Are you really going to argue that the probability of single events A, B, C can be analyzed - but the probability of a chain of A-B-C events, rigidly causally related to each other, cannot be analyzed? All deterministic processes, if they are possible, in the same way must occur beyond the infinity of the past, as individual random events. The fact that dhammas replace each other naturally, does not change anything: if the process is possible, then for the infinity of the past the process would have happened.Dan74-MkII wrote: ↑Mon Mar 11, 2019 2:17 pm The case falls simply because it cannot be shown that all possible configurations will occur since the dhammas don't happen randomly but are causally related.

## Theravada against mathematics

### Re: Theravada against mathematics

### Re: Theravada against mathematics

Implicitly, you enter freedom of choice. But there is no freedom of choice — there is no subject of free choice, no satta. Events just happen. Therefore, any game — any sequence of dhammas in one life — will happen beyond the infinity of the past, if it is possible. All games will be played mechanically if these games are possible.Dan74-MkII wrote: ↑Mon Mar 11, 2019 2:17 pm

Chess has been offered as an analogy. Imagine infinitely many players playing on infinitely many boards. Will every configuration happen? No, of course not. Some are simply too ridiculous and chess player would not make moves leading to them.

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### Re: Theravada against mathematics

I won't enter into any more discussions with you, Germann, because you invoke mathematics which demands precision, but when questioned, resort to wishy-washy statements.

I will just reply that the analysis of deterministic events insofar as probabilities may be assigned, requires the superimposition of a sigma algebra in order to preclude the entanglement due to dependent phenomena and decompose the space into disjoint chains. But due to the impossibility of such superimposition, the Banach space corresponding to all possible events of the past may have cardinality Aleph-0 and yet not exhaust the entire Omega.

Hope this cleared it up for everyone.

I will just reply that the analysis of deterministic events insofar as probabilities may be assigned, requires the superimposition of a sigma algebra in order to preclude the entanglement due to dependent phenomena and decompose the space into disjoint chains. But due to the impossibility of such superimposition, the Banach space corresponding to all possible events of the past may have cardinality Aleph-0 and yet not exhaust the entire Omega.

Hope this cleared it up for everyone.

### Re: Theravada against mathematics

Here you implicitly imply that some of the games are impossible. But if certain sequences of dhammas are impossible in one life, they are not among the possible games. All possible games - since they are possible, their probability is greater than zero - would necessarily have been played for the infinity of the past. The probability of any possible game for an infinite period of time = 1.Dan74-MkII wrote: ↑Mon Mar 11, 2019 2:17 pm Some may be too clever and no human chess player is capable of such levels of play.

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### Re: Theravada against mathematics

Look how many time you've repeated yourself in this thread alone. I think the probability that you break out of a cycle of ignorance at least in regards to mathematics in this lifetime is close to 0.Germann wrote: ↑Mon Mar 11, 2019 4:52 pmHere you implicitly imply that some of the games are impossible. But if certain sequences of dhammas are impossible in one life, they are not among the possible games. All possible games - since they are possible, their probability is greater than zero - would necessarily have been played for the infinity of the past. The probability of any possible game for an infinite period of time = 1.Dan74-MkII wrote: ↑Mon Mar 11, 2019 2:17 pm Some may be too clever and no human chess player is capable of such levels of play.

### Re: Theravada against mathematics

may be assignedDan74-MkII wrote: ↑Mon Mar 11, 2019 4:49 pm analysis of deterministic events insofar as probabilities may be assigned

### Re: Theravada against mathematics

In this case, probabilities may be assigned too.Dan74-MkII wrote: ↑Mon Mar 11, 2019 2:17 pm The case falls simply because it cannot be shown that all possible configurations will occur since the dhammas don't happen randomly but are causally related.

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### Re: Theravada against mathematics

You are just repeating yourself, without refuting any points. This is argumentum ad nauseam, attempting to get the last word and therefore, state that you have "won" the debate. Having the last word, as I expect you will, does not necessarily mean you had the best argument.Germann wrote: ↑Mon Mar 11, 2019 5:41 amThere is no contradiction in the fact that we have not yet met with extraterrestrial civilizations. The observation period is not infinite. The probability of their existence is less than 1 (there is a non-zero probability that humanity is lonely in the Universe). The probability of contact is less than 1 (there is a non-zero probability that, for some reason, the contact may not take place).DNS wrote: ↑Sun Mar 10, 2019 9:36 pmExactly, which just confirms my point. World systems (solar systems with planets) are vastly far apart, thousands of light years apart. As beings perish on one planet from a planet extinction activity, it is impossible for all of them to have attained nibbana in one instance, one moment, at the same time. According to Buddhist cosmology, they are reborn in another world system, thus samsara continues. Planets, solar systems arise, perish, re-evolve, the cycle continues ad infinitum. You have confirmed my point.

As for infinity, the situation is different. In the infinite past, all possible events should have happened. Since the past for each flow of dhammas is infinite, has no beginning (non-permanent dhammas do not arise for no reason, and the first dhammas in the flow would arise for no reason) - The path from beginning to end should have been passed in the past.

Others and myself have already shown that the Buddha never said the universe is finite or infinite. The teachings actually say no first beginning is discernible. And my post above explains how not all 'beings' attain nibbana when their planet goes extinct, even if there were some kind of infinite type of time. And nibbana can only be attained by humans or devas or other such intelligent species. And no planet could exist with just humans (or other intelligent species). Those other species don't make it to nibbana/awakening. Therefore, samsara continues . . . .

Check and mate.

just kidding, i know you're not finished.

### Re: Theravada against mathematics

Your premise has no basis, hence your wrong conclusion. Basically you're saying that there's only a finite number of sentient beings in the universe. But you really don't know that. So before even proceed with any further claim, you're gonna have to prove that statement first. Furthermore, you continuously fail to prove your claim that the negative infinity point in the past up to this moment as we speak is the only "infinity" and there's utterly nothing beyond that. Obviously that's not true, for there're still infinite infinite infinite future ahead after the present moment. Matter of fact, you've just distorted the concept of infinity by putting a cutoff point at the present moment. So if all sentient beings in existence have to attain Nibbana as of the current moment without exception, then the time length for them to achieve this is no longer infinite. It's finite! And if it's finite, your whole monkey theorem no longer applies.Germann wrote:The number of guests arriving at a hotel with an infinite number of roomsis a set of a finite number of elements. The number of possible combinations of a finite number of elements is finite.

### Re: Theravada against mathematics

Germann,

I've used several examples to show that there are things which are not-random, which, even though they've had an infinite past, attain in the future a never-before-achieved result. These examples show that conceptually, there are such things. The examples are rooted in mathematics, using functions, which can be described as "rules" or "laws" or "processes". People and the minds associated with them also have rules, laws, processes, they are not random. It doesn't matter whether or not there is free choice.

Dan74-MkII also provided examples, but you don't seem to have understood the points that we were making. (If you did understand the intention behind our messages, my apologies for misperceiving.)

I will re-iterate using another example.

Let's take the function f defined such: f(n)=0 if n<0, and f(n)=1 if n>=0.

If n = -10, then all other values of n used "in the past" (< -10) return 0 through the function.

Yet 1 is a possible return value (but only after n>=0).

The reasoning that you're using is essentially claiming that because 1 is a possible value for f(n), and there are an infinite of possible values for n < -10, then f(n) must have value 1 at some point "in the past" (n < -10), which is not possible by definition of f.

The return-value of 1 is indeed possible, but only after a certain point, even if there were an infinity of values fed to the function "before that".

Having an infinitude of past events in no way implies that all events already happened (unless the event is totally random) -- this is an assumption that you make which is conceptually wrong, as the mathematical counter-examples produced show.

The Buddha also didn't say whether or not everyone would attain Nibbana, just that those that do, do so by taking a certain path.

Finally, your argument makes the claim that we should've all attained Nibbana by now, which is not the case. So either your argument is flawed (which is what I'm trying to point out), or the Buddha is wrong.

I've used several examples to show that there are things which are not-random, which, even though they've had an infinite past, attain in the future a never-before-achieved result. These examples show that conceptually, there are such things. The examples are rooted in mathematics, using functions, which can be described as "rules" or "laws" or "processes". People and the minds associated with them also have rules, laws, processes, they are not random. It doesn't matter whether or not there is free choice.

Dan74-MkII also provided examples, but you don't seem to have understood the points that we were making. (If you did understand the intention behind our messages, my apologies for misperceiving.)

I will re-iterate using another example.

Let's take the function f defined such: f(n)=0 if n<0, and f(n)=1 if n>=0.

If n = -10, then all other values of n used "in the past" (< -10) return 0 through the function.

Yet 1 is a possible return value (but only after n>=0).

The reasoning that you're using is essentially claiming that because 1 is a possible value for f(n), and there are an infinite of possible values for n < -10, then f(n) must have value 1 at some point "in the past" (n < -10), which is not possible by definition of f.

The return-value of 1 is indeed possible, but only after a certain point, even if there were an infinity of values fed to the function "before that".

Having an infinitude of past events in no way implies that all events already happened (unless the event is totally random) -- this is an assumption that you make which is conceptually wrong, as the mathematical counter-examples produced show.

The Buddha also didn't say whether or not everyone would attain Nibbana, just that those that do, do so by taking a certain path.

Finally, your argument makes the claim that we should've all attained Nibbana by now, which is not the case. So either your argument is flawed (which is what I'm trying to point out), or the Buddha is wrong.

### Shannon number

All _possible_ chess games would be played for the infinity of the past, since the number of all possible games is limited. All the _possible_ combinations of dhammas during life would have already been formed in the past, since their number is also limited. It is greater than the Shannon number, but not infinite.

### Re: Theravada against mathematics

The number of "living beings" (mechanical flows from dhammas) does not matter. Each stream of dhammas, without exception, does not have a first link. Each stream of Dhammas, without exception, continues endlessly into the past. Therefore, any possible life (any possible series of combinations of dhammas) would already have occurred in the infinity of the past. If there is such a life in which Nibbana can be realized, this realization would already have happened in each particular case.santa100 wrote: ↑Mon Mar 11, 2019 5:41 pm

Your premise has no basis, hence your wrong conclusion. Basically you're saying that there's only a finite number of sentient beings in the universe. But you really don't know that. So before even proceed with any further claim, you're gonna have to prove that statement first.

### Re: Theravada against mathematics

It's not because the rules of a game allow for certain combinations to potentially exist that supposing an infinite past, and an infinity of games played, all those games were played. As was said before, a lot of games with really stupid moves were never played before, because the players follow certain rules, reasoning, etc. For example, a game where chess players just freed up their kings to move and then only moved their kings for the rest of the game would not have happened if played by human players (in an infinity of games) -- simply because it is "stupid" to do so and humans would not play such a game. Yet this is a potential configuration acceptable by the game of chess.

One has to be careful how one defines "possible". If "possible" means: could be realized if X Y and Z were done, just by looking at the system and its rules, then, sure, the bizarro chess game is "possible", but in no way does it mean it happened, because X Y and Z were not necessarily done. This is because the game is not played at random, but it is played by conditioned players who have a partial understanding of the game, enough to avoid nonsensical games. If you define "possible" as "has happened or will happen for sure either in the infinite past or the infinite future", then the specific game of chess presented is not necessarily "possible" (and in fact, most likely isn't).

One has to be careful how one defines "possible". If "possible" means: could be realized if X Y and Z were done, just by looking at the system and its rules, then, sure, the bizarro chess game is "possible", but in no way does it mean it happened, because X Y and Z were not necessarily done. This is because the game is not played at random, but it is played by conditioned players who have a partial understanding of the game, enough to avoid nonsensical games. If you define "possible" as "has happened or will happen for sure either in the infinite past or the infinite future", then the specific game of chess presented is not necessarily "possible" (and in fact, most likely isn't).

### Re: Theravada against mathematics

Up to this point I agree.

Now I disagree, the assumption you are making is incorrect. It's not because a certain combination of dhammas has the potential to be realized in the totality of time, that it necessarily HAS happened in the infinite past.Germann wrote: ↑Mon Mar 11, 2019 5:57 pm Therefore, any possible life (any possible series of combinations of dhammas) would already have occurred in the infinity of the past. If there is such a life in which Nibbana can be realized, this realization would already have happened in each particular case.