יום טוב שני

The Solar Year and the Constellations: How One Measures the Year Through the Stars

Introduction: The Difficulty of the Solar Year

Speaker 1:

Let's say, we're learning here, which chapter did we learn last night? Chapter 7? 8? 9? Where are we holding? Chapter 9, right? About the topic of... we finished 9, actually, the topic of the tekufot (seasons).

Ah, so I feel like I never really grasped, what's the story here? It's something like, there was some difficulty in knowing how long the year is? It seems like yes.

We think that you look at a light, and you know everything. Because we don't grasp it. And also, there are the years, it's a simple thing. People always say, ah, the lunar year is a bit complicated, you have to look at the moon when it comes, the molad. And the solar year, when is the molad of the sun? In my head something was lying that the gentiles...

Speaker 2:

Very good.

Speaker 1:

So how do you also know that there is such a thing as a solar year? What does that mean?

Speaker 2:

Okay, so I guess the word is, when it's gone through a year and you see again the same length of the day, that the day and the night are the same length, otherwise because... so today we have a clock, it's quite easy to see.

Speaker 1:

Very good, but just be clear. And actually in Chazal (our Sages) it says that this was the first thing that Adam tried to figure out. And it was a short day. A beautiful midrash. But except for one who lives in nature, can indeed see that the sun shines strong and light. It's actually not.

Let me tell you the actual history, or what Chaitchevitz told me, I don't know. So, we're trying to talk about this now.

So, it's actually, first of all, obviously, you can see that the days get longer. First of all, it depends on where you live. So, well, you live. But let's say...

So, in short, we think, I always learned in my head that the solar year is just a thing, even the gentiles know about it. It's not complicated. Turns out, it's about as complicated as the lunar year. And perhaps even more.

Why the Lunar Year is Actually Easier

Speaker 1:

The moon is quite easy. You can struggle with when exactly the molad was, but that the moon has a cycle, it's very obvious. You can see, everyone can look up and see. The moon is white today, it's the middle of the month, first it's about the four quarters of the month.

It's much harder to see. Ah, very good. You can, all these things you can see, but first of all it's much more compact. Say between exactly. Again, roughly that it's in the summer, that I grasp. But to know exactly, even within a few weeks, it's not so easy.

The Difficulty of Measuring the Length of the Day

Speaker 1:

Will I say now how long the day is. You have a clock, with having a clock you can easily calculate how the day is. But you didn't have a clock, the clock itself is based on the sun, so you actually have to check the shadows, it's very complicated.

And why do we notice because we have a clock? Because we don't live with the sun, we live with the clock. The clock has equal hours, it's easy to calculate relatively. But once there wasn't a clock, right?

So he shows me a few things that you can see, right? So it seems, for some reason, I didn't understand that properly. So, I'll tell you maybe like this, maybe you can think that it's hard to know, to make a calculation how long it takes. I don't know.

For some reason, I asked the chacham (scholar) today, why is it so? But for some reason, what the astronomers see, that is, there is, certainly, a normal person saw, it gets longer, it even gets colder, such sorts of things.

First of all, it can be that it's harder to imagine with this. You can see that today it got longer, but how... it doesn't always go the same size, right? Not every day does it get so much shorter, so much longer.

So, for some reason, it wasn't so easy to know when winter will come. By the way, this is something you need to know, a farmer needs to know when to prepare your fence.

The Constellations: The Most Precise Way to Measure the Solar Year

Speaker 1:

So, the most precise way, for some reason, truly, at the root the cause is always the same cause, but the thing that they found is the thing called mazalot (constellations). Very interesting, I don't know about this, the scholars also talk about it.

Speaker 2:

You should live which stars the sun comes out with.

Speaker 1:

Very good, you have it. The stars don't move, when will the stars stay in the same place.

Speaker 2:

Very good, very good.

How the Constellations Work

Speaker 1:

So the two you figured out. I wondered about this today. The answer is roughly like this: the stars, not just the stars, so there are very many stars and very many stars that you can even find such pictures, as if you connect two stars together. There are about eighty counted today. Eighty are counted today. That you can see in 88 if it's a number. This has nothing, these are just imaginations.

Speaker 2:

No, just what always you the pictures...

Speaker 1:

Not always. You only see half of it every night, right? It depends on which season of the year which you see at night, or where you live. Normally, any night you can only see half of the sky, but what you can indeed see any night, that's not entirely true.

At once you can only see half, but it rotates. That is, beginning of night you see different stars than end of night. The stars have a setting. With a rising just like the sun and the moon. The moon also has a rising, it goes up and down, you know?

Speaker 2:

If someone looks at the stars for a whole night, he'll see changes.

Speaker 1:

Exactly. It's simple, you can even make pictures. There are people making pictures, it rotates. It's a bit different than the sun, but it rotates. It goes up and it comes down. Also from east to west. Everything comes up from the east and it goes to the west. Okay? So?

Speaker 2:

Or the stars also go from east to west, so?

The Sun and the Constellations: How They Rotate Together

Speaker 1:

Exactly. Roughly so in a day, roughly in the same length as the sun goes, from east to west. Therefore, the gedolim (great scholars) today say the world rotates, one would have said, there is a galgal hamazalot (sphere of constellations), it rotates around every day from east to west, every twenty-four hours, roughly it rotates the whole thing.

Now, besides this there is the sun. The sun also goes every day from east to west, you can see that by day. But it doesn't go exactly... it's not on the same cycle exactly as the constellations. So it travels together with the constellation. But notice that every month, the constellations eighth, what are called twelve constellations, are eighth that they divided the sky into twelve precise parts.

Just as the Rambam said in Hilchot Yesodei HaTorah, precisely in that area were the pictures, they call it by the name of the pictures, but mazalot don't actually make the pictures. Clock time.

So the sun, every month stands in a different twelfth of the sky. It comes up with a different twelfth. As if it travels a bit faster than the... yes, a drop faster than the... do you understand what I'm saying? As if now to say it travels a bit faster than the constellations, so it moves with one degree every day roughly, 365 degrees, there are roughly 360 degrees, it moves roughly with one degree every day around that.

But the constellations are also in the direction of north to south, but they only move to the constellations, further must to the constellations. The reason why... it moves to from every day comes out a bit different, but the on the constellations on the thing.

Discussion: Why Does the Sun Move Relative to the Constellations?

Speaker 1:

Something, I didn't understand that clearly. Something, the reason why, this is not just today, the reason why I say they should be. Simple way that it's fast. The true reason is actually about this. It changes, it doesn't go so fast, it goes just as fast. But anyway, the world rotates, but actually about this it tilts a bit, about that it looks different. I didn't understand properly what the calculation is.

So, I don't know the difference, if they're both on the same sphere, if they're certainly different spheres. About that it's different, because they have a different... they go a bit differently. I didn't understand that clearly, I need to review that.

How One Notices in Which Constellation the Sun Stands

Speaker 1:

But what I understood is simple, I want to still... I simply understood, what does a person see? Simply, I go outside. The answer is like this: I see, you can't see which stars. In the day it's not dark, it's light.

So what do I do? I go at sunset and I see from the other side which it is, I make a calculation. Or I can see which star comes up right before the sun. You know that the sun is right after. These are roughly such calculations.

But you can see that every day the sun is in a certain constellation. That is, there are twelve constellations, there are twelve, yes, twelve months roughly of the solar year. So the meaning is simple that the sun travels with, the month it travels with that group of stars, with that area in the sky, in other words. That's the whole thing of the constellations.

Solar Year = Year of the Constellations

Speaker 1:

Therefore, this is a precise thing, this is awesome, much more precise, easier to see perhaps, or more precise than it's easier to calculate it than the other things that were discussed, that the day gets longer, all these things. For some reason it's easier. Therefore, the sages of the tekufot mazalot always calculated, the tekufot mazalot calculated, how the sun is according to the calculation, because you can know tekufat taleh (season of Aries), Nisan, etc.

Discussion: Do the Constellations Have an Influence on the Sun?

Speaker 2:

Did they only take it as a sign, or did they already take it more significantly, they held something that the stars bring the sun?

Speaker 1:

No, not necessarily. Again, how it works, as you always said, as you, there are two spheres, one carries the sun, one carries the stars, and it has something different, therefore it comes out. But the... not that the constellation has some pull on the sun. No, no, that's not necessary for me.

The idea of the constellation is, it's an astronomical idea. It's simple to calculate, this is the simplest way, a person can look in the sky, or perhaps the most precise way, I don't know precisely.

It can be that, I'll tell you, it can be that to calculate, as I say, to calculate how long the day is, you need special instruments, you need to be able to measure precisely, today you'll have a clock, once there was a sun clock, you need to calculate. Roughly you can, you can make a mark, true, but you need to make the mark.

For the constellations you don't need any mark. You simply need to see, go at night, see which constellation comes out before the sun, or which at sunset, the opposite, which is the first that comes up, you'll know that the sun is in the other from that. It's very simple. You don't need any instruments at all, it's supposedly the easiest way to know.

Innovation: The Solar Year is the Same Thing as the Year of the Constellations

Speaker 1:

So I didn't grasp this until today, that simply the solar year is the year of the constellations. The same thing. What does the solar year mean? It means that the sun travels through the twelve constellations throughout the year. And when it comes again to where it started, you know that a year has passed. And to calculate this precisely was hard to calculate. Precisely. Obviously roughly, what's ten days roughly, everyone always knew. But to be precise was a great...

Discussion: Why Not Make More Than Twelve Constellations?

Speaker 1:

I found this... let's say, why did they make twelve?

Speaker 2:

Let's say, if they made twenty-four it would have been easier, because every two weeks it would have been a different byte. I don't know why is it hard to calculate? I don't know why is it hard to calculate that he can always make three hundred and sixty-five lines on the sky with stars. Then one could have known to the precise day, or is it simply relevant?

Speaker 1:

Yes yes, technically you can, it's hard. You need to say not just clear stars that will be able to... it was indeed, it's good. The stars stand in one place, but you need to have a calculator. I don't know why it's hard actually to calculate. I didn't understand why is it actually so hard to...

No, I mean the word is because you don't calculate against living a specific star, because it's very hard for a person to recognize which star is a specific star. But a group of stars you can indeed see, and can see whether the sun is before the group of stars, in the middle of the group of stars, or after.

You need to stand there and... you simply need to stand there and calculate. You need to have a calculation, you need to know a few years, to know precisely, right? Not at once will you know precisely, because you make a small mistake it's ruined in your calculation, right?

So, the sages of the ancient nations, he has a chart of this. Not the person, but the person. He made a nice chart. How is it? The sages of the ancient nations, this was one of the things that they struggled with how long precisely is a year.

Generally, until this very day it's a question, to know precisely, and you need to calculate two on one year, ah, very good.

The Historical Development of Astronomical Calculations and the Dispute Between Tekufat Shmuel and Tekufat Rav Ada

The Difficulty of Precise Astronomical Calculations

I don't know why it's hard actually to calculate. I didn't understand why is it actually so hard to... No, I mean the word is because you don't calculate against living a specific star, because it's very hard for a person to recognize which star is a specific star. But a group of stars you can indeed see, and can see whether the sun is before the group of stars, in the middle of the group of stars, or after.

Okay, you need to stand there and... you simply need to stand there and calculate. You need to have a calculation, you need to know a few years, to know precisely, right? Not at once will you know precisely, because you make a small mistake it's ruined in your calculation, right?

The Sages of the Ancient Nations and Their Institutions

So, the sages of the ancient nations, he has a charge of this. Not the person, but the person. He made a nice charge. How is it? The sages of the ancient nations, this was one of the things that they struggled with how long precisely is a year.

Generally, until this very day it's a question, to know precisely, and you need to calculate, so on one year, ah, very good, to know one year is no great wisdom, it's approximately. But you want to be able to calculate for a thousand years around, and if you make a mistake of one minute, you're off by a few days.

Here begins the difficulty, our friends of the calendar, yes? We make the cycles of the years of Creation. If you're a few minutes on... but you'll understand the few minutes, because it can't be, one year can't be bigger than the small. All years are the same. If you'll add every year a few minutes, let's say... after a few years, today for example, as he says, today that we go with tekufat Shmuel, our calendar goes with tekufat Shmuel, we're already off, roughly twelve days from the sun. It accumulates, right? It adds up. All the time.

So, this is the wisdom, to know precisely. And for this you need... what do you need? You simply need someone to stand every day and calculate with you. I don't know if there's something a greater wisdom than this, but it's simply a... it's not easy. It's not simple that someone who doesn't know such a near roughly you can know, but to know precisely is complicated.

The Sages of Babylon and Their Astronomical Tradition

So, he has a long list the person found from the ancient nations how long each one said the year is. There was generally, once people thought that the year is three hundred and sixty days. Supposedly about that they have three hundred and sixty degrees and not three hundred sixty-five, I don't know, because they made the degrees.

Afterwards, finally found out that it's already three hundred sixty-five. Afterwards, this is the... three hundred sixty-five and a quarter, this is more or less tekufat Shmuel, right? And so on.

Chapter 10 - Another Calculation for the Solar Year

He says that the most accurate from ancient times was the Maya, that they had a truly punctual calendar, which was off by only seventeen seconds. Very interesting.

This is the interesting story, that once, let's leave aside the Maya, that's not relevant to us. What is relevant to us is that the ancient astronomy that existed in the time of the Sages (b'zman chachamim), was more or less the Babylonian, and afterwards the Greek which they took over from the Babylonians.

And Babylon was a very... he also brings Persians, I don't know who the Persians are, I haven't grasped it yet, but I know that the Babylonians, I said that the Sages of Babylon are already mentioned in the Book of Jeremiah, it's a very ancient thing. For hundreds of years they had lists of exactly when there is a solar eclipse, also something that had lists for hundreds of years of exactly how it works.

And each one was some sage. No, not one sage, rather it's an institution, that the king supported a kollel, there was some kollel that was engaged in this. And not, they wrote down, it was an institution, they wrote down over hundreds of years, so, they make averages, you know, each time one can have the calculation. So they had good calculations, and their calculation was three hundred and sixty-five and a quarter. This is approximately tekufat Shmuel.

The Historical Development of the Calculations

Hipparchus and Tekufat Rav Ada

Later came the Greek sage Hipparchus, he discovered that it's a bit better. It's only six and a half minutes off from reality. It's a bit less than three hundred sixty-five and a quarter, right? Four minutes less.

Later, this is approximately the calculation that is called tekufat Rav Ada. It's not exact, but approximately, because Rav Ada goes with chalakim, perhaps that's the reason? I don't know. Approximately, this is the calculation.

Al-Battani and the Rambam

Now, later there is, he says that in the Rambam's time there was already Al-Battani, and he made an even better calculation, even more accurate. That means, it was known that tekufat Rav Ada is also not accurate, but according to what he says it's only two minutes off.

And the Rambam says, he has an even better calculation, it's only four seconds off from reality. We know exactly, that means they calculated by hand, the sages of our time. Okay? Also, the sage should say that it actually changes, the earth rotates a bit, okay, a second every year or something. I don't know, I don't know, what's the story with that? So that's...

The Dispute Between Tekufat Shmuel and Tekufat Rav Ada

The Author "Avidan" and His Approach

I don't know, what is it? There is a question from the Rishonim, that's what the person is talking about. I'm just saying more or less the person's Torah, a rav, whatever his name is, he considers himself terribly clever. Not Ya'avetz, no, Ya'avetz says more Chasidic Torah. This person, he's called, it's a fake name just. Avidan, that's not his name. Amitai is not usually a real name. There are people called Navitai, but I don't believe that's his name.

The Question of Shtutim V'havalim (Foolishness and Nonsense)

There is the question from Chazal, what is the shtutim v'havalim? But the point is that the reasoning is seemingly correct. There are, we have in our sefarim of ibbur, books of astronomy from the Rishonim, there are the two calculations, called tekufat Shmuel and tekufat Rav Ada.

If one wants to present it, tekufat Shmuel is more or less the calculation of the Babylonian sages, which was accepted. Tekufat Rav Ada is approximately Hipparchus's calculation, right? The Greek calculation is a bit later.

The Historical Understanding: Shmuel and Rav Ada in Their Times

And therefore, a normal person would say that Shmuel was indeed from the first Amoraim, he didn't yet know, perhaps he did know, but he didn't know about the calculation of the Greeks. In his region, he lived in Babylon indeed, there were the sages, not in Babylon, the Parthian Empire, whatever. Sorry, the Sassanians. In short, he held an astronomy, he didn't have everything. He knew his calculation in his time (b'zmano).

Later was Rav Ada who is much later, according to what they say, he knew that later he had the more correct calculation.

The Proof from Maor Einayim: The Calculations Were Correct for Their Times

This is what he says, and he has a nice proof, not him, he says further from Maor Einayim, whatever, that it's so, because the calculation of Shmuel is correct for his time. That means, since the error accumulates, if one calculates the time of Shmuel, and in the time of Shmuel one makes the calculation of the tekufah according to this calculation... one must be smarter than everyone.

No, no, no, it's correct. Since the error, if this is a small error, we're talking about a few minutes of error. In total four minutes is the difference between Shmuel and Rav Ada, approximately, right? Shmuel is three hundred sixty-five and a quarter, and Rav Ada is four minutes less. Four minutes less, right? It's only four minutes difference. It's a bit less, a bit less, a whole day's difference.

Take a few hundred years, I don't know how long, whatever. So, in the time of Shmuel according to his calculation it came out correct. And in the time of Rav Ada his calculation came out correct. Later on they caught that it's also not correct. Because more time passed, we saw that more errors accumulated.

So therefore, very nicely one can see that there is indeed a difference in the tekufot, seemingly the two things. This is what today's, the enlightened Acharonim have said, and so it is seemingly correct in reality.

Approaches in the Rishonim

The Approach of Rabbi Chiya: Tekufat Shmuel Publicly, Tekufat Rav Ada Secretly

In the Rishonim we find two approaches. There is the approach that we already said that Rabbi Chiya, I don't know who wrote it, and others all said that essentially tekufat Shmuel is only approximate, tekufat Rav Ada is the accurate one, and it was that the language was tekufat Shmuel b'farhesya, tekufat Rav Ada b'tzin'a (Shmuel's tekufah publicly, Rav Ada's tekufah secretly).

Now, the problem is that they meant that Rav Ada is indeed accurate, they didn't know that Rav Ada is also not accurate. Therefore they said this, they said that an approximate calculation was made for the public, but in truth there was a secret.

The Rambam's Approach: It's a Dispute

The Rambam, who knew that tekufat Rav Ada is also not accurate, didn't say that it's so, didn't say that Shmuel essentially also knew Rav Ada, rather he said that it's actually a dispute, and the Rambam even said that the gentiles also have this dispute, don't get lost, it's a dispute. They didn't know, today we know better.

The Chazon Ish's Approach: Halacha L'Moshe MiSinai

The Chazon Ish and such other pious ones are terribly upset, and they are very interested in saying that all are halachot l'Moshe miSinai, all calculations, everything everything. So? Yes, very funny. It's not about "ki yachach mitachtecha mimunatecha," because the Rambam says so... No, about the entire halacha.

He is very worried that our calendar goes according to a falsehood, according to something that is an error, and he is terribly concerned. The Chazon Ish was terribly concerned to say that the Sages didn't know something, even a science that we know clearly, even the things that we know, even though there is the Gemara in Pesachim. He was very against this, therefore he invented all kinds of halachot l'Moshe ben Sinai with things.

But he brings it like this. Rabbi Asher, Kashya Shlomo, "v'yada d'tekufat Shmuel b'chlal haTorah. You see the piece about nitnah ben Sinai, d'tanhag bahem b'mah shemu'am, l'nakesh l'edim one doesn't go with that". So regarding what does one conduct oneself with tekufat Shmuel?

In short, it's not... it's very not... not clear, because the entire nafka mina of tekufat Shmuel is regarding Kiddush HaChama.

The Problem of Kiddush HaChama (Birkat HaChama)

What Is the Point of Birkat HaChama?

If one wants to find a halachic difference, because the opposite, tekufat Shmuel is only... why did they make tekufot? To know Kiddush HaChama? Seriously? It doesn't make sense. Tekufot should be known when the year will be.

No, no, no, besides the yearly cycle, does the sun have another cycle? Not from north to south... No, another cycle is just a calculation. The twenty-eight is only... if I understand correctly, it doesn't do anything. The sun doesn't change anything. The only thing that changes is that we... again, all these calculations which is how one is human, other... other cycles one to the second, right?

What is the tekufat hachama? Right, not chama relative to levana. What did we learn? Birkat HaChama is simply the sun with the days of the week. That's all it is. I don't know what's the point of it.

Every ninety-eight years Nissan begins on the same, not only the same day, on the same day and at the same hour, as it began on Shabbat Bereishit according to the calculation that we also thought. What's the point? I have no idea. It's fake. I don't know.

Birkat HaChama Is a Human Invention

It's very interesting, because what is there to see? Okay, perhaps the blessing is made on the fact that one should be able to make calculations. It's simple. It's simply a human invention that was found. Yes, it's a... all kinds of fears are added to make a mitzvah.

Ah, you would have wanted to make that blessing? Okay, ma'aseh bereishit goes with an order, with a calculation. But one can... the sun doesn't actually do anything in that blessing.

Tekufat Rav Ada – Another Calculation for the Solar Year

End of Chapter 9 – Tekufat Shmuel

Speaker 1: In total that the days of the week match with the same... because one says according to the calculation, there is indeed four times seven. That's the whole calculation. I don't know why that's so interesting.

It doesn't make sense to say that because of this Shmuel made the calculation, he made the calculation for the calculation for astronomy, and it was a bit wrong. What's bad that it's a bit wrong?

The other person is also about the other thing that I didn't actually talk about the calculation of the circle and square, and the calculation of pi, which stands in the Gemara that it's one to three and it's a bit more. And he says that it's actually what they thought then. What do you want from us? Seemingly he's right, and it's not a problem.

No, one doesn't need to be foolish. I'm not accustomed to being more foolish than the standard. One must be approximately the same. You must be every sage of the inheritance of Israel, you are an expert in halacha, in Kabbalah, you must also be an astrolabe, it's not possible, it's above the natural way.

One must want inheritance, it's not a problem. On the contrary, as the Rambam says, "nachlu chachmei Yisrael v'gam nachlu chachmei umot ha'olam" (the Sages of Israel disputed and also the sages of the nations of the world disputed). Presumably, the sage who held this way, saw the proofs of the one who says that way, and well, it appealed to him, the second is exactly the opposite. It's not that it's extreme, you understand to say, it's nothing interesting here. Okay, enough.

This is up to here what I understood until now, the topic of the tekufot. And enough. What we call tekufot, simply the quarters of the, when the sun is the longest, the shortest, and so on, as you said. Enough.

Why is it so interesting to know which day of the week these things can be? I haven't understood that yet at all. But these are all the calculations of Chapter 9. They are more or less only about this.

Afterwards there is Chapter 10, and another chapter which is simple. Afterwards, Chapter 11 begins the real astronomy. If you want, we can learn it. Yes. Okay.

Chapter 10 – The Solar Year According to Another Calculation

Law 1: The Solar Year According to One Who Says It Is Less Than a Quarter

Speaker 1: Chapter 10, let's learn. Okay? The solar year, what is there?

Speaker 2: Do you have a thought? What are the words here? Another calculation for the solar year.

Speaker 1: Ah, the real one, the correct one. Earlier we spoke about tekufat Shmuel, now we're speaking about a more correct tekufah. The Raavad doesn't call it tekufat Raavad. The Raavad is just an invented thing. It's not a clear... The Rambam already says there, I don't know.

Speaker 2: Yes, it's a Baraita brought in the Rishonim, I know.

Speaker 1: Okay, this asks our master... No, sorry, I'm in the wrong place. The solar year, I went to the wrong place. Well, where is my... Not there? No, not good.

What is the great virtue of knowing these things, to calculate tekufot and mazalot? Simply to know when how we stand in the year. Perhaps one can say today that a... "ki chochmatechem" (for this is your wisdom), whoever has a good watch understands well. It's such a bit of wise conduct of a person, that he can reckon with time, something like that, I don't know.

Okay, Chapter 8, 10. The solar year according to one who says it is less than a quarter from the Sages of Israel. What? It's interesting, there is already there, "l'mi mei'chachmei Yisrael she'yomar" (according to one of the Sages of Israel who says), yes? What does he mean? That it's less than a quarter of a day?

Speaker 2: Quarter means 365 and a quarter.

Speaker 1: But the earlier Sages, that there are Sages of Israel who say it's a quarter, there is a measure less than a quarter. Okay, so the one who says it's less than a quarter, what does he say? Like a quarter of today's Sages of Israel. That is to say, he will also say that the length of a year is three hundred and five... what is the less than a quarter? That's what he just wants to say, what is the less than a quarter?

It's 365, five hours, 997, and 870 chalakim? What is a rega? A new thing, have you never heard of it? A rega.

Speaker 2: No, a rega is one of seventy-six in a chelek. I know.

Speaker 1: 5? I need to make numbers. 997? And 48, rega? What this is a 67th on... 900 chalakim, one doesn't remember anymore how much it is. How many chalakim are there in an hour?

Speaker 2: 800.

Speaker 1: 800. Ah, it's about half an hour. Whatever.

Discussion: The Difference Between the Two Calculations

Speaker 1: According to this calculation the calculation comes out differently. He won't calculate the calculations of the cycle of the moon and the sun according to this calculation. It comes out according to this calculation, the addition of the solar year to the lunar year is not eleven days, but... ten days and the end of ten and most of fourteen chalakim, and seventy-eight he brings others. The sign is 35 14 21 101 48.

How did it say earlier the addition of the solar year to the lunar year? I don't remember.

Speaker 2: He held a different number.

Speaker 1: Yes, that is seemingly in chapter. Chapter 6, very how did we learn the calculation of nineteen years? Perhaps he says, 6 a different one? Yes. Chapter 6? Chapter 6 end or what? No, why? It remains... No, that doesn't speak about this. How did it say the... He doesn't say how it was. Already sir, it's already not a moon. Whom do we ask about it?

In the solar year, three hundred and sixty-five and six hours. It comes out that it's hours and days and one and an hour, and four chalakim, right? That's the number according to the calculation that was spoken about earlier of a quarter day. And according to what we learn, right? 11 days, 21 hours, and 204. 1080, there are one thousand and eighty. There are one thousand and eighty chalakim in an hour. I'm making a mistake. One thousand and eighty.

And here, according to this calculation how much is it? How much is that? 10 days and 21 hours. 10 days, 21 hours, and 121 out of 1080. 48 out of 67, correct? It's less, right? It's a bit shorter than that one. That one was 204 chalakim in the end, and this is 121 chalakim. These are the main chalakim. Here it says 47, here it says 48, it could be in the end. Yes, 48.

Speaker 2: What's the difference?

Speaker 1: Yes, yes. No, not the earlier one. The earlier one he added here the rega'im. The rega'im weren't there before. Earlier there was only the topic of how long is the solar year, which this was 21 and 204, right? The difference between the solar year and lunar year. Correct? Yes. Is there a difference here? Here it says how many chalakim is it? Both are 21 hours, right? Correct?

It's only a difference of about one hundred chalakim. Here it has two hundred. Four chalakim, here is one hundred with... four such chalakim, no? One hundred with one hundred and twenty-one chalakim, okay? Correct? About a difference of eighty chalakim, with more rega'im with things.

And according to this it's a bit shorter, that's the difference. They caught that according to the second tekufah, the approach of Rav Ada as it's called, the approach of Rav Ada, the year is a bit shorter.

The Great Advantage of This Calculation – No Addition in 19 Years

Speaker 1: It comes out, according to this calculation there is no addition in the nineteen years. The nineteen years match exactly. And one makes seven leap years in nineteen years, it comes out exactly the other one comes an addition, of about one hundred chalakim.

What was said that something remains left over after each year, an hour with something, and after each nineteen years something remains? According to this calculation nothing remains left over, it's on this one reason why it's a better calculation, right?

And according to this calculation also, there are different numbers between the tekufos (seasons), because the numbers are smaller. Consequently, between one tekufah it's not 91 days and whatever it was there, but 91 days and seven hours exactly, right? Correct? Just 91 days with... with... yes? And the calculation from between one tekufah and the next tekufah is also a different number. 91 days... and 7 hours, and 519 chalakim, and also rega'im, 31 rega'im.

You see then why the calculation is more complicated, you need rega'im also, true? Right? Why it's more complicated.

Halacha 2: The Same Calculation According to the New System

Speaker 1: Okay, for us according to this calculation it's the same thing. According to this calculation you'll know when one tekufah, you'll calculate from this, you'll know the same thing, just as was done in the previous calculation. From here you calculate the number of days, you arrive at the next tekufah. Correct.

And another thing, according to this calculation, there's something different. For some reason, the first molad is also calculated differently. The first tekufah is also calculated differently. Earlier, remember, we said that the first tekufah was approximately seven days before the first molad.

According to this calculation they say differently, that tekufas Nissan, according to this calculation, was in the first year, before the world Nissan, the six hours and six hundred years and six hundred, and two why less? Because the reason why the calculation was made that way, at that time you would have had too much left over... that's somewhat the reason. Rabbeinu le'olam, lekol sha'ah in the shoresh it comes.