The Biblical Accuracy of PI Hidden in Gematria

2010-03-14T13:45:00.000-07:00

It is well known that the Gemara and Mishnah uses the value of 3 for PI. However we know that PI is 3.1415926... Various answers on this discrepancy have been given, the simplest is that the Gemara/Mishnah are using 3 as an approximation to make it easy for the common man to calculate when halachah dictates a measurement that uses PI.

However, the Gemara (Eruvin 13B?) says that we learn that PI is 3 from the verse in Kings 2 Chapter 7 Verse 23:

And he made the molten sea, 10 cubits from brim to brim: round all about, and a height thereof 5 cubits: and a line of 30 cubits did compass it round about

So it seems that the prophet is telling us that PI is 3 as well!

One could say that this too is a known approximation, and is not meant to tell one the true value of PI. From an e-mail I was directed to from RationalistJudaism.com, a very interesting gematria comes out of this verse.

This gematria is attributed to the Vilna Ga'on (although there is no source to substantiate the claim that the Vilna Ga'on said it. The actual source for the insight may be credited to Matityahu ha'Kohen Munk (Frankfurt-London), who published the thought in the journals "Sinai," Tamuz 1962, and "ha'Darom," 1967).

In the verse quoted above, there is a kri/ksiv on the word "and a line" (v'kav) describing the 30 cubit line around the circle. The ksiv is spelled "v'kavah" with a hey at the end, while the kri is "v'kav" without the hey. The gematria of 'kava' is 111, while that of 'kav' is 106. With this we get something interesting:

The ratio of the kri/ksiv is: 111/106 = 1.047169811320755...
While the ratio of PI to 3 is: PI/3 = 1.047197551196598...

So the ratio of the written/actual word to the practical/read word is extremely close to the ratio of the actual value of PI to the practical/approximation of PI.

In fact, if one uses the ratio 111/106 to derive an approximation of PI, one gets:
333/106 = 3.141509433962265... which is an approximation of PI that is over 99.997% accurate!

So from this we see that it is possible that the prophet knew to very good precision the actually number PI but used a value of 3 nevertheless to show that using 3 is a good enough approximation when it comes to halachic measurements.

(And a happy PI day to everyone!)

Cool Cell Movie

2009-05-06T14:38:00.000-07:00

In grade school, the picture of the cell we are given is quite simplistic. The real cell is anything but. Here is a really cool animation depicting parts of the cell. Truly a marvel of Hashem!

Click here to view!

Saying a Beracha on a River Formed After Creation

2009-04-03T15:56:00.000-07:00

Just a quick interesting halachic issue I found. Everyone knows that on a large impressive river, one says the beracha "oseh maaseh bereshis". However, what I didn't know was that there is a condition on this beracha:

According to Artscroll Yerushalmi Berachos 88b1-2 footnote 11, the Pri Megadim to Magen Avraham says that one may NOT recite the beracha of "maaseh oseh bereshis" on a river unless the river has always been there since the time of Creation. I.e. if there was a large earthquake/volcano/atom bomb that caused a new river to form today, then we would not say the beracha upon seeing such a "new" river. Also, if we purposefully change or add to a river (like a canal), then we cannot say the beracha on the new part of the river.

The question arises that if one holds like the authorities (mostly kabbalists) that say that the world is very ancient (on time scales like those that scientists have determined), then it is possible that we could never say this beracha. Since according to geologists, the Earth has gone through huge changes over time, any river we see today is likely not to have existed in the distant past. (For example, during the ice ages, and especially during the gathering of the first water on Earth).

It would seem one would have to say that the Creation is not considered truly completed until Adam Harishon was formed. According to that, (and the opinions that the world simply looks old but in reality is only as old as the time of Adam Harishon), we would need to determine if any particular river was around for the last 6000 years before we could say a beracha upon seeing it. It would be interesting to see if it is halachically permissible to use the findings of geologists to make such determinations.

Scientific Techeles Gematria

2009-03-06T13:26:00.001-08:00

I already had this on my web site before I started this blog, but I realized today that I have no link to it anymore (and I am very tired). So, rather then retype it, here is the link:

Techeles Gematria

It is an interesting gematria that I came across in yeshiva. Basically, if you combine some gematrias of the word techeles, and then convert that number (assuming it is in units of amos (~18 inch)) into nano-meters, you get the maximum absorption frequency of light of indigotin (in the visible range), which is the chemical composition of the dye from the murex trunchulus snail (and the indigo plant). Take a look!

When is the Gender of an Unborn Child Determined?

2009-02-06T14:03:00.000-08:00

The mishnah in Berachos Chapter 9 says:

One who cries out for that which is past - this is prayer in vain. How so? His wife is pregnant, and he says, "May it be Your will that my wife give birth to a male," - this is a prayer in vain.

It would seem at first glance that this implies that the gender of the child is determined before a woman (or perhaps her husband) notices that she is pregnant. However, this seems not to be the case, for the Yerushalmi says:

The academy of Yanni say: The Mishnah was speaking about a woman on the birthing stool. But before that point, one may pray [for the gender] in accordance with "Behold, as clay in the hand of the potter...."

This implies that the gender is not set until right before birth! And further, in Midrash Bereishis Rabba 72:6 we see the opinion of R' Yehudah ben Pazi who says that even on the birthing stool the fetus can be transformed, and thus one can still pray.

Most people today go by the rule that up to 40 days, one can pray for the gender, but not after that. [I have not yet found the source for this.]

According to modern science, the gender of the child is determined at conception (although I remember seeing something to the effect that there is a possibility of gender change at the very beginning of pregnancy, but I cannot recall where I read about it). This seems to contradict the gemara's interpretation of the Mishnah in Berachos.

However, it does not necessarily. There is a concept in the gemara that one should not count his grain too much, because then G-d will not cause a miracle and give him more. Meaning, that G-d does not want to do open miracles, but hidden ones He does. Therefore, if no one has detected the gender of the child, it would seem that G-d could perform a hidden miracle of changing the gender all the way through pregnancy. (However, today, with ultrasound, it would seem we cut this time down quite a bit - once we detect the gender, a gender change would be an open miracle). This would explain the Gemara's opinion of the Mishnah, that the prayer in vain refers to the time during birth, i.e. where the gender can be observed for the first time.

However, there is a source in Chazal that gender is determined at conception. The Midrash Tanchumah, Parashahs Pekudeh, sif 3 discusses what happens during conception and says that G-d tells a certain angel to go down and protect the droplet, and cultivate it into 365 parts. After doing so the angel shows the drop to G-d and says:

"I have done just as You have commanded me, so what has been decreed for this droplet?" The Holy One, Blessed is He, immediately decrees the destiny of the droplet; if it will be male or female, weak or strong, ...

This Midrash is seemingly saying that the gender is decreed at conception! If this is the case, then perhaps (unless this goes against psak halachah) one could take this view and say that indeed gender is determined at conception, and explain the Mishnah above accordingly.

The Number of Stars in the Universe

2009-01-09T11:33:00.000-08:00

As is mentioned in many outreach lectures, the Gemara in Berachos 32B says the following:

Hashem said to her (Israel): My daughter, 12 mazalos did I create in the rakia, and for each one I created 30 hosts. For each host, I have created 30 legions, for each legion I have created 30 cohorts, for each cohort I have created 30 maniples, for each maniple I have created 30 camps. To each camp I have hung365,000 myriads (10,000s) of stars corresponding to the days of the solar year. All of them I created for your sake.

This Gemara seems to be telling us how many stars there are in the rakia (which I have found is best defined as the view of the sky from the Earth). It is obviously rounding the number off because it was well known when this was written that the solar year is a bit longer than 365.25 days.

If you multiply out the groups, you get a total of 1.06434X10^18 stars. As many point out, this is within a few orders of magnitude of the current scientific estimates of the number of stars in the visible universe.

I thought I would add a bit to this idea as follows:

First, according to this Gemara, it is only mentioning the 12 mazelos of the zodiac. The zodiac covers a 16 degree band across the sky. Therefore for the total number in the whole sky, you must compute the surface area of the 16 degree band and apply the stars-per-degree^2 to the rest of the celestial sphere. This is pretty straight-forward, and one finds that the whole sky (assuming the same star density) yields 7.6476 X 10^18 stars.

Now, according to sceintific studies, there are anywhere from 10^21 -> 7 X 10^22 stars in the observable universe. These numbers are computed by taking a small strip of the sky, and counting the number of galaxies in that strip, and then assuming each galaxy has an average number of stars similar to our own Galaxy. They then use this to estimate the whole universe. This can be problematic for a couple for reasons.

First, besides the fact that we don't know how many stars are in earlier galaxies, we also don't know if we are seeing different galaxies to begin with. This is because through the bending of light around other galaxies, sometimes you can see two or more images of the same galaxy. This is referred to as an "Einstein Ring." Now, we can detect these, but it is entirely possible that there are other lensing effects we can't immediately detect. This phenomena reduces the number of galaxies in any view of the sky. Also along these lines are topological concerns. There is debate about the shape of the universe, but it seems that it is flat. This means that if the universe is finite (which is accepted) then the universe behaves like a pacman game in that if you fly too far in one direction, you will loop around and come back to where you started. With this in mind, it is possible that some the the most distant galaxies we see are actually the same galaxies we see elsewhere.

Second, assuming each patch of sky is equal to the others is highly extrapolative. A perfect example of why is found here. In this article it describes a huge, vast empty "hole" in the universe devoid of stars and galaxies that was not noticed previously. How many other holes there are we may never know for sure. These "holes" reduce the estimated number of galaxies in the universe even more, and if there are enough of them, could invalidate the extrapolation of one patch of sky to the next.

With all this in mind, the difference of 7 X 10^18 and 7 X 10^22, while enormous, is not conclusive. (For a quick example, say we find out that most old galaxies only have about 10^9 (1 billion) stars and that there are really only about 10 billion unique galaxies, then the number comes to 10^19.)

Scientific Confirmation of the Reason for Issur Yichud

2008-07-23T23:44:00.000-07:00

For this post, I get off easy, since FKM posted a nice post on the topic.

Check it out here:

http://fkmaniac.blogspot.com/2008/07/research-that-vindicates-issur-yichud.html

Basically, researchers found that when a man was alone with a woman, for a few min., his testosterone levels rose about 8% even if he did not find the woman attractive...

Cool Torah and Science Movie

2008-05-04T09:09:00.000-07:00

I found this movie on YouTube. It is a computer animated movie that deals with Torah and Science issues in an entertaining way (I think meant for children). It is made by Nathan Aviezer, author of "In the Beginning: Biblical Creation and Science", and "Fossils & Faith: Understanding Torah and Science" (both available at Amazon). "In the Beginning" is highly recommended by me, as it goes step by step through the Creation narrative and gives a possible scientific explanation of the events that are going on each "day". (He is of the opinion that each "day" was a "phase" of variable length). Anyways, that book is now an entertaining movie, where RamBam, Einstein, and Darwin fly through time in a space ship, so here it is (in 5 parts):

PART 1 of 5:

PART 2 of 5:

PART 3 of 5:

PART 4 of 5:

PART 5 of 5:

They can be found in Hebrew as well at: faithship's Videos

Where Does Rain Come From?

2008-04-28T23:36:00.000-07:00

As part of a "double dare" I have to start posting more frequently, so here is a quick post to get things rolling again.

The Midrash Tanchumah on Parashas Mikeitz states the following:

"And from where do the rains descend? Rabbi Eliezer says: All the world drinks from the waters of the Ocean. Rabbi Yehoshua said to him: But are not the waters of the Ocean salty? He said to him: They are sweetened by the clouds of the sky (rakia); for Rabbi Shimon ben Lakish said: Why are they [the heavens] called shechokim? Because they grind [shochakin] the waters and sweeten them, and after that, they descend."

There are a few interesting things to note in this passage:

1) Chazal seems to have known that the water in the Oceans rises up in vapor to form clouds, which in the process filter out the salt, and then the clouds blow onto land to give rain (I don't know if this knowledge was prevalent then or not, but it seems to me to be pretty advanced knowledge for that time).

2) The rakia includes the sky which contains the clouds, meaning that it cannot refer only to the "dome" or to space, etc. but is more inclusive.

3) Rabbi Eliezer says that ALL the world drinks from the Ocean [ok'yanos]. What about underwater springs, rivers, lakes, wells, etc? Some possible answers I can think of off the top of my head (i.e. may be totally wrong) are that for rivers, they flow due to the rain, for lakes, they formed from rain, or from when the land was gathered during creation, and hence from the same body of water as the Oceans (before they complained and became salty), and underwater springs and wells could be formed from absorbed rain.

Very Cool Movie/Music-SlideShow about the Convergance of Torah and Science

2008-02-17T22:19:00.000-08:00

I came accross this and thought it was pretty cool. One must excuse the "quote" of Rashi which is given, as I think it is a stretch of what Rashi actually says, however the rest of the quotes are very interesting indeed!

Stars, Angels, Space, and the Firmament

2007-12-18T22:38:00.000-08:00

According to the Abarbanel quoted by Rabbi Aryeh Kaplan, stars are in a way the "bodies" of angels. Not that the star-angel relationship is exactly comparable to the body-soul relationship, but there is a strong connection between the stars and angels.

This idea helps to show a Torah-Science parallel in the Midrash Tanchuma on Parasha Vayigash, sif 6.

The Midrash writes: "Rabbi Shimon said: The entire firmament (rakiah) is of water, and the angels of fire, and those ministering to Him of burning fire (lohait), and the water does not extinguish the fire, and the fire does not burn/consume the water."

Now, the definition of the rakiah is something that I have never gotten a definitive answer to.

According to this Midrash, it is completely made of water. However, as on the 2nd day of Bereishis, "water" may have multiple meanings. I have never heard a definitive explanation of the separating of water and water, etc.

Perhaps, the "water" that is being described is the fabric of space-time or the vacuum of space. Like the water we know here on Earth, the vacuum of space extinguishes fire almost immediately (since fire requires oxygen to burn). Thus, one (who is ignorant of current Science) would expect that all the stars should burn out and vanish immediately!

On the other hand, perhaps space is like a small amount of water, which here on Earth can be consumed (i.e. evaporated) by fire, in which case one (who is ignorant of current Science) could expect that the stars would consume all of space!

The truth as it now appears to be, is that the "fire" that stars run on is based on fusion reactions and hydrostatic equilibrium, and is not the sort of fire that requires Oxygen to burn. Thus, the stars shine away, and everything is fine.

This could parallel what this Midrash is saying. The firmament/water (space) does not extinguish the angels/stars, and the stars do not consume the space.

I don't have any idea at the moment what the difference in physical representation between the angels of fire and the "ministers" of burning fire are. Perhaps, "those who minister Him", are those objects in space that are immensely more powerful than stars, such as gamma-ray bursts, black hole flares, quasars, AGNs, etc.

Astrophysics of the Baal Shem Tov

2007-11-28T20:43:00.000-08:00

Updated (in bold) 11/9/08

Since I haven't posted in a while, here is a quick Torah-Science question with a very nice answer from the Baal Shem Tov:

In parashas Lech Lecha, we read: "And He took him outside, and said, "Gaze now, towards the Heavens, and count the stars if you are able to count them!" And He said to him, "So shall your offspring be!" (15:5).

I always had a question on this verse. With modern Astronomy, we can estimate the number of stars in the Universe. The number comes to anywhere between 10^22 to 10^25. This is a huge number. The number of people on the Earth today is roughly 6.5x10^9.

Now, if we are to take this pasuk completely literally, this would mean in the future, the population of the Earth will reach 10^22! I haven't done the calculations, but I am almost certain that that many people cannot fit on the Earth!

(Update: After learning through Isaiah, I found the pasuk which speaks of a "new Earth". Thus, the huge amount of people could fit on this new, potentially larger, Earth).

One possibility I thought of, is that the pasuk is only referring to stars that we can see with the naked eye. This however, doesn't help things because even in the best conditions, and the best pair of eyes, there are only around 2000-10000 stars the human eye can see from the Earth. (And there are a lot more than 10,000 Jews in the World!)

Which brings me to the Baal Shem Tov:

The Baal Shem Tov on parashas Lech Lecha (sif 27) states the following (in my free translation):

"In the name of the Baal Shem Tov the holy, remembered for a blessing, that he explains; That just as the stars when seen from the Earth (the bottom) are small, but above in the Heavens they are extremely big, so too the Children of Israel are seen as small in the lower, present World (Olam Hazeh), but in the Upper World (Olam Haelyon) they are extremely great (big).

This solves the problem. According to this Baal Shem Tov, the second part of the pasuk, "So shall your offspring be!" is not referring to the number of stars counted earlier in the pasuk, but rather is referring to the stars themselves.

This could also answer the question of why the pasuk needs to be split up into two "sayings" of Hashem. Although it would seem like both statements could have been combined into one longer statement, by splitting them up, Hashem is possibly telling us here that we will be like the stars, not like the number of the stars.

(As a side note, according to rough estimations, the number of stars in the Universe and the number of grains of sand on the whole Earth are the same (around 10^22), a possible parallel to elsewhere in Chumash where it mentions the count of the stars in the sky and all the sand together.)

Yerushalayim at the Top of the World: Fun with Google Earth

2007-08-23T12:29:00.000-07:00

My thanks to Yossi Nahavandi for pointing this out to me.

We know that the Gemara (I don't know where) states that Yerushalayim is the highest point of the Earth. Now, any survey of the surrounding hills will show that this cannot be taken literally at face value. Some say that it means that Yerushalayim in the highest spiritual place on the Earth. This is indeed correct, but I think one can show a more literal meaning to this.

If we look at the Earth as a perfect sphere, the "highest" point will obviously be the "top" of the sphere. However, since the Earth is in space, every point can be seen as the "top" - it all depends on one's orientation.

Now, another idea I have heard on this topic, is that Yerushalayim is the center of the civilized world, or that it is the center (or top) of the Earth's land mass.

I do not know of anyone who has performed a scientific center-of-mass calculation of all land masses on Earth to come up with a spot which is the "top".

However, with the help of Google Earth, we can see a nice result of this idea, at least visually.

Here is a picture of the Earth, positioned so that the Holy of Holies is directly at the center (marked here by the glowing yellow dot):

[For you techy types it is roughly at (31 46' 41" N) (35 14' 06.6" E)]

Now using an online tool (or simple math), we can calculate the exact opposite spot on Earth from this location, and we see that the Earth centered on THAT spot looks like this:

[It is at: (31 46' 41" S) (144 45' 51" W)]

Interesting, no? The opposite of Yerushalayim in smack dab in the middle of the Pacific Ocean, thousands of miles away from the nearest continent!

So, we see that there can be a possible literal meaning to the idea that Yerushalayim in indeed at the highest point on Earth, when land mass in considered.

(If anyone wants to take the time to calculate the true center of mass on a sphere, be my guest - be sure to give weighting to populated areas).

Midrashic Architectural Engineering Advice

2007-08-13T08:15:00.000-07:00

This is a question for all those frum mechanical engineers or architects out there:

The Midrash Rabbah on Eichah states:

"If any object's width is not a third of its height, it cannot stand!"

Although this must be true at some level, I am wondering if the pshat understanding is in fact correct? From what I remember, as long as the center of mass is above the base, the object will stand. I assume the Midrash is talking about a free-standing structure - i.e. no underground base or support. Also if we are talking about an object of constant density, does the stability of balancing the object become sensitive after the width-height ratio mentioned in the Midrash?

In either case, does anyone know of a deeper explanation (if any)?

Have You Ever Seen An Ox Eat Grass?

2007-08-13T08:08:00.000-07:00

Here is an odd Midrash that I would like someone to explain to me.

The Midrash Rabbah on Ruth Chapter 7 sif 11 states:

"There is nothing as vulgar, abhorrent, and outlandish as the sight of an ox eating grass".

My question is... why?

Is this telling us that an ox eating grass is more vulgar than maggots devouring a carcass?
Or vultures eating a dead ox?

If there is a deeper meaning to this Midrash it escapes me (as most would).

Any ideas?

(I ask this knowing full well almost no one, and perhaps mamash no one comes to my blog. But maybe someday someone buki in Maharal will stumble here and be able to answer my question. :) )

Isaac Newton's Religious Side

2007-06-19T09:19:00.000-07:00

Here is a link to a very interesting article on CNN by AP about documents on display in Israel showing Isaac Newton's religious writings including some Hebrew, a calculation of the worlds end time, the return of the Jews to Israel, the dimensions of the Temple, etc.

According to the site, I am not allowed to re-publish or distribute the article, otherwise I would just copy it here.

The link is:

http://www.cnn.com/2007/TECH/science/06/18/newton.papers.ap/index.html

UPDATE:

The official link for the web site of the exhibit is:

http://www.jnul.huji.ac.il/dl/mss/newton/

There you can find more information and see the original documents.

Processing the Universe?

2007-06-03T21:35:00.000-07:00

An open question on a Midrash:

In the Midrash Rabbah on Megillas Ruth, Introduction, Sif 7, it is stated:

"Everything (kol) that was created (bara) in [the] six days of Creation (bereishis) requires processing (asiyah)".

It then lists as an example of this, the fact that mustard seeds and lupines need to be sweetened, and wheat needs to be ground up.

My question is: How does one process a star or galaxy?

If ALL (kol) that was created in the six days needs processing like wheat does, then how do we process stars, comets, galaxies, lava, etc?

At first I thought this could be a hint at some kind of evolutionary process (Hashem Created things, and then they needed to be processed to get to where we are today), but since the two (really three) examples given involve human processing, I do not think it would be correct to say that.

Now, to be sure, some things we know now can be processed in ways we didn't know before.
A couple of examples:
- We use solar panels to process the light from the sun into usable electricity.
- We process Uranium in order to make nuclear power to provide electricity and large explosives.

But how would far away things in outer space come into play here?

Well perhaps, since we have gained so much knowledge of Hashem's Creation by observing outer space, that this is considered "processing" those far away objects.

Another idea would be, as per my QM post below, that when we observe the objects in space, we collapse their wave-function, and thus bring them retroactively into "real" existence. This could be the "processing" of those objects, and their use for us would be the knowledge we gain from observing them. This might be tied into the use of the term "asiyah" by the Midrash, where perhaps a connection can be made to the concept of the level of the world called "asiyah" in Kabbalistic thought.

I know it's pretty far-fetched, but I cannot think of anything else.

Anyone else out there have a good pshat on this?

Souls and Brains

2007-05-29T13:58:00.000-07:00

I just stumbled on a very interesting article on Scientific American's web site.
http://www.sciam.com/article.cfm?chanID=sa029&articleID=BE96F947-E7F2-99DF-3EA94A4C4EE87581

Here is a quote:

"The operation known as hemispherectomy—where half the brain is removed—sounds too radical to ever consider, much less perform. In the last century, however, surgeons have performed it hundreds of times for disorders uncontrollable in any other way. Unbelievably, the surgery has no apparent effect on personality or memory."

Now, according to most views, memory, intelligence, and personality are three areas that either reside completely in the soul, or are affected and changed by it.
For example, a person born with a angry temperament can work on himself, and become gentle and kind. This "working on it" is a function of the soul which alters the personality of the person.
Another example would be intelligence. At least the function of expressing intelligent ideas through speech ("man became a speaking spirit").

Now of course at some level these parts of our souls connect to the physical world somewhere in the brain, otherwise expressing them would be impossible.

According to this article:

"If the left side of the brain is taken out, "most people have problems with their speech, but it used to be thought that if you took that side out after age two, you'd never talk again, and we've proven that untrue," Freeman says. "The younger a person is when they undergo hemispherectomy, the less disability you have in talking. Where on the right side of the brain speech is transferred to and what it displaces is something nobody has really worked out.""

So in effect, no matter which side of the brain one removes, the person's memory is still there, their power of speech comes back after a while, and their personality stays the same.

Now, if memory is stored all over the brain, then the information in one half would be gone with its removal. And obviously the brain does not store memory in just the half of the brain that is bound to not be removed! We could suppose that the brain could store duplicate copies of memories in different locations in the brain, but this has never been shown to be true as far as I know.

Also, the ability to express intelligent ideas through speech is a hallmark property of a soul. The fact that it is "relearned" "somehow" on the other side of the brain is not remarkable to those who believe in a soul.

Therefore, I propose that barring any other explanation or experiment, this phenomenon could easily be considered as an additional piece of evidence that the soul is real and interacts with our bodies.

(Not that Torah Jews need such evidence, but it is always nice to see.)

The Cosmology of an Open Universe and Isaiah 51

2007-05-27T19:52:00.000-07:00

Just a quick Torah and Science parallel:

According to most cosmologists today, our Universe is an "open" Universe, meaning that it will never collapse back in on itself, and instead will expand forever.

This leads to what is called the "heat death" scenario for the Universe.

Basically, since everything loses energy in the form of heat, especially when two things interact, then the Universe will eventually be a huge cold blob of heat, with everything we see now either in a dissipated blob of energy or chunks of cold objects (such as black holes, rocks, and perhaps dark matter if it exists).

In the Midrash Rabbah on Megilas Ruth, it is stated:

"The heavens are destined to disintegrate, as it is said (in Isaiah 51:6):
For the Heavens will dissipate like smoke and the Earth will wear out like a garment."

Now, this cannot be talking about the spiritual Heavens, because those are eternal, therefore it seems to be talking about the physical Heavens, i.e, the Universe.

Smoke is produced by fire, a source of heat, and is dissipated in the air by spreading out indefinitely. This would be analogous to the stars energy, and light, and all hot processes in the universe slowly fading over eons until they are completely dissipated.

Earth wearing out like a garment could be analogous to the planet Earth after being cooled to the point that it becomes a super cold rock. A worn out garment still is mostly the same material, but diminished in its use to the point of uselessness. Earth without any of its internal heat, or energy from a star would be analogous to that, and be a "worn out garment".

So we see that if the Universe truly is an open Universe, as current Cosmology says, then we see a parallel to this idea in Torah.

40 days and nights equal one "moment" for Hashem

2007-05-18T13:10:00.000-07:00

Here is an interesting idea I came across in a book called "The Bible Unauthorized" by H. Moose:

It says in Tehillim(30:5): "His anger lasts but a moment"
and in Isaiah (26:20): "Hide yourself or one moment until the anger (of Hashem) is past over".

Now one event stands out from the rest in terms of Hashem's anger, that of the flood.
The flood was started by 40 days and nights of rain.

Another important event that took 40 days and nights was the giving of the Torah to Moshe.

One explanation is that Hashem extends the time it takes Him to do an act if the world would not be able to handle it in one moment.

In the case of the flood, the destruction occurring in one moment would have been too much for the world to tolerate, and in the case of the Torah, the whole Torah being given to Moshe in one moment would have been too much for him to endure.

According to "The Bible Unauthorized" (I would very much appreciate it for someone to find a source for this), a "moment", (not a rega, but rather the shortest time for a person to do a meaningful act) is (864/90) seconds, which is about 10 seconds.

Now, in one day we have (24hours/day*60min/hour*60sec/min) = 86,000 seconds.

The number of "moments" in a day is then: 86,000/(864/90) = 9000.

Now, from tehillim, we know that one "day" for Hashem is equivalent to 1000 years for us.

Now this next part is a little fudgey. What definition of "year" do we use? The solar year would be 365 days, and the lunar year would be 354 days plus a bit, which could be said to be 355 days (this also happens to be the gematria of the Hebrew word for year, shanah). So here, we take an average of 365 and 355, so a year for our purpose is 360 days.

So now, one "day" for Hashem is (1000years*360days/year*24hours/day*60min/hour*60sec/min) = 31,104,000,000 seconds.

We note that (40days*24hours/day*60min/hour*60sec/min) = 3,456,000 seconds.

So, the number of 40 day long "moments" in Hashem's "day" is:

(31,104,000,000/3,456,000) = 9000.

So we see that IF the year can be thought of as having 360 days, and IF the (864/90) has a real source, then we see that both our day and Hashem's "day" each have 9000 parts, and one of Hashem's "moments" is 40 days and nights.

A Quantum Mechanical Torah Thought

2007-01-04T14:17:00.000-08:00

According to "Orthodox" view of the Copenhagen school of quantum mechanics, it seems that things are only "really" real when observed/measured.

This leads to the "measurement problem".

The problem states that if it is true that particles are in superposition states and are not really "there" unless measured, but the measuring devices are themselves made out of particles, which according to the theory would "absorb" the uncertainty of the thing being measured, at what point is something truly observed and therefore real?

One solution is that observing requires something "outside" of the rules of quantum mechanics (read: outside of natural law), and therefore the human mind (read: soul) is the only thing capable of actual observation.

Hashem of course is also "outside" natural law, and therefore can also observe and hence make things "really" real.

This leads to an innovative way of explaining Bereishis:

When the Torah says "and Hashem saw", rather read it as "and Hashem observed", that is to say at certain steps along the evolution of the Universe, Hashem "sealed" and "made real" the Universe by observing the quantum wave function(s). Also "and it was good" could be read as "and it became real" (since having something exist is good!).

Thus, the 13.7 billion year history of the Universe takes place in 6 days. This is calculated either by counting the time during observation, or reading "night and day" as chaos and order, i.e. superposition and "real".

Why have these steps? Possibly to teach all the deeper lessons extracted from the 6 days, as well as setting the length of the week so there can be a Shabbos.

Today, either Hashem is constantly proving us with a wave function which we in turn observe and make "real" (thus being a partner in creation), or Hashem "observes" at every moment in order to make mostly everything "real" but our individual decisions, etc. observe things near and relevant to us, and thereby makes us partners in creation.

(This or course could all be sheker, but I thought it was a neat thought)

Torah for Free

2006-06-05T12:50:00.000-07:00

I have published a collection of Rabbi Yosef Gavriel Bechhofer's writings, as well as a pamphlet from Rabbi Aryeh Kaplan about the age of the universe. To download these for free or to order printed copies (non-profit), go here:

http://www.lulu.com/reuven