Can you explain this Free Will / Predestination illustration?

As long as you do not know the future, you experience free will (some would say the "illusion" of free will). But God knows everything from His point of view in Heaven.

This does nothing to answer: "If God has predetermined what we do, then why are we to blame?"

That question only relates to Heaven's point of view, which is the only point of view that ultimately matters.

But life on earth feels EXACTLY like free will, because we can't even predict the future 1 second in advance (at any moment you heart could sieze).

I believe that the Bible clearly shows that in the beginning, God created man to love and worship Him. He knew, in His Sovereignty, that man would sin and allowed them, in their 'free will,' to do so.

If He predetermined each person's salvation, why were all destroyed in the flood?

I maintain that the scriptures show that God foreknew and predestined a group of people, who of their own free will, would respond to His call and invitation to "drink of the water of life freely" (Revelation 22:17)

It is obvious that He directs history, that He knows the hearts and minds of people and that accordingly He sets people in positions, knowing beforehand what will happen, so that His will is accomplished, but that is not the same as choosing from the foundation of the earth who will go to Heaven and who will suffer eternal damnation. This contradicts His Word and His character.

Take Israel as an example: They are His chosen people and He loves them, yet he 'foreknew' that they would reject Him. If He determined the will of the people, wouldn't His "elect" have received Him?

He led them out of captivity and away from death (freedom from sin and Hell), He showed them His mighty works and a means to be saved from slavery, He showed them His goodness and His mercy. They were His chosen, yet, after they had been called out by Him and led away from slavery, despite being called out, they "chose" to create their own god and reject Him.

This is the path that all follow. He calls us, shows us His goodness and mercy, but in the end, we make the choice.

Those who choose to drink the water of life are those that He predestined and foreknew, they are his adopted children, "whoever" believes on Me.

The problem with these two doctrines in reformed theology is that we see a certain liberty and predestination exposed in the Bible. So saying that predestination is the result of foreknowledge would not be accepted by Calvin for example.

Calvin seemed to foresee that there would be people that would argue that God "distinguishes among men according as he foresees what the merits of each will be" (Inst. III, 22, 1). Calvin, accordingly, writes against this notion, "by thus covering election with a veil of foreknowledge, they not only obscure it but feign that it has its origin elsewhere" (Inst. III, 22, 1). Calvin contests that this view of foreknowledge makes man God's co-worker in salvation, and implies that election is ratified only by man's consent. This is to make the gravest of errors because it suggests that man's will is superior to God's plan, or at the very least, implies God's plan is partially dependent on man(Inst. III, 24, 3). In refutation of this view, Calvin asserts that "this plan was founded upon his freely given mercy, without regard to human worth" (Inst. III, 21, 7 emphasis added). Source: http://www.reformedtheology.ca/calvin.html

This being said, predestination is not foreknowledge on the part of God, but an act of his sovereign will over his creation.

But the Bible still presents a great degree of liberty. For example, the brothers of Joseph went to him after Jacob's death to seek protection. Gen 50.20 As for you, you meant evil against me, but God meant it for good, to bring it about that many people should be kept alive, as they are today.(ESV) In this case the brothers used their liberty to plan evil, but it was the will of God that was executed. So to take the illustration of the OP in this scenario: the brothers used their freedom, but when they looked behind them they saw the sovereign God at work or predestination to save all the sons of Jacob.

The analogy I heard the most about these two doctrinal statements is: they are like the two rails of the railroad. The never join, but you still need them both to ride the train. This illustration demonstrates how some reformed theologians hold these views. They are both presented in the Bible and in the mind of God they do not conflict one another. It is not a clear-cut answer or an airtight argument, but to a certain degree it is one that does justice to the whole teaching of the Bible and does not place our view of reality over God's view of reality.

In the illustration presented by the OP: the individual makes a choice of his own liberty, but when he looks back on it he sees the hand of God guiding him in his choice. It is as if the freedom of the will and predestination was two sides of the same coin in the mind of God.

EDIT NOTE: Thanks to the question and comment of @Hammer and @Nathan Bunney which helped me to clarify my thoughts and correct an error that I left in my first response.

A similar illustration to demonstrate the concurrent nature of God's sovereignty and our freedom to act on our desires...

I read a book a while back on classical Arminianism (Grace, Faith, & Free Will). The author, Picirilli, is an expert in Greek but I would say not the best at arguing a free-will position. His writing is highly technical from a language standpoint, but I found it a little weak from a logic standpoint.

In this book, he gives an example of predestination with which as a reformed believer I would fully agree. Picirilli used it as demonstration of God's "hands off" approach to guaranteeing an outcome while never touching man's freedom.

Let's say that a man wants to go into his garden in the late afternoon. Let's also say that God does not want to go into his garden in the late afternoon. God also knows that the man will choose not to enter the garden if there is rain. To keep the man from the garden, God sends rain at the time the man would have gone into the garden. Thus, the man freely chooses not to enter the garden, and God's sovereignty is preserved in that His purpose was not overridden. Picirilli wouldn't tell you this, but it is a brilliant illustration of how God accomplishes His divine will for man in all circumstances (both in man's sin and man's acts of righteousness) and yet remains Holy.

The big point of both illustrations though is that man always acts in free agency, and God's will is always accomplished.

Since you asked about it, what the door illustration lacks however is the explanation that by nature since the fall, our inclination is to not enter. God plants within us the desire to enter the door, and by God not actively planting such a desire in us, we are left in our natural state of wanting nothing to do with entering the door. For point of fairness, a classical Arminian would say that God has given prevenient grace to each man and has enabled us to want to enter the door, but we choose to not want to enter the door.

It seems to me to be saying that you have complete freedom to act, but God knows all ends. You have freely chosen to walk through the door; but it was always known that you would (because God is God).

My preferred analogy is this: given the choice between, say, eating poop and eating ice cream, my son will always choose ice cream. I do not need to use coercion, I know he will make that choice because I know my son. He has free will and freedom to act, but I will plan to give him ice cream because I know my son.

The point of the illustration is to reconcile God's sovereignty in salvation with man's free will to choose salvation. I believe it originated from H.A. Ironside:

It has been pictured in this way. Here is a vast host of people hurrying down the broad road with their minds fixed upon their sins, and one stands calling attention to yonder door, the entrance into the narrow way that leads to life eternal. On it is plainly depicted the text, "Whosoever will, let him come." Every man is invited, no one need hesitate. Some may say, "Well, I may not be of the elect, and so it would be useless for me to endeavor to come, for the door will not open for me." But God's invitation is absolutely sincere; it is addressed to every man, "Whosoever will, let him take of the water of life freely" (Rev. 22: 17). If men refuse to come, if they pursue their own godless way down to the pit, whom can they blame but themselves for their eternal judgment? The messenger addressed himself to all, the call came to all, the door could be entered by all, but many refused to come and perished in their sins. Such men can never blame God for their eternal destruction. The door was open, the invitation was given, they refused, and He says to them sorrowfully, "Ye will not come unto Me, that ye might have life." ... [But some will say], "I am going inside: I will accept the invitation; I will enter that door," and he presses his way in and it shuts behind him. As he turns about he finds written on the inside of the door the words, "Chosen in Christ before the foundation of the world.

H.A. Ironside, In the Heavenlies (Ephesians), pages 27-28

The illustration distinguishes the cause of salvation into two perspectives: the perspective of man, and the perspective of God. The idea is that from our perspective, we use our "free will" to choose to be saved. And from God's perspective, God uses his sovereignty to choose who will choose salvation.

The point of the illustration is to defend against the the objection to Calvanism that if predestination is true, then not everyone who wants to be saved can be saved. This illustration counters this by arguing that everyone who wants to be saved can - because everyone who wants to be saved was predestined to be saved. It attempts to reconcile the notion that anyone who wills to be saved can be saved, with the notion that God chooses who will be saved.