The Rambam has an idea of what constitutes the Oral Law that gives some support to the idea that learning Physics and Meta-Physics is an actual obligation.
And it is important to know whether this is an obligation or not because of the concept of Bitul Torah.
And the idea of Bitul Torah is that it is not just a mitzvah to learn Torah but it is a sin not to learn Torah. ביטול תורה כנגד כולם. That is we have a statement from that sages talking about the worst types of sin (גילוי עריות שפיכות דמים עבודה זרה) a person can do and then they and on the end of this discussion that not learning Torah during a time period when one could be learning Torah is the worst of all sins.

In the Rambam's  Laws of Talmud Torah about how one should divide his day, the Rambam says  הענינים הנקראים פרדס הם בכלל הגמרא "The things called Pardes are in the category of learning Talmud"
And that obviously refers to what he said at the beginning of Mishna Torah the the subject matter discussed there is called "Pardes." [Orchard]  That means the Rambam understood "Pardes" to means Physics and Metaphysics and he considered learning these two subjects as a part of the mitzvah of learning Torah. [There is no surprise here. The Rambam in the Guide says what the sages means by the work of Creation and the work of the Divine Chariot the Greeks called Physics and Metaphysics. And if you put his ideas about this in Guide together you get the same conclusion]

I looked into the history of Pultusk, Poland.[http://yizkor.nypl.org/index.php?id=2548] And I can see that the idea of public school [secular studies] was frowned on by the some religious people.  But  regular Jews did not share that attitude. For example when my grandparents came to the USA they sent my Dad to public school and later he majored in Mechanical Engineering at Cal Tech worked on almost every top secret project that was around, the U-2, the Orion, SDI, etc.
Clearly there were and still are plenty of Jews that think Science and Math are an important part of Torah study like the Rambam.

But as far as things are today  both ultra orthodox religious schools and also public schools in the USA are extremely bad. If I had the choice I would home school my children in Torah and natural sciences. And if that was not an option I would send my children to some kind of Religious Zionist school like Bnei Akiva [or whatever they are called in the USA]

At the Mir in NY the books of Breslov were in the Musar section.
And that was during the era right after they got to the USA from the Mir in Europe.
That means the books were considered a regular part of the cannon of Musar books by Reb Avraham Kalmonovicth, and the Mashgiach Reb Feldman.
And it goes without saying that Breslov was an important part of the world view of the Mashgiach that came after Reb Feldman that is Don Segal, the Mashgiach of Ponovicth.
And I specifically asked both Don Segal and Leibel Berenbaum about this subject. And this was definitely in the context of the\ issue of the excommunication that was signed by the Gra.

The excommunication is as valid today as it was when the Gra signed it.

Certainly no one thought that is has expired. And in a large degree this seems also to have been the opinion of Rav Shach of Ponovitch was was the Gadol Hador at that time.

But the books of Breslov are kosher

My path is a balance between different things.
I can't justify everything here right now and also I can't claim that everyone should be doing everything on my own private list.
But at least for those who are curious here is my basic list of things to do.
(1) Math or Physics session for an hour after I get up, and had coffee and tea in the same cup and folic acid.
(2) A session of Gemara (Talmud) Rashi and Tosphot with a learning partner.
(3) Music session.
(4) Rosh HaShanah  in Uman.
(5) Musar.[Jewish Ethics] That could be classical Musar or Musar from the school of thought of the Geon from Villna or his disciples. And try to fulfill what the books of Musar say to do especially the Gra. [Musar has two parts: (a) Classical Musar like the חובות לבבות Obligations of the Heart and also  (b) a Israel Salanter part that includes books of his disciples like Navardok.]

The above I do as a kind of service towards God. But sometimes there have been practical benefits  also. There was for example a time I was in the Mir in NY and was getting a monthly salary. But in general I try to intend what I do to be not for personal benefit.

Also, it seems to me that my wife, Leah came to me to NY mainly because I was at the Mir. That is I think she was attracted to me more by what I was doing [learning Torah] more than by who I am, or my personality.

If you do any sin from the set of all sins in the Bible where it says he that does such and such will be cut off from his people, you bring a sin offering to the temple in Jerusalem. That is a she goat or a she sheep. (Leviticus 4) If you did idolatry by accident you bring only a she goat. Numbers 15
[Examples, Shabat, sex with close relations, sex with males, walking into the Temple without having gone to the mikvah and the ashes of the red heifer, eating a sacrifice before having gone to the mikvah, four kinds of service to an idol burning, pouring, sacrifice, bowing, or a service special to that idol.]





 If a person bows to a statue that he forget was an idol,  he is not liable a sin offering. What is the difference between this and if a person forgot it is the Sabbath day?

I want to answer that the difference is that Sabbath he is expected to remember from the very beginning of the week. There is a degree of liability in just forgetting Shabat all by itself and if furthermore he acts  on that forgetting then he is liable.
Idols one is supposed to forget.

In more detail here is my idea:
Abyee  and Rava argue if serving a false god from love or fear is liable. To prove his point Abyee finds any random place in the Mishna where the idea of serving an idol accidentally is liable. And he tries to go through the different possibilities what that could mean until he reaches to the point that it cant mean anything but serving a false god from love or fear. Then Rava says it means he says serving it is allowed.

Why don't Abyee and Rava both say serving a false god accidentally is the exact same case as Shabat? What is an accident on Shabat that one is liable for? He did one of the 39 types of work because he forgot it is Shabat today.
Say the same thing about idolatry. He knows idolatry is forbidden by he forgot this particular statute is an idol. An example would be when he was at the ceremony consecrating the idol but got mixed up later and forgot that he was there and thought he was at a different ceremony on the other side of town celebrating a statute built to honor a king.
That is the question my learning partner posed.
My answer is that Shabat he is expected to remember, not idols. He is not supposed to be thinking about idols all the time. So if he forgot about an idol he did a mitzvah.

I want to suggest a connection between good character traits and mitzvahs.
The main points are the Reshash ר' שלום שרבי. To him the traits are the actual soul of a person.
The subject of the soul is contained in the Eitz Chaim of Isaac Luria is great detail. But I forgot the whole thing. But also Reb Chaim Vital goes into some detail in his Musar book Shaarai Kedushah.
His idea is that in fact there is a connection. And keeping the mitzvot brings light and sustenance to the soul.
1) Also to Reb Chaim Vital  and the Chafetz Chaim the main purpose of the mitzvas is to bring to good character traits.
2) But in theory good character and mitzvas might be completely separate. You could in theory have someone keeping all the mitzvas with 100% perfection and have  bad character.[This is well known from the Ramban about מנובל ברשות התורה]
3) This fits well with the Rambam that the purpose of mitzvas is divided into several sub categories, one of which is in fact to bring to good character.
Character here means what men want from other men--to be a man. That is,-- to be someone you can trust in an emergency. When the chips are down and you are with a small group of men fighting for survival, then good character means someone loyal and trustworthy and has the skills that contribute to the group. If you put him on  watch to guard the perimeter to guard from other groups of men that want what you have,- you don't want him sleeping on the job. Character in terms of women means a wife you can trust. Not someone who will betray you for gain-- unlike the vast majority of women today.

Places that are openly connected with the path of the Gra the Villna Geon you can see Torah being studied and kept to a high degree of accuracy.

 I would like to propose that to get to the Torah it is impossible expect by means of the Gra.
I admit that on the face of this, it seems ridiculous. But I think I have see enough evidence to make this proposition  believable.

What this means is that if you look at places that are openly connected with the path of the Gra the Villna Geon you can see Torah being studied and kept to a high degree of accuracy. But outside that perimeter you see nothing but catastrophe.

The Gra, The Villna Geon, held is is an absolute obligation to go through the Oral and Written Torah.

Once he was with his disciple Chaim from Voloshin and saw some person in a inn who was not keeping Torah. The Gra said he will have to give an account of why he did not learn the secrets of the Chariot [mystic aspects of Torah] also.

We know that there is a statement in the Talmud that when a person goes up to stand before the higher court of law in Heaven to decide his fate, he will have to give account  and answer these questions:"Did you learn the Written Law?  [the Old Testament]? Did you learn the Oral Law?Did you finish the Mishna? Did you learn the Talmud? Did you learn the work of the Divine Chariot? Did you do your business dealings with honesty?"

The Gra understood this to be literal. There will not be an excuse on the day of judgment for a person to say, "I was not religious."
And further he held that one does not need to understand every word he learns. Sometimes people say that the Gra held that one needs at least to understand the meaning of the words. But f you look in the new edition of the אבן שלמה that brings down the sources from the actual language of the Gra you can see that is not so. You can just say the words and what you don't understand in this world they will remind you of in the next world. The main thing is to have gone through every single last word of Gemara, Rashi, Tosphot, and Maharsha, and the Jerusalem Talmud with the Pnei Moshe, and also all the writings of Isaac Luria.

I don't want to make it sound as if I have done all this. I am embarrassed and ashamed to admit that I am still in the middle of this process. And even the small amount of time I have to learn Torah I spend most of it on a tiny in depth session with a learning partner. So I am well behind schedule. So I hope at least I can explain this subject to others that might be able to take up this project.
[To some degree I have an excuse that my time in limited. I also have to give violin lessons and other kinds of activities in order to pay the rent.]