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Fruit trees programmed to produce fruit of their kind
1. Fruit trees programmed to produce fruit of their kind
Plants, such as fruit trees, have DNA which determines which fruit is produced by which trees.
A peach tree always produces peaches.
An apple tree always produces apples.
By looking at what Jesus says about trees and fruit in Matthew 7:17-18, one can make an interesting case for what is often called predestination.
2. Ginkgo leaves falling
As an example, the leaves of ginkgo trees appear to fall on one day. The superficial reason is involves scarring in their stems that happens quickly in the ginkgo trees given certain weather conditions (cold air, etc.).
The underlying reason is that the DNA is programmed to do so. From an applied programming language theory perspective, this can be a higher-order effect.
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Details are left as a future topic.
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3. Kung Fu Panda
For those who like to watch animated movies, such as Kung Fu Panda, Master Shifu (Dustin Hoffman) tells Oogway that he can decide what tree to plant. Oogway tells Shifu that the tree will always be the tree determined by the seed - which came from that type of tree.
4. Genesis 1: A seed within itself, the chicken or the egg
Genesis 1:11 And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. [kjv]
… σπειρον σπερμα … ξυλον καρπιμον ποιουν καρπον … αυτου εν αυτω … [lxx]
In general, the question, "
Which came first, the chicken or the egg" refers to a situation where there are two objects that each depend on the other and the problem is to determine which came first.
Somehow, the information for the egg needs to be within the chicken. This is a self-referential system.
In Genesis 1:11-12 we have an example of this with fruit, "
whose seed is in itself". Modern self-replicating programs provide an example of this idea.
5. Jesus and fruit
In Matthew 7 (and elsewhere) Jesus makes some interesting remarks about fruit trees.
6. Matthew 7:16
KJV: Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles?
Greek: απο των καρπων αυτων επιγνωσεσθε αυτους μητι συλλεγουσιν απο ακανθων σταφυλην σταφυλας η απο τριβολων συκα
The above verse is the context. We are interested in the next two verses.
7. Matthew 7:17
KJV: Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.
Greek: ουτως παν δενδρον αγαθον καρπους καλους ποιει το δε σαπρον δενδρον καρπους πονηρους ποιει
8. Matthew 7:18
KJV: A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit.
Greek: ου δυναται δενδρον αγαθον καρπους πονηρους ποιειν ενεγκειν ουδε δενδρον σαπρον καρπους καλους ποιειν
We are interested in the two above verses. Here are the verses that follow, for context.
9. Matthew 7:19
KJV: Every tree that bringeth not forth good fruit is hewn down, and cast into the fire.
Greek: παν δενδρον μη ποιουν καρπον καλον εκκοπτεται και εις πυρ βαλλεται
The casting into the fire is important but not discussed here.
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Details are left as a future topic.
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10. Matthew 7:20
KJV: Wherefore by their fruits ye shall know them.
Greek: αραγε απο των καρπων αυτων επιγνωσεσθε αυτους
How would the observed fruits allow one to distinguish them?
In conditional probability, the inverse conditional probability is usually different. This makes reverse inference difficult and is the source of many deceptive verbal tricks (e.g., as some lawyers will use if they can get away with it).
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Details are left as a future topic.
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Here, Jesus provides the necessary conditional probabilities going both ways.
11. Good and bad fruit
Let us return to Matthew 7:17-18. From what Jesus says, we have the following relationships.
Good trees bring forth good fruit and cannot bring forth bad fruit.
Bad trees bring forth bad fruit and cannot bring forth good fruit.
12. Specialization
This binary idea appears to be specialized as follows.
A peach tree brings forth peaches.
An apple tree brings forth apples.
... and so on ...
And, to use the analogy made by Jesus:
A thorn tree brings forth thorns.
A thistle tree brings forth thistles.
... and so on ...
How many different types of fruit might there be?
13. Induction
A tree is determined by the seed, that seed by the tree from which it was taken, etc.
The programming (DNA and associated molecular machines) appears to be simpler in plants than in animals and simpler in animals than in humans (a subset of animals, if you wish to classify it that way).
14. Information and randomness
The increased complexity of the information at each level appears to include a degree of randomness.
AIT (Algorithmic Information Theory) makes this connection much more precise.
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Details are left as a future topic.
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15. Conditional probability
Let us use the following abbreviations in binary mode with the extension to specialized instances left for the reader to consider.
GT = Good tree
GF = Good fruit
BT = Bad tree
BF = Bad fruit
The categories are mutually exclusive and collectively exhaustive.
16. Sets: Mutually exclusive and collectively exhaustive
Items in a set can be partitioned into categories in many ways. Given a set, such as "
yes" and "
no".
Mutually exclusive means that "yes" or a "no" are distinct and cannot be both at the same time.
Collectively exhaustive means that everything must be either a "yes" or a "no". There are no other possibilities.
Let us look at this in conditional probability terms from what Jesus said.
17. Conditional probability
One way to deceive people is to use
conditional probabilities as if they go both ways equally.
The probability that one speaks Spanish given that one lives in Spain is very high.
The probability that one lives in Spain given that one speaks Spanish is very low.
P(GF | GT) = 1.0 = P(GT | GF)
P(GT | BF) = 0.0 = P(GT | BF)
P(BT | BF) = 1.0 = P(BF | BT)
P(BT | GF) = 0.0 = P(BF | GT)
From the conditional probability equations (omitted) we have the following.
P(GF) = P(GT)
P(BF) = P(BT)
The probabilities, however, are not known. In Matthew 7, we are told the following.
The probability of going through the narrow gate is very low.
The probability of going through the wide gate is very high.
The aspect of interested here is just the conditional probabilities that allow us to determine good trees from good fruit and bad trees from bad fruit (and the other way in reverse).
18. Bayes rule
Inverting the probabilities can be done with Bayes Rule. The interesting part is that if the conditional probabilities are 1.0, no new information can change the original probabilities. We know (or assume) the following.
19. Predestination
The above observations appear to have implications for the arguments of "
predestination".
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Details are left as a future topic.
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20. End of page
