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Miracles You Can't See

Miracles You Can't See

Sometimes our vision gets better when we close our eyes.


It's a blazing night in August. You grab a PowerAde and sneak in a serene midnight repose on the porch swing. The faintest tinge of a breeze wafts at your sweltering brow. It is a few minutes before midnight.

Suddenly, a bluster of blinding light douses the darkened sky. The breeze is abruptly transformed into a ferocious gust that lifts you inches off your seat. Fear abounds, but strangely, it is accompanied by a remarkable tranquility that confuses and calms you at the same time.

In a flash you find yourself in a scene from a sci-fi movie as a spacecraft, the size of two football fields, lands before you. A short ladder descends and a creature of sorts makes his way out of the vessel and walks towards you. You are too dazed to move.

"I am Kriz from the planet Magxac," he says. "I come in peace, just to explore your land. Can you show me around?"

He invites you into his Trans-orbitor and instructs you to push a button and choose any location on Earth in any time period.

"It is a combination of your GPS/Time machine/Super-sonic jet. It can take you anywhere in just seconds. Try it," he cajoles.

After taking a few minutes to allow the shock to wear off, you decide to show off some of Earth's wonders. You set the dial for 1476 BCE and you are whisked off to the shores of the Red Sea. Three million Jews are waiting in angst as Egyptian chariots rumble in the distance.

"Watch this," you whisper to the alien.

The mighty waters part and the dry path is quickly filled by ecstatic Jews.

Kriz is not impressed.

"Big deal," he says. "Happens every day on Magxac."

Undaunted, you set the dial ahead a few months and together witness manna descending from the heavens in the desert. Same ho-hum reaction.

Frustrated and disappointed, you head back to the present and emerge from the craft with your newfound friend. It is 7 A.M.

"Whoa! What is that?!?!" cries Kriz, pointing to the sky.

"What is what?" you reply innocently.

"THAT! That giant orange orb that is blinding me!"

"You mean the sun? Haven't you ever seen the sun?"

"On Magxac, it is always dark. This sun of yours looks awfully close. How far away is it?"

"Actually, it is 93 million miles away."

"Incredible! I can't even look at it!"

Do we ever stop to realize that the existence of the sun or its perfect placement is truly miraculous? Had the sun been 92 million miles away we would probably burn to death; 94 million miles away and we would freeze.

Frequency is blinding. We don't appreciate things as miraculous because we are inured by the limitations of our vision.

The only reason we don't immediately think of the sun as a miracle is because it is always there – rising and setting and shining exactly the way we expect it to. But frequency is blinding. The sun, like so many things in life, is genuinely miraculous. We don't appreciate things as miraculous because we are inured by the forces of habit and the limitations of our vision.

In Ethics of Our Fathers, our Sages teach that ten miracles occurred in the Temple. No sacrificial meat ever became putrid, no fly was ever seen (for hundreds of years) in the butchering stations, the rains never extinguished the pyre on the Altar plus seven others. The laws of Nature were transcended in the Temple.

But there is something strange about this list of ten. Each miracle mentioned relates something that did NOT happen. Our customary dictionary definition of what is a miracle is quite different:

  1. An amazing or wonderful occurrence
  2. A marvelous event manifesting a supernatural act of God

But what about things that don't happen? Can they also be considered miraculous?

Example: Of all the hundreds, if not thousands, of blessings that Jews recite, there is only one that mentions "God's Heavenly Throne." That, believe it or not, is the blessing that we say several times a day after exiting from the bathroom:

Blessed are You, HaShem, Our God, King of the universe, Who created the human with wisdom and created within him many openings and many cavities, exposed and known before Your Throne of Glory, that if one of them were to be ruptured or one of them were to be blocked it would be impossible to survive and to stand before You for even one hour. Blessed are You, HaShem, The physician of all flesh who acts wondrously.

Essentially we are marveling at the wonder of how the many openings and cavities in our bodies are NOT blocked or ruptured – allowing us to function and exist. What does NOT happen is miraculous, and we must see it as such.

Similarly, when we sit in a doctor's waiting room and fill out forms describing our medical history, we should count every 'check' in the 'no' box as a miracle of something that did not happen – and there are hundreds of them.

Americans are loathe to speak about it (bad karma?), but who would have predicted in 2001, after 9/11, that no major terror attack would take place on US soil in seven years? Is that not miraculous?

And what about our precious little children? Any mother will tell you that it is inexplicable that toddlers don't choke on things every single day – marbles, popcorn, pennies, watch batteries – while crawling around the house. Stairwells are too often left unblocked, yet these tiny treasures seem to live with a special protection from Above.

Safe sky travel is considered a given. While we all deplore the ever-growing incidence of departure and arrival delays, we forget how astounding the safety statistics are. Get this. The total number of flights scheduled to operate worldwide this month is 2.55 million. 307,000,000 seats will be offered to travelers around the globe! Only a tiny percentage of those passengers will experience a mishap of any kind. Incredible.


No one doubts that the establishment of the State of Israel, after Hitler's decimation of European Jewry, was an open miracle. Scattered around the world, hated everywhere they lived, persecuted in the north and the south, the east and the west, Jews survived and even thrived. But sometimes we forget that every day that Israel doesn't implode – surrounded by its sworn enemies, many times its' size – is a miracle we should never take for granted.

And most astonishingly is the following framework for something we have all become intuitively aware.

Do we realize the magnitude of the miracle we recently experienced in Gaza?

The world is now far too well acquainted with the fright and terror experienced by the Jews who live within striking distance of our enemies in Gaza. The panic and hysteria that occurs when a siren goes off and a missile is imminent has been depicted in a frightening film on this website and has been viewed over a million times.

As painful as each and every casualty is, thank God, the losses have been comparatively minimal. But do we realize the magnitude of the miracle before our eyes?

Harold Gans is a mathematical consultant and international lecturer throughout North America, Israel, Australia and South Africa. He was a Senior Cryptologic Mathematician with the National Security Agency, United States Department of Defense until his retirement after 28 years of service. He recently reported the following:

On Jan. 5, 2009, Ehud Barak, Defense Minister of Israel, announced that 125 Grad-Katyusha missiles had fallen on populated areas of Beersheva, Ashkelon and Ashdod. This is 40% of the missiles fired; the remaining 60% fell in open areas. Of the 40% that hit populated areas of these cities, 2% hit buildings. I obtained satellite photos of Beersheva, Ashkelon and Ashdod. My analysis indicated that the average percentage of the ground covered by buildings in these three cities is 39.7%. This takes into account the different sizes of these cities.

Now, the expected rate of rockets hitting buildings should be the same as the percentage of the ground covered by buildings: 39.7%. Yet it is only 2%. The odds of this happening by chance are 100,000,000,000,000,000: 1.

Note that this has nothing to do with the bad aim of these missiles; we are only counting the 40% that actually did fall in populated areas of these cities.

God has given us a universe that is saturated with wonder and amazement. When we tune in to the marvels that surround us we can feel His presence and experience unparalleled joy. But there's a whole class of miracles that is easy to miss – the "non-events" of life. In some ways, they can be even more providential than the obvious ones.

Just ask Kriz.

January 31, 2009

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The opinions expressed in the comment section are the personal views of the commenters. Comments are moderated, so please keep it civil.

Visitor Comments: 27

(27) MABSH"Y, August 5, 2013 4:42 PM

strive for accuracy

You state "Had the sun been 92 million miles away we would probably burn to death; 94 million miles away and we would freeze." But in fact, the sun is each of those distances away each and every year. The sun's orbit is elliptical, going from about 91.4 million miles away in January to 94.5 million miles away in July. And the actual range of habitable orbits is even larger (see "circumstellar habitable zone") While this can still be considered miraculous, efforts at kiruv towards those of scientific bent is not served by inaccuracy and making things seem even more more remarkable than they are. They will accuse you of fudging. Re'eh's "lo tosef v'lo tigrah" should be observed no less here than in halacha

(26) anon, July 29, 2013 9:28 PM


An opportunity to salute Rabbi Salomon and Mr Gans for this and all their fantastic efforts! ; [but, I'd love to see Brendan McKay (if i got the name right, and if he's still around?) add his "haskama" on this one). [won't hold my breath]

(25) Harold Gans, February 17, 2009 6:05 AM

Response to comments

I appreciate the fact that people have done the math and come up with similar results. I would point out however that some have missed a critical point. There were 125 missiles THAT LANDED IN POPULATED AREAS of these cities. This was only 40% of those fired. Thus, bad aim and weather conditions are totally irrelevant. We are concerned only with those missiles that succeeded, somehow, in landing in a populated area. Now for the math. I took a shortcut and used the normal distribution. The sample size = N = 125. The observed number of hits = n = 3, (since it has to be an integer). The probability of a hit (once the missile succeeds in landing in a poplulated area) = p = 0.397. The variance = Np(1-p) > 9 so the normal distribution applies. The sigmage, or number of standard deviations from the mean is (n-Np)/sqrt(Np(1-p)) = -8.523. The two sided right tail probability is thus 7.7736E-18. One more thing: I am not "Dr.", just "Mr.".

(24) Joe, February 10, 2009 1:24 PM

I did the math

In response to Dan, This really is a miracle. I just did the math. For the sake of simplicity, let's say it was 100 rockets. I responded earlier that I would need the number of rockets to do the calculation. I missed that the article said it was 125. Let's say it was 100 though for simplicity. Let's also say it was (0.4) instead of (0.397) for chance of a hit. You have 100 "trials with a 0.4 chance of success and a 0.6 chance of failure. We find the 2% of the trials, or 2 of the rockets "win." that means that there are 100 choose two cases outcomes total. Of those arrangements you had (0.4)^2 odds of "winning" and (0.6)^98 odds of "loosing" for each of the 100 choose 2 cases. So the probability of this happening is {100 ,2} * (0.4)^2 * (0.6)^ 98. {100,2} is the best I can manage for notation here for 100 choose 2. Calculate that and you get 2X10^-19. I believe the numbers given by Dr. Gans. Now to be certain, this calculation assumes that the rockets have equal probability of landing *anywhere* withing city limits (which we can not assume) and it does not take into account any number of confounding factors like weather conditions, fear of getting clipped by the IDF, when you launch or set up your rocket (so you do it quickly) and variable propellent quality in the rockets - to name a few. We really need to no the statistical center of the distribution of hits in the cities and see how many standard devs out, the city limits are from that center. None the less, I have often been a skeptic of statistical arguments for Divine agency, but this one is certainly a bit compelling to me.

(23) Joe, February 10, 2009 11:36 AM

Statistics in reply to Dan

First off, thank Hashem that so few people in Israel have been hurt. It is not fo lack of trying on the part of our foes. It is miraculous and wonderful. In reply to Dan, I'm a physicist and I also wondered when I saw the statistics. I am not going to say that Dr. Gans did his mathematics incorrectly. However, I will say that this article did not report enough data to repeat the calculation. It is certainly very easily possible to quickly - and accurately calculate astronomical odds. For instance, the probability, in a coin flip trial of getting n heads in a row is 1/2^n. So what is the probability of getting 100 heads in a row? Answer, 1/2^100, which is easily calculated and much smaller than what we was reported here. The smallness of the odds reported is not in of itself cause to assume the calculation was incorrect. That said, I too would be interested in enough data to do the calculation myself. I do not see how that is possible without knowing the number of rockets fired. The way to phrase the question statistically is, what is the probability that n rockets fired with a 39.7% chance of hitting only hit 2% of the time. I suspect that since we are talking thousands of rockets that the number is indeed very small.

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