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I had heard that a dish that's 59 parts pareve to 1 part milchig to 1 part fleishig is pareve, as the fleishig portion is batel by a 1:60 ratio, as is the milchig portion.
My question is twofold. First, is this halachah accurate? I find it odd that one can use batel b'shishim to make a mixture pareve, though I suppose it's no less odd than using it to turn fleishigs into milchigs. Second, im timtzeh lomar that it is indeed a correct halachah, what is the source for it?
קדירה שיש בה נ"ט זיתים היתר ונפלו בה שני זיתים אחד של דם ואחד של חלב כל אחד מצטרף עם הנ"ט של היתר לבטל חבירו וכן כ"ט זיתים של היתר שנפל בהם כזית חלב ובקדרה אחרת היו שלשים של היתר ונפל לתוכם כזית של דם ונתערבו בשוגג מותר (וכל שכן בב' זיתים אחד של גבינה ואחד של בשר דכל אחד מבטל חבירו):
A pot that had in it 59 olive['s worth] of permitted food into which fell 2 olive['s worth] one of blood and one of suet, each combines with the 59 [olive's worth] of permitted food to nullify its friend...and all the more so if [the] two olive['s worth were] one of cheese and one of meat, that each nullifies its friend. (my translation)
The answer of Rabbi @Double AA is perfect but I have a great desire to talk about this topic with a couple of mishnayot and Gemarot.
see mishna Orla (2, 2-3):
הַתְּרוּמָה מַעֲלָה אֶת הָעָרְלָה, וְהָעָרְלָה אֶת הַתְּרוּמָה. כֵּיצַד, סְאָה תְרוּמָה שֶׁנָּפְלָה לְמֵאָה, וְאַחַר כָּךְ נָפְלוּ שְׁלֹשָׁה קַבִּין עָרְלָה, אוֹ שְׁלֹשָׁה קַבִּין כִּלְאֵי הַכֶּרֶם, זוֹ הִיא שֶׁהַתְּרוּמָה מַעֲלָה אֶת הָעָרְלָה וְהָעָרְלָה אֶת הַתְּרוּמָה: הָעָרְלָה מַעֲלָה אֶת הַכִּלְאַיִם, וְהַכִּלְאַיִם אֶת הָעָרְלָה, וְהָעָרְלָה אֶת הָעָרְלָה. כֵּיצַד, סְאָה עָרְלָה שֶׁנָּפְלָה לְמָאתַיִם, וְאַחַר כָּךְ נָפְלָה סְאָה וְעוֹד עָרְלָה, אוֹ סְאָה וְעוֹד שֶׁל כִּלְאֵי הַכֶּרֶם, זוֹ הִיא שֶׁהָעָרְלָה מַעֲלָה אֶת הַכִּלְאַיִם, וְהַכִּלְאַיִם אֶת הָעָרְלָה, וְהָעָרְלָה אֶת הָעָרְלָה:
you can see more: the prohibited cancel one another. (we do not start to detail this hard mishna.)
See Gemara AZ 73a:
א''ר יוחנן המערה יין נסך מצרצור קטן לבור אפילו כל היום כולו ראשון ראשון בטל ודוקא צרצור קטן דלא נפיש עמודיה אבל חבית דנפיש עמודיה לא כי אתא רבין אמר רבי יוחנן יין נסך שנפל לבור ונפל שם קיתון של מים רואין את ההיתר כאילו אינו והשאר מים רבין עליו ומבטלין אותו
We see a "creation of the mind" that the prohibited wine encounter the water before allowed wine.
But for your question you don't need all this. The Issur BBCh is issur Noten Taam. objectively, volumetrically, the dish participate to the dilution of the meat taste. Finally the taste is canceled. So, the meat is totally "neutralized" from his power to give taste in milk. The container also, if he will absorb a part of the prohibited product can neutralize it. The BBCh issur is also not already existent before the taste-giving. So the problem of cancellation of taste precede the problem of cancellation of the prohibited food.
I find it odd that one can use batel b'shishim to make a mixture pareve, though I suppose it's no less odd than using it to turn fleishigs into milchigs
While the Halacha you quoted in your questions is correct, the assumption above may be not. A similar case is discussed in Shulchan Aruch Yoreh Deah 99:6. The Rama says that if a kezayis of milk fell into 60 kezaysim of water, and then that mixture subsequently fell into meat, one can consume the final mixture. Sifsei Kohen 99:22 comments that one would be permitted l'chatchilah to mix the water-milk mixture with meat. The Pri Migadim, commenting on Sifsei Kohen writes as follows:
ומה שכתב הש"ך לכתחלה, היינו ליתן לקדירה אבל לערב החלב עם המים ליתן בבשר אסור כמו שכתב הצמח צדק סימן פ
My own translation:
And that which the Sifsei Kohen wrote "l'chatchilah" is only regarding putting [the water-milk mixture] into a pot [of meat], however to mix milk with water in order to put into meat would be prohibited, as the Tzemach Tzedek wrote in Siman 80.
This opinion is quoted as the Halacha in Aruch HaShulchan 99:46 and Badei HaShulchan 99:75.
As an aside, I was pretty excited to make a "milky" chulent until I saw this Pri Migadim.
I find it odd that one can use batel b'shishim to make a mixture pareve
It would be "assur to make such a dish. There is a concept of "ein mevatlim isur lekartrile". You not allowed to make something assur and then by manipulating it, making it mutar.
