Theravada against mathematics

[Germann]

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).

I don't follow.

Of course, you lost. Life is a finite sequence of combinations of a finite set of elements (dhammas). The properties of such sequences can be discussed in mathematical forums, which I willingly do - and mathematicians are ready to discuss sequences of combinations of elements (as opposed to discussion of specific religions).

An infinite number of possible lives (no matter if there are random events or not random events) is a countable set, with the smallest cardinality for infinite sets. Each possible life can be compared with a sufficiently long series of kshanas (moments of the past): the infinite past is enough for the realization of any possible life.

[Dan74-MkII]

Long enough for realisation of any life, but depending on the kamma, only certain lives may be realised.

Once again you do not phrase your point in the concrete terms of the grid example. This would make it clear that depending on the kammic rules governing a move from a state to a state, nibanna may be attained after finite time, infinite time or never.

Even on a finite grid (finite space of possible dhammic configurations), one can take as an example, a path from nibbana state Xn to some other state Xf (for the final life), then from Xf to Xf-1 (not including Xn) and so on until a cycle - cyclically repeating lives. Then run the time backwards, with Xn being attained at some fixed future time and infinitely long time spent in cycling, until at some point in the past the cycle is ended and the sequence of lives leading to Xn begins.

So this example illustrates that even under your assumptions (finitely many dhammas with finitely many levels, infinite past and nibbana corresponding to a special combination of dhammas) nibbana may be attained only after infinitely long time.

[chownah]

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

This is a huge assumption offered without support.
chownah

[Pseudobabble]

I wonder if Germann is just trolling.. His avatar is the Sphinx, he speaks in riddles, etc..

[Germann]

Long enough for realisation of any life, but depending on the kamma, only certain lives may be realised.

Once again you do not phrase your point in the concrete terms of the grid example. This would make it clear that depending on the kammic rules governing a move from a state to a state, nibanna may be attained after finite time, infinite time or never.

Even on a finite grid (finite space of possible dhammic configurations), one can take as an example, a path from nibbana state Xn to some other state Xf (for the final life), then from Xf to Xf-1 (not including Xn) and so on until a cycle - cyclically repeating lives. Then run the time backwards, with Xn being attained at some fixed future time and infinitely long time spent in cycling, until at some point in the past the cycle is ended and the sequence of lives leading to Xn begins.

So this example illustrates that even under your assumptions (finitely many dhammas with finitely many levels, infinite past and nibbana corresponding to a special combination of dhammas) nibbana may be attained only after infinitely long time.

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.)

NO.
http://mymathforum.com/number-theory/34 ... ences.html

[Freddie]

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.)

NO.
http://mymathforum.com/number-theory/34 ... ences.html

It isn't acceptable to present a thread where no mathematical proof is provided on some forum as proof of your propositions. Can you actually provide any rigorous mathematical proofs of any of your claims or do you just have threads from some math forum where you ask "is this claim true" and somebody says either yes or no? Step up your game!

[Germann]

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.)

NO.
http://mymathforum.com/number-theory/34 ... ences.html

It isn't acceptable to present a thread where no mathematical proof is provided on some forum as proof of your propositions. Can you actually provide any rigorous mathematical proofs of any of your claims or do you just have threads from some math forum where you ask "is this claim true" and somebody says either yes or no? Step up your game!

The text of the novel is the final sequence of a finite number of elements. The monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare.

A countable set of all possible lives (and they can be counted in the order of 1,2, 3 to infinity, without missing a single possible option) can never be greater than the set of past lives (which is also a countable set: you can count lives in the past to infinity, 1 , 2, 3 ... without missing a single one). Each element of the first set can be uniquely associated with an element of the second set. All possible lives are already lived.

[Freddie]

The text of the novel is the final sequence of a finite number of elements. The monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare.

This isn't a proof, it is a claim. Furthermore the monkey hitting keys isn't analogous to the motion of particles in a spatial continuum as already explained.

[Germann]

The text of the novel is the final sequence of a finite number of elements. The monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare.

This isn't a proof, it is a claim. Furthermore the monkey hitting keys isn't analogous to the motion of particles in a spatial continuum as already explained.

This is proof of the validity of the thesis through an example.

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.)

NO.

Otherwise, the text of Shakespeare could not have been printed for an infinite time. The sequences of a finite number of elements (letters and signs) follow each other, the set of all such sequences of length equivalent to the collection of Shakespeare’s works is infinite.

[Germann]

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? It can only if the rules prohibit such a finite sequence.

In this case, life with the achievement of Nibbana is impossible.

[Freddie]

A countable set of all possible lives (and they can be counted in the order of 1,2, 3 to infinity, without missing a single possible option) can never be greater than the set of past lives (which is also a countable set: you can count lives in the past to infinity, 1 , 2, 3 ... without missing a single one). Each element of the first set can be uniquely associated with an element of the second set. All possible lives are already lived.

You added this part after I made my last post. From my understanding , in the Abhidharma lives are not discrete entities (discrete past-lives being only a conventional reality) but rather what is actually occurring is that dharmas are continuously passing away and being reborn every instant therefore the set of possible lives is not a countable set because each possible instant cannot be mapped onto a unique real number inasmuch as the change from one dharmic moment to the next is continuous (instantaneous).

[Nicolas]

A countable set of all possible lives (and they can be counted in the order of 1,2, 3 to infinity, without missing a single possible option) can never be greater than the set of past lives (which is also a countable set: you can count lives in the past to infinity, 1 , 2, 3 ... without missing a single one). Each element of the first set can be uniquely associated with an element of the second set. All possible lives are already lived.

Let's see... If we replace "all possible lives" with "all integers" and "the set of past lives" with "the set of even numbers", we have:
"A countable set of all possible integers can never be greater than the set of even numbers. Each element of the first set can be uniquely associated with an element of the second set. All integers are even numbers."
That last part is obviously untrue.
A bijection or one-to-one correspondence just means that both sets are countable. It doesn't mean they have the same elements.
Just as the set of all integers contains elements which the set of all even numbers doesn't contain, it is the same for all possible lives and all past lives.
It doesn't matter if both sets have the same cardinality.

Let's suppose that I have a countable infinity of apples, and a countable infinity of oranges, and a countable infinity of all fruit.
It sounds like you're saying that because the set of all apples and the set of all fruit are of the same cardinality, it must mean that all fruits are apples! Not the case.

[edit: removed the words "you can" from the last paragraph, which were from another sentence construction and should have been removed from the final one.]

[Germann]

A countable set of all possible lives (and they can be counted in the order of 1,2, 3 to infinity, without missing a single possible option) can never be greater than the set of past lives (which is also a countable set: you can count lives in the past to infinity, 1 , 2, 3 ... without missing a single one). Each element of the first set can be uniquely associated with an element of the second set. All possible lives are already lived.

Let's see... If we replace "all possible lives" with "all integers" and "the set of past lives" with "the set of even numbers", we have:
"A countable set of all possible integers can never be greater than the set of even numbers. Each element of the first set can be uniquely associated with an element of the second set. All integers are even numbers."
That last part is obviously untrue.
A bijection or one-to-one correspondence just means that both sets are countable. It doesn't mean they have the same elements.
Just as the set of all integers contains elements which the set of all even numbers doesn't contain, it is the same for all possible lives and all past lives.
It doesn't matter if both sets have the same cardinality.

Let's suppose that I have a countable infinity of apples, and a countable infinity of oranges, and a countable infinity of all fruit.
It sounds like you're saying that because you can the set of all apples and the set of all fruit are of the same cardinality, it must mean that all fruits are apples! Not the case.

We get a pair of items. If there are a couple of elements, then life is lived. A pair of items is not the same item. There are two of them.

Possible life is like a guest. Past life is like a hotel room. Guest is not a hotel room. But if a room was found for each guest, then all the guests were accommodated in the hotel: all possible lives had already been lived.

Here, in this topic, it is constantly argued that there are such guests on whom there were not enough free rooms. Guests not settled in the hotel. This can only happen if there is a rule that does not allow some guests to stir in a hotel.

[Nicolas]

We get a pair of items. If there are a couple of elements, then life is lived. A pair of items is not the same item. There are two of them.

Possible life is like a guest. Past life is like a hotel room. Guest is not a hotel room. But if a room was found for each guest, then all the guests were accommodated in the hotel: all possible lives had already been lived.

Here, in this topic, it is constantly argued that there are such guests on whom there were not enough free rooms. Guests not settled in the hotel. This can only happen if there is a rule that does not allow some guests to stir in a hotel.

Actually, in this context, it would be more fitting to say that possible lives are the rooms and past lives are the guests.

Each of my guests (my past lives) has their name written inside one unique room in the hotel of possible lives.

Now, there are other rooms where none of my past lives are, with names written in each of those rooms which don't fit the name of any of my guests, simply because there are "more possible lives" than past lives, in the same sense that there are "more integers" than even numbers, even though they have the same cardinality.

Let's suppose all of the rooms that have my guests' names in them all happen to have a door number that is even.
Any odd-numbered room would not match any of my guests.

Now, I can still say "okay, I can still connect all of my guests with all of the rooms, because they have same cardinality", but this is only saying that they have same cardinality, that for each possible life I can assign one of my past lives to be paired up with it, it just means you've formed an arbitrary pair, not that the elements of the pair are the same.

[Germann]

We get a pair of items. If there are a couple of elements, then life is lived. A pair of items is not the same item. There are two of them.

Possible life is like a guest. Past life is like a hotel room. Guest is not a hotel room. But if a room was found for each guest, then all the guests were accommodated in the hotel: all possible lives had already been lived.

Here, in this topic, it is constantly argued that there are such guests on whom there were not enough free rooms. Guests not settled in the hotel. This can only happen if there is a rule that does not allow some guests to stir in a hotel.

Actually, in this context, it would be more fitting to say that possible lives are the rooms and past lives are the guests.

There will be no unoccupied room.

Now, there are other rooms where none of my past lives are, with names written in each of those rooms which don't fit the name of any of my guests, simply because there are "more possible lives" than past lives, in the same sense that there are "more integers" than even numbers, even though they have the same cardinality.

But there are no more rooms than guests.