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### But it is a countable set.

Posted: **Tue Apr 16, 2019 3:22 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:19 pm

Germann wrote: ↑Tue Apr 16, 2019 2:29 pm

It is absurd to believe that a deterministic algorithm (if there are no random events, a deterministic algorithm is obtained) in an infinite number of steps will not give a deterministic step - the final sequence of dhammas leading to the manifestation of Nibbana.

This is not a proof. Why should it give this sequence?

One of the steps of the deterministic algorithm may be missing in an infinite set of its steps?

For this, the cardinality of the infinite set of all steps of the deterministic algorithm must be greater than the cardinality of the countable set. But it is a countable set.

(For simplicity, I took one final step before the manifestation of Nibbana.)

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 3:34 pm**

by **Dan74-MkII**

Germann wrote: ↑Tue Apr 16, 2019 3:22 pm

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:19 pm

Germann wrote: ↑Tue Apr 16, 2019 2:29 pm

It is absurd to believe that a deterministic algorithm (if there are no random events, a deterministic algorithm is obtained) in an infinite number of steps will not give a deterministic step - the final sequence of dhammas leading to the manifestation of Nibbana.

This is not a proof. Why should it give this sequence?

One of the steps of the deterministic algorithm may be missing in an infinite set of its steps?

For this, the cardinality of the infinite set of all steps of the deterministic algorithm must be greater than the cardinality of the countable set. But it is a countable set.

Why should it trace out any particular sequence of steps?

This has nothing to do with countability. The set of all infinite paths of this algorithm may be finite or infinite and still not contain a given sequence. Why should it?

So we take every sentient being today as the starting configuration of your algorithm. You run the time backwards and suppose that it goes on for ever into the past. You get a finite set of paths - one for each sentient being alive today, each of infinite length (infinitely many moments each containing a finite combination of dhammas, based on your assumptions). Now why should each one of them, or even one of them contain the magic sequence leading to nibbana??

### The infinite set of all steps of algorithm still not contain one of the steps of this algorithm ???

Posted: **Tue Apr 16, 2019 3:40 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:34 pm

Germann wrote: ↑Tue Apr 16, 2019 3:22 pm

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:19 pm

This is not a proof. Why should it give this sequence?

One of the steps of the deterministic algorithm may be missing in an infinite set of its steps?

For this, the cardinality of the infinite set of all steps of the deterministic algorithm must be greater than the cardinality of the countable set. But it is a countable set.

Why should it trace out any particular sequence of steps?

This has nothing to do with countability. The set of all infinite paths of this algorithm may be finite or infinite and still not contain a given sequence. Why should it?

So we take every sentient being today as the starting configuration of your algorithm. You run the time backwards and suppose that it goes on for ever into the past. You get a finite set of paths - one for each sentient being alive today, each of infinite length (infinitely many moments each containing a finite combination of dhammas, based on your assumptions). Now why should each one of them, or even one of them contain the magic sequence leading to nibbana??

The infinite set of

**all** steps of algorithm still not contain

**one of** the steps of this algorithm ???

### Re: The infinite set of all steps of of algorithm still not contain one of the steps of this algorithm???

Posted: **Tue Apr 16, 2019 3:47 pm**

by **Dan74-MkII**

Germann wrote: ↑Tue Apr 16, 2019 3:40 pm

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:34 pm

Germann wrote: ↑Tue Apr 16, 2019 3:22 pm

One of the steps of the deterministic algorithm may be missing in an infinite set of its steps?

For this, the cardinality of the infinite set of all steps of the deterministic algorithm must be greater than the cardinality of the countable set. But it is a countable set.

Why should it trace out any particular sequence of steps?

This has nothing to do with countability. The set of all infinite paths of this algorithm may be finite or infinite and still not contain a given sequence. Why should it?

So we take every sentient being today as the starting configuration of your algorithm. You run the time backwards and suppose that it goes on for ever into the past. You get a finite set of paths - one for each sentient being alive today, each of infinite length (infinitely many moments each containing a finite combination of dhammas, based on your assumptions). Now why should each one of them, or even one of them contain the magic sequence leading to nibbana??

The infinite set of

all steps of of algorithm still not contain

one of the steps of this algorithm???

Firstly, not one step but a sequence of steps. Secondly, yes, even a step may not be contained. Suppose there is a diamond hidden in a rock since eternity. Why would it be guaranteed that anyone would find it? Maybe no one even got close to it.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 3:56 pm**

by **Dan74-MkII**

Even better - imagine the following:

1. In a particularly simple world, every that there is, is described by one's position on a 3-dimensional grid. So this moment Mr X is described as (29764, -64529, 308524893). This describes all the dhammas that make up Mr X right now. In the next moment, Mr X moves no more than one step from his current position in a direction described by certain rules (kamma algorithm).

And in this world, Nibbana is attained by arriving at a particular secret location.

Now according to you, if we take the current inhabitants of this grid world and run their kamma algorithm backwards in time, they will all of necessity come to the secret location of Nibanna. This is patently not true. For instance the kamma algorithm may specify that one never departs more than 10 steps from a certain position, so that each inhabitant's dhammas will stay confined within a bound and if they all start further than this bound from Nibanna, they can never reach it.

### Re: The infinite set of all steps of of algorithm still not contain one of the steps of this algorithm???

Posted: **Tue Apr 16, 2019 4:33 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:47 pm

Germann wrote: ↑Tue Apr 16, 2019 3:40 pm

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:34 pm

Why should it trace out any particular sequence of steps?

This has nothing to do with countability. The set of all infinite paths of this algorithm may be finite or infinite and still not contain a given sequence. Why should it?

So we take every sentient being today as the starting configuration of your algorithm. You run the time backwards and suppose that it goes on for ever into the past. You get a finite set of paths - one for each sentient being alive today, each of infinite length (infinitely many moments each containing a finite combination of dhammas, based on your assumptions). Now why should each one of them, or even one of them contain the magic sequence leading to nibbana??

The infinite set of

all steps of of algorithm still not contain

one of the steps of this algorithm???

Firstly, not one step but a sequence of steps. Secondly, yes, even a step may not be contained. Suppose there is a diamond hidden in a rock since eternity. Why would it be guaranteed that anyone would find it? Maybe no one even got close to it.

Each step is deterministic. Each step is necessarily implemented in an infinite sequence. In order to have at least one step that is not realized, it is necessary that the infinite set of

all possible steps have cardinality, which exceeds the cardinality of the infinite set of steps already implemented. But the infinite set of

all possible steps is a countable set. That isn't possible.

If for an infinite number of steps of a deterministic algorithm a step is not implemented, then this step is not deterministic, it is an impossible event, it is an impossible step for this algorithm.

The manifestation of Nibbana is considered possible. If each step is deterministic, then the step of the algorithm that leads to the manifestation of Nibbana is predetermined. It is necessarily implemented in an infinite set of steps of a deterministic algorithm.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 4:48 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:56 pm

Now according to you, if we take the current inhabitants of this grid world and run their kamma algorithm backwards in time, they will all of necessity come to the secret location of Nibanna. This is patently not true. For instance the kamma algorithm may specify that one never departs more than 10 steps from a certain position, so that each inhabitant's dhammas will stay confined within a bound and if they all start further than this bound from Nibanna, they can never reach it.

An infinite number of events have already happened, an infinite number of steps have already been taken. All predetermined, deterministic events have already occurred. If events continue to occur, Nibbana cannot be found either in the past or in the future. It is unattainable, never manifests. Just repeated cycles of events that exclude the possibility of a chain break.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 4:59 pm**

by **Germann**

It does not matter whether sequences of combinations of a finite number of elements (possible lives) are randomly formed, totally deterministic formed, or a combination of random and deterministic events. Any possible sequence of combinations of a finite number of elements is included in an infinite countable set. If each possible sequence can be uniquely compared with a period of the past sufficient for its realization (and this can be done because the past is infinite, and the countable set has the smallest cardinality for infinite sets), then any possible sequence of combinations of a finite number of elements will be realized in the past.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 5:09 pm**

by **Dan74-MkII**

Firstly, if there are finitely many dhammas with finitely many levels, then you cannot have infinitely many events or dhamma combinations. So there goes your very first statement.

Secondly, which events occur depends on the kamma.

Please think and respond to my example.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 5:18 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 5:09 pm

Firstly, if there are finitely many dhammas with finitely many levels, then you cannot have infinitely many events or dhamma combinations. So there goes your very first statement.

Secondly, which events occur depends on the kamma.

Please think and respond to my example.

You have already given an example of an infinite number of combinations of a finite number of elements yourself — the set of all possible records of a natural number. Of the ten elements (characters from 0 to 9) an infinite countable set of records of all natural numbers is formed.

If we assume that the limit of the life of the gods of the sphere of light is not limited and can be as long as desired (as the length of the record of a natural number), it is possible that an arbitrarily long sequence of combinations of a finite number of elements is an as long as possible but finite life.

Your example is based on the fact that events continue to occur right now. In this case, Nibbana cannot be found in the past, there will be only repeated cycles in the past - just like in the future.

Dan74-MkII wrote: ↑Tue Apr 16, 2019 3:56 pm

For instance the kamma algorithm may specify that one never departs more than 10 steps from a certain position, so that each inhabitant's dhammas will stay confined within a bound and if they all start further than this bound from Nibanna, they can never reach it.

Nibbana is unattainable in your example.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 5:34 pm**

by **Dan74-MkII**

You spoke of events, not the unbounded combination of events. The former, which I took to mean a moment's configuration, make a finite set.

Yes, events keep happening, just as they are.

In my example, the kamma rule does indeed make Nibbana unattainable. But a different rule may make it attainable, but not attained in the infinite past. Why not? Do you want to say this is impossible? To have a rule that run backwards never reaches a certain point, but run forwards does? Seems to me that it should be possible.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 5:38 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 5:34 pm

You spoke of events, not the unbounded combination of events. The former, which I took to mean a moment's configuration, make a finite set.

Yes, events keep happening, just as they are.

In my example, the kamma rule does indeed make Nibbana unattainable. But a different rule may make it attainable, but not attained in the infinite past. Why not? Do you want to say this is impossible? To have a rule that run backwards never reaches a certain point, but run forwards does? Seems to me that it should be possible.

How do you imagine it mathematically if an infinite set of all possible lives is a

countable set? Each possible life can be uniquely compared with the period of the past, sufficient for its realization. The past is enough for all possible lives, and the set of past lives is infinite. All the infinite set of possible lives fit in the infinite past.

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 5:46 pm**

by **Dan74-MkII**

I am not sure why you talk about "all possible lives". We have a finite number of sentient beings. They have their unique pasts. Think of the grid example, can you phrase your question in its terms, so that it is more concrete and understandable?

### Life is a finite sequence of combinations of a finite set of elements (dhammas).

Posted: **Tue Apr 16, 2019 5:50 pm**

by **Germann**

Dan74-MkII wrote: ↑Tue Apr 16, 2019 5:46 pm

I am not sure why you talk about "all possible lives". We have a finite number of sentient beings. They have their unique pasts. Think of the grid example, can you phrase your question in its terms, so that it is more concrete and understandable?

If you do not deny the limit on longevity for the gods of the sphere of light (not the fact that their lifespan can be arbitrarily long), then the set of all possible lives is a finite set, similar to the Shannon number (when the length of a game of chess is limited to 40 moves). A finite set of possible lives with an infinite set of past lives also means that all possible lives have already been lived ... But an infinite set of possible lives will be lived, because their set is

countable.

http://mymathforum.com/number-theory/34 ... ments.html
Life is a finite sequence of combinations of a finite set of elements (dhammas).

### Re: Theravada against mathematics

Posted: **Tue Apr 16, 2019 5:57 pm**

by **Pseudobabble**

Germann wrote: ↑Tue Apr 16, 2019 2:38 pm

Pseudobabble wrote: ↑Tue Apr 16, 2019 2:30 pm

Germann, this 40-odd page thread is based on your presupposition that Theravada can be reduced to Abhidhamma. You're wrong.

Theravada is called a school. What is a school? This is the tradition of comments. If we call Theravada a set of books, then the Chinese Mahayana is exactly the same Theravada, since there are Agamas.

How was Suttas interpreted at Theravada School? Only in the way it was taken in the school Abhidhamma. (Except for boran kammatthana maybe.)

The very thing that the school Abhidhamma says was mastered in meditative practice until it was interrupted after the 14th century. (Except boran kammatthana.)

None of that means that Theravada is

**reducible** to Abhidhamma. In any case, who said Abhidhamma is correct? Or that Theravada has an exclusive claim on truth? I certainly don't believe that, because if there is a truth, it stands to reason that it can be observed in many places, more or less clearly.

Earlier you 'refuted' Theravada on the basis that the Abhidhamma is mathematically incoherent. So what if it is? Do you think that the Dhamma stands or falls on the scholastic expositions of some ancient monks? Or the mathematical ramblings of some lunatic on an internet forum?

I believe in what works. If it was the case that standing on your head and singing the national anthem reduced suffering, that's what I'd be doing twice a day. But that doesn't work. The meditations work. Right View works. The Path works. My suffering is reduced because I follow the instructions. Your mathematical gymnastics are about as relevant to the effectiveness of the practice as the motions of the fly outside my window.