Mildly Infuriating

I wish

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The questions still valid.... Why would I simply be aware what year I was born in under the Chinese zodiac so that I could get a new SS card. You are missing the forest for the trees.

Zodiac signs are about as accurate as tarot readings or reading tea leaves. They're even wrong about what they are based on. The star locations and sun precession hasn't coincided with the original 12 zodiac constellations for centuries. People use the dates and signs as they were set by astrology tradition ages ago, but the dates when the sun changes from one constellation to the next is also absolutely arbitrary to make it match exactly 4 and a half weeks.

The personality descriptions for zodiac signs are textbook examples of cold reading. A technique of making intentionally ambiguous but agreeable affirmations so that people project their self-view onto the descriptions disregarding evidence or specifities.

It is a superstition as it is the belief on the supernatural influence of the relative apparent position of stars in the sky over the behavior and personality of individuals. It's a, mostly, harmless superstition, but superstitious none the less.

I think it's at a sort of weird crossroads between superstition and factual data, because it is trivial to calculate the factual data regarding the position of any star in the sky at any point, but the superstition comes in when you associate the positions of a rather arbitrary group of stars in relation to a date of birth.

I just thought of this though- you could argue that this is an anti-astrology security measure because it proves that you can't guess someone's zodiac sign based on things like their interests and personality traits.

This isn’t a CAPTCHA, It’s identify verification. Similar to those ID verifications when they ask you where you had a previous address, who you opened a loan with, how much the loan was for, etc.

CAPTCHA is intended to ensure that a human is logging in, not a bot. Identity verification is to make sure that the person creating the account is actually that person. Completely different use cases.

The purpose of these questions is to verify your identity; they have your DoB, and are asking the question to confirm that you are who you say you are, so if you answer N/A when the correct answer is one of the other 4, you'll be denied access to whatever you're signing up for.

All that said, "What month were you born in?" would have been a much better question for the reasons OP notes.

I know mine because my personality is the stereotype of my sign. It’s just a coincidence, but it’s one that comes up from time to time

It probably relates to your age. When I grew up there were still newspapers (and dinosaurs) and you probably ran across a small horoscope section somewhere in there (especially on or near the comics page), so for me seeing the dates was virtually unavoidable. But I haven't run across a random horoscope in over 20 years, so if you're born after the millennium I'm sure it was much less prominent in your life.

While the wording is stupid, and "astrological" indeed refers to the superstitious bullshit, the zodiacs are not a believer/non-believer thing, but based on an astronomical(!) constellation being at a particular position in the sky in the period of said zodiac. That said, however, and without checking, I am sure that this does not align with the dates assigned to the zodiacs at all anymore because the Earth wobbles on it's orbit & also because the zodiac cycles could never possibly align precisely with a year on Earth, simply because the dates are fixed and don't account for leap years (the ~0.25 day extra each year).

Why did I make this point? Because it appears that in Europe at least, everyone knows their zodiac - I would be surprised if it's any different in countries that use the same calendar.

Do most nonbelievers know their sign, or do they have no idea?

In the very rare case where it comes up, I almost always have to look up the answer. Why would I have the signs and their date ranges memorized? This is like asking someone whose only tangentially heard of D&D to name his favorite first level spell.

I was thinking more along the lines of “Based on your connection to the Force and your relation to the Jedi Order, what color would your lightsaber be: A. Green B. Blue C. Red. D. Purple E. None of the above”, or “Which Pokémon was based on the Chinese Zodiac animal of your year of birth? A. Swinub B. Rapidash C. Lopunny D. Chimchar E. None of the above”