I found many personal book about Buddhism; witnessing; life story; spiritual encounter, experiences, meditation. I never found however a book that explain and summarize the classical Buddhism : a consensus clear that none Buddhist can read to understand that philosophy better.
Science is really the Scientific Method.
The Scientific Method is:
As a Zen Buddhist, specifically Vietnamese Engaged Buddhism here is what I see.
Most all of the studies (book, dharma talks, dharma sharing, sutra) have the elements listed above. A typical dharma talk (whether oral or written into a book) discusses observations. These observations lead to "insight" or a hypothesis/predictions about the true nature of reality/the mind/etc. Every dharma talk I have ever heard in zen has always asked us to take these insights and test them. Apply them in your life and see the outcome for yourself. I am not just told theories but asked to practice them. This is the Experiments phase. Then I am always asked to examine the practice to see the fruits of my effort. This is Analysis.
So basically I find that Zen Buddhism follows the scientific method quite perfectly. Thus I would say any Zen text could be considered a scientific text by the standards of the scientific method.
Now of course you are asking for a single book that "none Buddhist can read to understand that philosophy better". As a Zen Buddhist, this is pretty all-encompassing of Zen Buddhism: The Heart of the Buddha's Teaching by Thich Nhat Hanh. I read this book with non-buddhist weekly, as well as read this book with monastics. The approach in this book follows the methods I described above and is written in a way that is very approachable regardless of your skill level in the practice.
Here is the Table of Contents of the Book so you can see what is all covered.
Part One The Four Noble Truths
Chapter One Entering the Heart of the Buddha
Chapter Two The First Dharma Talk
Chapter Three The Four Noble Truths
Chapter Four Understanding the Buddha's Teachings
Chapter FiveIs Everything Suffering?
Chapter Six Stopping, Calming, Resting, Healing
Chapter Seven Touching Our Suffering
Chapter Eight Realizing Well-Being
Part Two The Noble Eightfold Path
Chapter Nine Right View
Chapter Ten Right Thinking
Chapter Eleven Right Mindfulness
Chapter Twelve Right Speech
Chapter Thirteen Right Action
Chapter Fourteen Right Diligence
Chapter Fifteen Right Concentration
Chapter Sixteen Right Livelihood
Part Three Other Basic Buddhist Teachings
Chapter Seventeen The Two Truths
Chapter Eighteen The Three Dharma Seals
Chapter Nineteen The Three Doors of Liberation
Chapter Twenty The Three Bodies of Buddha
Chapter Twenty-One The Three Jewels
Chapter Twenty-Two The Four Immeasurable Minds
Chapter Twenty-Three The Five Aggregates
Chapter Twenty-Four The Five Powers
Chapter Twenty-Five The Six Paramitas
Chapter Twenty-Six The Seven Factors ofAwakening
Chapter Twenty-Seven The Twelve Links of Interdependent Co-Arising
Chapter Twenty-Eight Touching the Buddha Within
The question asks or literature about Buddhism which is:
- the most ancient form
This is probably "the Pali canon" (and/or the "Theravada" school of Buddhism). I say that because someone asked about the 'Buddhism which Siddhartha taught', and I tried to answer that here with an introduction to the earliest schools and extant literature.
Other questions whose answers are references to the early literature (which I therefore recommend you read as anwering your question) include:
- Why isn't there a Buddhist Bible?
- English (or other European) translations of Pali Canon
- Chronological or other sequence for beginners
A very popular classical summary is the Dhammapada (there are many translations available online).
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I don't know what you mean by a "scientific" book. In my opinion "science" just means "knowledge" and Buddhism is its own branch of science/knowledge. The clearest introduction to Buddhism might be the Buddha's, which is The Setting in Motion of the Wheel of Dharma.
You might find that Wikipedia provides quite a good summary, of classical terms like,
- Four Noble Truths
- Noble Eightfold Path
- Three poisons
- Three marks of existence
- Three Jewels
- Four immeasurables
- Five Precepts
Apparently or allegedly a lot of the early canon is intended more for monks than for laypeople. This answer summarizes a book I read recently, written by a monk for laypeople. I found it surprising because its message (i.e. "prosperity" instead of "renunciation") is unlike the message you would normally/easily/naturally get from casually reading from the Pali canon.
You tagged this question with "east asian buddhism", I'm not sure why, so perhaps you're interested in later Buddhist traditions too (the earliest Buddhism i.e. the historical Buddha was around modern-day Northern India, so the spread to Sri Lanka, Tibet, China, Vietnam, Thailand, Japan and so on happened later): see for example Mahayana.
The Mūlamadhyamakakārikā is a systematic and thorough deconstruction of how we mis-interpret reality. It is considered a classical text in Mahayana Buddhism however I don't think I would refer to it as orthodox because I'm not entirely sure of its relevancy in the Theravada tradition, and it's not a sutra. Its meaning is the heart of the Buddha's message, however it is a difficult read as an introduction. It does kind of fit the bill for what you're asking though.
I highly recommend the foundation of Buddhist thought series for introductory texts. You can find translations of the MMK on Amazon as well as the foundation of Buddhist thought series.
I recommend the book "Gombrich, Richard : What the Buddha thought". It is written from an academic point of view and employs a historical method of investigation. Probably "academic" matches your meaning of "scientific".
Of course I am biased, but I would recommend this book: "Quantum Buddhism - Mahajrya Bodhana Sutra, Teachings on Awakening to the Great Field". It is written by Maha Vajra, who is the founder of the tradition I belong to. This book helped me immensely to understand some of the problems as well as some highly interesting correlations. Not necessarily correct or incorrect; merely interesting.
And before you jump to the idea that what he's talking about has been disproved, consider that what he's trying to talk about is an experience, not a proof. That point has caused a lot of trouble because it wasn't made incredibly clear.
Other than that, there are lots of books on Quantum Buddhism, and books that allow someone with a scientific background to understand what they're reading before diving into the up-to-2500-year-old texts. These other books will give you enough of a background to really understand what you're reading. But as I said, I'm biased in this case. :-)
For example in this book, using the holographic universe concept, it offers the idea that universal wisdom could be viewed as universally-pervasive quantum datum, repeated everywhere, at every time, and at various scales. Thus, nonlocal, atemporal, and scalar in nature (three terms that many Buddhists might actually be familiar with in English). We can learn to detach from the limitations of human perceptions of time and space, perceiving the higher wisdom (which is more refined than typical intellectual information) in a way which is more direct and with greater clarity, thus perceiving the quantum world for a moment or two at a time.
But there are also examples given of the double-slit electron experiment, simplifications of the Unified Quantum Field concept, and correlations to Buddhist texts (written both for Buddhists who want to understand quanta and scientists who want to understand Buddhism).
It then leads people through the basics of Quantum Buddhism, such as meditation, fixity, and other practices that help bring about this greater clarity and heightened perception.
Though I don't have a math background per se, a couple of my friends say that the simple equations in this book are philosophically deep and really get your mind going.