You are not alone in asking this question. Many struggle with trying to find meaning and inspiration in the formulated prayers and in the formal structures like minyan and synagogue attendance. There have been many attempts throughout Jewish history for those who sought greater inspiration and meaning—many within the traditional framework and many without.
The simple answer to your question is “Yes,” there is value to attending a daily organized service even though you are feeling alienated.
There is a halakhic (Jewish law) obligation to do so. Prayer, from a traditional perspective, operated on two levels. It is a religious obligation that prescribes what, where, when, and how to pray. It is known as avodah she-ba-lev, service of the heart, but it is an avodah, a duty and responsibility. But prayer is also a spiritual, mystical experience, the prayer not of the lips, but, as Rav Kook suggested, the prayer of the soul. That requires inspiration. Jewish prayer finds its ultimate expression when the two are merged.
Like any skill, practice and experience help bring us closer to perfection and appreciation. Why is the minyan so alienating? Perhaps it’s a problem with the minyan you are attending and you should try others. Perhaps it's that you haven’t yet learned the rhythms and patterns of communal prayer and, with more investment of time, energy, and learning, you will find meaning, purpose, and understanding.
Jewish prayer is fundamentally tefillah ba-tzibbur, communal prayer. We pray as part of a collective for the needs of the community. While prayer can be and needs to be personally meaningful, it should not be selfish. Praying with a group reminds us of that.
There are prayers—the most important ones—that we cannot recite privately: kaddish, kedushah, Torah reading. These are experiences and opportunities that we should not sacrifice.
There are times throughout communal prayers that we have opportunities for private reflection, petition, and gratitude. Seek them out and take advantage of them.
Jewish life is not solitary. It is about community. Connecting with the other members of the community for a sacred purpose binds us together is special, unique, and holy ways.
There is no reason you cannot do both. Pray with the minyan. And find opportunities to pray—daily blessings, recitation of Psalms, Torah study, etc.—that speak to you personally.
These are just a few approaches to your question. I welcome you to the group of us that yearns and seeks for a meaningful prayer experience. Some of us are blessed with the divine connection daily. Others at solitary moments in our lives. King David wrote in Psalms 27, “Hope in the Lord, Strengthen your heart, and Hope in the Lord.” The Midrash explains that “Hope” hear means prayer. David tells us to pray, and if we feel unanswered or uninspired, strengthen ourselves, and pray again. Perhaps the best prayers are in the attempt to pray and the desire to pray. There is reward in that as well!
There are several reasons why davening with a minyan is preferable to davening on your own:
1) There are some parts of the service -- Barkhu, Kedushah, Kaddish -- that you may say only in the presence of a minyan.
2) Because of this, mourners and those who have yahrzeit need a minyan to say Kaddish, and so attending a minyan makes it possible for them to do this. It also makes it possible for those who do not know the service to fulfill their obligations to pray three times daily by answering "Amen" to the leader's blessings -- and probably eventually to learn the service. For that matter, you yourself may learn the words and proper melodies of the various times of the year when davening in a minyan if you do not already know them. Fulfilling the Rabbinic enactment to hear the Torah read on Monday, Thursday, and Saturday mornings as well as Saturday afternoon also may take place only in a minyan. The failure to take these communal needs into account makes you a "bad neighbor," according to Maimonides.
3) Davening in a minyan will make it less likely for you to make mistakes, especially on days when the litrugy we are supposed to say is different in some way from the ordinary liturgy.
4) We are by nature people who need people, and davening together helps to bond us to the davening community both religiously and socially.
There are undoubtedly other reasons to daven in a minyan beyond those noted above. These factors make it desirably that one's regular regimen includes davening with a minyan. That said, if on occasion one cannot do so, it is clearly better to daven on one's own , skipping the parts that you may not say without a minyan, rather than not daven at all.
For a Rabbi – please forgive me – this query has echoes of the trick question, when (heaven forbid) did you stop beating your wife? By which I mean a Rabbi would always want folks at the minyan, even as in many communities. There is no shortage of days when a significant amount of scrambling, pleading (dare one say, praying) is required to assemble for community worship.
As to the substance, several responses come to mind.
1.Pirkei Avot points out that a mitzvah not done for its own sake may lead to that desired level of intent (i.e. for its own sake), but not doing at all likely concludes with our not acting, or in this case not worshiping whatsoever.
2. As one with a regular worship life, I am very much aware that there are times when the prayers are only being recited by me, yet being part of a practice means there are times – not always anticipated or expected – when the prayers and the community come together, more precisely, penetrate into and inspire, challenge and grow me. But if I only showed up when I felt like it, I well might never show up at all, and while the community might be poorer for that, I know I'd be poorer because of that. So, even though there are times – even frequent occasions – when I "don't feel like [I am] connecting to structured prayer," I have found that the more I participate in communal worship, the more I need, want, learn from, connect with, value and am inspired by, in and through communal worship. Be it Carnegie Hall or moments of transcendence, the method is still the same. Practice. Practice. Practice.
3. Assuming that clear moments of holiness are rare or never, at least not yet, there is still another argument for attendance at the daily minyan. Namely, your presence makes it possible for others to fulfill their sense of obligation and privilege, something they may not have been able to do without you, and there may come a day when that favor comes back to you many times over.
In brief, keep trying, keep praying and write back again.
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