In Astrology, something doesn't become accurate or correct because it has been repeated a million times. At the time of writing this, Astrology is not part of "official science" hence authentic traditional text is the most reliable source of learning the same. Vedic astrology, thankfully still retains a good volume of text despite all the historical storms it has weathered.
Considering the sanctity of classical texts, 11th house IS the house of material gains but not house of friends in Jyotish. If you thought it was, you would be surprised to know that 4th house or bhava is the house of friends and relatives, collectively. Even 2nd house has a connection with them but with a difference. I will explain.
In classical text Brihat Parashar Hora Shastra (BPHS) chapter 13 verse 5, the Samskrit word "bandhu" (बन्धु) which is collective term for friends and relatives has been used for 4th house. The verse is very clear about significations of 4th house - "the 4th house signifies conveyance, bandhu, mother, emotional happiness, treasure, land and house".
Similarly, BPHS chapter 17 verse 5 goes a step ahead and calls 4th house as "bandhu-sthan" meaning house of friendship, says - "if lord of 4th house is a natural benefic planet who is aspected by another natural benefic planet while Mercury is placed in ascendant, the native is held in high esteem by friends/relatives".
So what's in 4th house of mother and emotional security that friends are also indicated from that house? It's no brainer that without emotional connection, there is no friendship. Oh yes, "networks" are your social or professional connections and you would be too naive if you confused your professional LinkedIn connections or social networks with real friends.
So, the house of friendship is NOT 11th house. But hang on, there is a twist.
Uttara Kalamrita in chapter 5 verse 3 used the Samskrit word "sakha" (सखा) which means friends for the 2nd house. So what's the difference between friends in bandhu versus sakha? There are two differences that I know about - bandhu could be friend of any age with whom one doesn't necessarily have daily/routune involvement in affairs. Sakha (or sakhi in female gender) on the other hand, is someone of same age group and with whom one has some kind of regular routine involvement, perhaps of some transactional nature (another signification of 2nd house).
Uttara Kalamrita however in chap 5 verse 5 mentions bandhu among 4th house significations, thereby maintaining consistency across the board as far as the house of friends in Jyotish is concerned.
Phala Deepika, another backbone classical text of Jyotish, throughout in chapter 8 which is about effects of various planets in houses indicates favourable friends if natural benefic planets are placed at 4th house whereas challenging (or lack of) friendships if natural malefic is placed at 4th house. As a matter of principle, Phaladeepika is unambiguously clear about the house of bandhu i.e. friends/relatives as 4th house.
Saravali, another major Jyotish classic in chapter 30 which is about effects of planets in different houses, repeatedly maintains that natural benefic planets in 4th house are good for relatives and friends e.g. in verse 41 uses the word bandhu for Mercury placement, verse 17 uses bandhu for Moon placement, verse 64 uses bandhu for Venus placement, verse 53 uses the word "swajan" (स्वजन) or "own people" for Jupiter placement in 4th bhava.
I think it's amply clear that if any human bonding (outside family) has to have emotional connection then 4th house is the primary bhava for the same. Friends, by usual definition would therefore be seen from that bhava.
How about 11th house in terms of friendships?
I think 11th house in modern times better shows network of either professional connections or sycophants (better understood as "chamcha" in Hindi) those who always sing "yes sir, yes sir, 3 bags full sir" for you. The focus here is necessarily rooted in some material gain or potential benefit. It's NOT about anything like emotional bond between two friends. 11th house, being 6th from 6th (bhavat bhavam) does not support human connections based on emotional value.
In fact, at many places I found the term "das" (दास) that's synonymous with servant being used for 11th house for example, in Saravali itself chapter 30 verses 72 (about Venus placement in 11th house) used the word "das" for 11th house, verse 48 (Mercury) used "bhratya" (भृत्य:) meaning servant, Verse 60 (Jupiter) used bhratya (भृत्य:) again.
These references to 11th house in classical texts don't connect friends with 11th house but to 4th and 2nd houses in different capacity which I have specified.
Author : Partho Banerjee