactly means "Unending". all mathematical concepts which originated in India have their origins in Spirituality, seeking the divine, the Infinite. 

Regards

Dear Amy,

Well said, sounds like Indian Vedanta to me. That said, will such a explanation hold good with empirical science?

Regards

Dear Amy,

Since the advent of euro-centric western empirical science, such notions such as yours have been pooh-poohed because they were not provable, the proof not replicable under all conditions, at all times. All the eastern religions which were unity and personal experience transformation based were dismissed  as 'faiths and beliefs', even when they were scientific, but not objective and material based.

Even now, views such as yours will not be accepted in major scientific journals, which demand objective proofs. Are we seeing a major shift from objective based empirical science to esoteric unity based transformational experience based science, as material science has reached the end of its tether?

Regards

Thank you, Larry, that's the point: according to the Kabbalah, other questions can be found “in the pocket” of a question. In which extent the scientific idea of a Big Bang has been influenced by the Western creationism - as a general scheme of thought - and thus is a "cultural oriented" idea? In which extent the Big Bang prefigure a Big Crunch and thus a "beginning" and an "end" of History? Maybe these questions explain why the idea of Infinite is clearly developed in “non-Western” metaphysics, while is vague - and confuse with the indefinite - in “Western” modern rationality. (Of course “Western and non-Western” overlap, as in the Jewish Kabbalah itself…).

This way, I think, the epistemology of Infinite meets the anthropological discourse.

Regarding the limits of Science, I would quote Gregory Bateson, when he reminded that a “not-written letter” is not a fact at all (and make no sense to be replicated), but nevertheless can make a Big Mess.

The “chemistry sets” drive me to another intriguing shift: “the same new one” is, all the times, alchemically, a Third…

Hi, Maybe you can find an approach to infinite´s concept from a religious point of view in the book of Mircea Eliade "The myth of eternal return".

I hope help you a bit.

http://www.amazon.com/The-Myth-Eternal-Return-Bollingen/dp/0691123500/ref=pd_sim_b_35?ie=UTF8&refRID=1JC6W7QQE5VTCH791D4H

I have been working hard on the concept of Infinite different from present traditional working train of thought for years, maybe we can share ideas.

Starting from Infinitude Related Paradoxes, I studied the concept of Infinitude, infinitude related number forms and limit theory from different points of view. In 4 papers I uploaded to RG, my “new infinity theory system” is introduced.

I hope what we are discussing here will offer constructive ideas and arouse a group of people thinking and marching in a fruitful direction….

Can we use the “brackets-placing rule"(１＋1/2 ＋（1/3＋1/4 ）＋（1/5＋1/6＋1/7＋1/8）＋．．．) applied in the divergent proof of Harmonious Series (1＋1/2 ＋1/3＋1/4＋．．．＋1/n ＋．．．) to produce infinite numbers bigger than 1/2 or 1 or 100 or 100000 or 10000000000…?

Try looking at Jacques Lacanʻs notion of the Real and cross it with the Polynesian concept of mana - then you would have an idea of what a cross-cultural notion of the infinite is

Answer was to Francesco Spagna question relating to "Metaphysical conceptions of the Infinite in particular cultures or in a cross-cultural perspective; interdisciplinary studies on this theme, between Philosophy and Cultural Anthropology" sorry canʻt do math

My personal interest relates to the literary and, in particular, the poetic interpretation of the concept of infinity and how it is used to explore the extent/limitations of the human condition. A notable author that has explored this area in a unique way is Brian Aldiss.

I offer my own little exploration. Infinity isn't the main theme of poem but 'time' and the concept of infinity are used to dramatic effect in the poem. 

Data BURGLAR - Poem

Thank you Christopher for your answer and your poem that reminds me William Blake

HI Francesco, would love to know if you found any.. since I am writing a book about religion and mathematics..