Dovid Ployni buys one lottery ticket involving one hundred million numbers, and he wins the big prize. Is that a miracle? Most people would say, no. We are used to people winning lotteries. Where is the miracle?

Now let's change the story a bit. Dovid and Miriam, who are very nice people, have a young daughter, little Miss Ployni. Miss Ployni has just been diagnosed with a terminal illness. Unfortunately the only possible cure is experimental and the medical insurance will not pay for it. The Ploynis say Pslams and Dovid eventually buys a lottery ticket. The ticket wins the lottery and the little Miss is cured.

Was this a miracle? Many people say, yes. But why is this situation different from the first instance?

The odds are a bit different because of the cure. But is the difference from one hundred million to three or four hundred million-to-one that big a probabilistic difference? No. If one hundred million-to-one odds does not make a miracle, then two, three or several hundred million-to-one, or more odds should not make a miracle. The difference is because we now know, and like, the Ployni family. The odds have nothing to do with it. Indeed, winning a lottery against odds, no matter how high, is arguably the worst science-based example one can choose as an indicator for a miracle, as I will shortly explain.

The Ployni family are likable people. Now let us consider someone who is not so easy to like. Mike Crackhead is a miserable character. He not only uses the stuff but he also sells it to children. One day he is offered a bet with, what to him seem to be, terrific odds. He is offered one hundred-to-one odds that he can not flip a coin 27 times and get 27 heads in succession.

Mike knows that for one flip the chance of getting a head is even at one-to-one. He decides that 27 flips yields a chance of 27-to-one against it. The offer of 100-to-one looks good, and he accepts the bet. Mike does not understand that in reality he is facing an almost impossible task with 134 million-to-one odds against him. Well, you guessed it. Mike flips the coin 27 times and he gets 27 heads in a row. He now has more money than he needs for his drugs, and he invests the excess in the only item he trusts - guns.

One day, while under the influence, Mike starts shooting and he kills all three members of the Ployni family. Virtually no one will suggest a miracle here when I ask this question during a lecture. People simply can not conceive that this horrible person would get Divine help so that he could kill the Ployni family. But if anything is to have scientific credibility as a miracle, it is the coin flips and not the lottery win, even though we are dealing with virtually identical odds. Equal odds does not mean equal likelihood or credibility, as I will soon explain.

So far I have dealt with "natural" occurrences and no rules or laws of nature have been violated. It is incredible to believe that someone could flip 27 heads in a row, but it is not impossible. But suppose we have a situation where something impossible happens? What does "impossible" mean? "Impossible" means that we violate a law of nature. Suppose we place a wick in vinegar and this "lamp" burns all day, as if the vinegar were oil? Many people would start thinking miracle as a logical explanation. After all, we "know" that vinegar does not burn. Miracle is the only possibility left after we exclude all other explanations.

So which of the above scenarios defines a miracle? The answer is, none. The above stories are not definitions, but simply the evidence to be tested against a definition. Most people would agree that a miracle involves Divine intervention. If the evidence points to Divine intervention then we have a miracle. Otherwise we do not have a miracle.

Most people would say that a violation of natural law requires Divine intervention and is indicative of a miracle. Many people would also say that to prevail against incredibly high odds also calls for Divine intervention. But "prevail" is not a simple concept. I illustrate this with the "circling the arrow" analogy in my book. Here is how this works. An archer shoots an arrow at ten million tiny targets and hits one. The archer then, truthfully, claims to have hit a target involving ten million-to-one odds. So what? The archer circled the target only after it was hit. Any target is just as good as any other target. There is no skill involved here and no miracle is implied.

The same holds for the winner of the lottery. Indeed, it is a certain event that someone will win if enough tickets are sold. Someone has to win, and it makes no difference who that is. But getting 27 heads in a row is in a totally different category. There is nothing at all certain about this happening. And if we extend the string of heads to one hundred and beyond, then ultimately science has to step in to look for an answer. This is no longer "natural", even though it is not impossible. Could there be a miracle here, as in Divine intervention?

The point of the matter is that it is the Divine intervention that makes the miracle. Taken to the extreme, we could say that any event, no matter what the odds, or how it comes about, or who is involved, is a miracle if it is due to Divine intervention. This common-sense approach is also the approach taken by the Torah, as discussed next.

When most of us refer to miracles in the Torah we are talking about Divine intervention to change the natural order of the world. These so called "open", or obvious, miracles are described by Rabbi Dessler, whom I quote extensively in my book. He notes that "On rare occasions... G-d will override the laws He has written into the cosmos and perform open miracles which have no physical cause." We also have hidden miracles which can be ascribed to a natural cause, but the Torah informs us that the event was due to Divine intervention. In other words, it was a miracle because the Torah tells us so. But we have no obvious physical proof of it.

There is yet a third category of miracles which most people are not aware of. The Torah assures us that all happenings, including that which we call nature or the laws of nature, are due to ongoing Divine intervention. These then are miracles also, if we go by the basic definition that Divine intervention means "miracle." Here is how Rabbi Dessler explains it in his book Strive for Truth. "What is the difference between the natural and the miraculous? ... We call G-d's act a 'miracle' when He wills an occurrence which is novel and unfamiliar to us and which consequently makes us aware of the hand of G-d. We call G-d's acts 'nature' when He wills that certain events should occur in a recognizable pattern with which we are familiar."

Indeed, to get back to the "natural" after a miracle can be as difficult, or even more difficult, than to get the miracle in the first place. We have a principle, noted in Talmud Tractate Taanith, that to undo a miracle is a greater miracle than to produce the original miracle. Rabbi Akiva Tatz provides an example in his book World Mask. Why was it necessary for Moses to stretch out his staff to bring the waters back to their original condition after the Israelites had crossed the miraculously dry sea? The waters simply had to go back to their natural, meaning normal, condition. This should have happened on its own once the miracle was finished. But there is no naturally normal condition that the waters want to assume.

Whatever condition G-d chooses is the normal condition at that time, and it takes miraculous Divine intervention to get something else. Even when that something else is what we are used to. This is because, as Rabbi Tatz tells us, "nature is miraculous no less than its rarest exceptions... The only difference is that we are used to the one and the other is unexpected... a miracle is no more wonderful than the natural."

Here is another well-known story about miracles that illustrates our point. We have tfollowing story, about the exceptionally pious Rabbi Hanina ben Dosa, in Talmud Tractate Taanith page 25a. One Friday, near twilight, he saw that his daughter seemed upset, and he asked what was the matter. The daughter explained that she had mistaken a bottle of vinegar for a bottle of oil and she poured the vinegar into the Sabbath lamp.

The implication being that they would not have any light on the Sabbath because vinegar does not burn. I do not know how the reader would react. But I must confess that my reaction would not be the same as for Rabbi Hanina. But then I am not as Rabbi Hanina in spiritual potential. He simply looked at his daughter and told her not to be sad. "This has nothing to do with you. He who tells the oil to burn can also tell the vinegar to burn." And we are told that the vinegar did actually burn.

The immediate reaction is to note that Rabbi Hanina was not surprised by the open miracle of burning vinegar. But there is a more subtle message here. Rabbi Hanina made it clear that oil, no less than vinegar, needs a Divine command to burn. Burning oil is no less a case of Divine intervention than burning vinegar.

It is clear from the above, and other Torah-based examples, that while the Torah does recognize unique events that people call open miracles, ultimately all that transpires is of the same miraculous category. There is no "nature." Everything is one continuous miracle. Clearly this is contrary to science. And it would appear that Torah is opposed to science. But that is not the case. The Torah is actually in full agreement with science in spite of the above analysis. This is because the Torah also holds that all can be described as part of "nature", even open miracles.

The Torah holds two realities to be true. One is the reality of this world of "nature" described by scientific laws. This is the world that we physically live in and interact with. The other is the spiritual world which is the cause of the physical result. Some people who are at a high enough spiritual level, such as Rabbi Hanina, can perceive the spiritual and it is as real to them, or even more real to them, as the physical world that we live in. But most of us only get an occasional glimpse of the spiritual, given our strong attachment to the physical. Yet both realities are true.

The Torah insists, absolutely insists, that we have free will to believe as we wish. That means that there must be the possibility of a scientific, naturalistic, explanation for everything, even though the underlying reality is the cause of it all. Here is how Rabbi Dessler puts it. "Nature has no objective existence; it is merely an illusion which gives man a chance to exercise his free will... What is real is the will of G-d and nothing else." But how many of us are at a spiritual level to actually perceive this? To most of us it is the physical that is the real reality. And the Torah accepts this because, even though "Someone who has no idea of the underlying purpose which these two different modes of perception serve, will see a conflict... The perception of causality is also necessary so that we may discern the hand of G-d behind the causes."

"We may discern", but we are not compelled to discern. We have free will to choose. The Torah provides for the possibility that there will be those who choose a purely natural universe, devoid of any spiritual dimension. This is a universe explained only by science. And even an open miracle, such as burning vinegar, is included. Let's take a look at how this works.

Richard Dawkins, who holds that belief in the Bible is not only wrong but actually damaging, tells us in The Blind Watchmaker that that which we call miracles are just "improbable natural events." Science insists that all can, or eventually will be, explained on a natural basis. Science does not agree to Divine intervention. Hence science does not agree to miracles. Furthermore, the Torah says that this is how it is supposed to be. How else can we have absolute freedom to choose what to believe? Surely we would be compelled to believe in the Torah if science agreed in principle to Divine intervention in "nature?"

Here is how Rabbi Dessler explains the scientific position respecting miracles. "They would look for, and find, some twist in a physical theory which would account for the miracle in materialistic terms, or they would invent an entirely new theory; in one way or another they would inevitably assimilate the miracle to the naturalist scheme. The miraculous would become 'nature'." Not only does science try to "account for the miracle in materialistic terms", but science actively searches for "miracles" for this purpose. This is how science makes progress.

The Nobel prize is not given to investigators who replicate a previously known result. Rather the honors and awards go to those who find something new that previous theory and experiments did not anticipate. There was great excitement in physics, early in 2001, because the standard model had apparently been broken. That is, it looks like we finally have experimental results that do not fit the model.

Now we can learn something new as the model is modified to incorporate these results or, if necessary, a new model will be crafted. As Rabbi Dessler says, "they would look for a new theory" and the results that can not currently be explained as natural (i.e. miracles) will be "assimilated ... to the naturalist scheme." This is how science works. This is how science progresses.

The Torah accepts that this is what science must do. The Torah recognizes the legitimacy of science. Yes, there are serious disagreements with certain science based results. But there is no quarrel with science, per se. But science is not that generous to Torah. Science refuses to agree to the Bible or to miracles. What are we to do?

What are we to do? I address this issue in my book The Heavenly Time Machine. We can examine two questions. To what degree do modern science and ancient Torah agree? The answer is that these agree to a most remarkable degree. That is the substance of the book. Another question that we can examine is whether science does, in fact, point to miracles, even though it is not supposed to. Surprisingly, the answer is yes.

Officially, science does not recognize a miracle, and even open miracles are eventually assimilated into "nature." But how many coincidences can the mind accept before one starts to wonder? Science tells us that it is not impossible for all the air in a room to suddenly concentrate in one corner leaving the rest of the room in a vacuum. But how many atheistic scientists would not start to consider, even a little bit, at the idea of a miracle?

The possibility for this universe to be here with creatures like us has been estimated by Oxford mathematician, Roger Penrose, as less than one chance in a googolplex. A googolplex is a one followed by a googol of zeros. And a googol is a one followed by 100 zeros. A googolplex is an impossible number to visualize. Suffice it to say that the air in the corner example is no big deal on this scale of probability. And it is all made up out a number of independent highly improbable events. How many coincidences can one accept before one starts to wonder if there is not some hidden mechanism controlling it all?

The Earth is at just the right place; not too hot and not too cold. But planetary formation processes say that there should not be any planet here. Planets should be spaced at a distance ration of roughly double each distance from the sun. This works perfectly if we include the asteroid belt as a planet that did not stick together, and we exclude Pluto as not a real planet. Venus is in the right place. Mars is in the right place. So what is the Earth doing in the middle where it does not belong? We need liquid water. Our type of life could not exist without liquid water. But solids are usually denser than the liquid state, and solid water should sink and not float. This would cause oceans and rivers to freeze from the bottom up and this would destroy the possibility of life. But ice is less dense than water and it floats, contrary to the rules.

All life on Earth depends on carbon. But carbon should really not exist. Except that it does. On and on, the coincidences keep piling on till we get into the googolplex range. No wonder the world renowned scientist, Stephen Hawking, tells us in A Brief History of Time that, given our current state of scientific knowledge, he is compelled to consider this universe "as evidence of a Divine purpose in creation." Astronomer Martin Rees asks in Just Six Numbers how this universe can be explained. He rejects coincidence as impossible and is left with just two explanations, providence or a conjecture that ours is one among many existing universes.

Over and over again, science at the highest levels, points to Divine intervention. A cover story in the July 20, 1998 issue of Newsweek tells us that "Science Finds G-d." "And although it cannot prove G-ds existence, science might whisper to believers where to seek the divine." To repeat from Rabbi Dessler, science and "causality are necessary so that we might discern the hand of G-d behind the causes." Science does not compel anybody to believe in miracles, but it is not forbidden, and science even points in that direction. We have freedom to choose. And that may be the greatest miracle of all.

Morris Engelson discusses miracles in several places in his book The Heavenly Time Machine: Essays on Science and Torah.