I said that 1 + 1 = 2 is based on underlying axioms and assumptions 1.e. the number system we are using is decimal, and so therefore the result is open to interpretation because in base 2, or binary, 1 + 1 = 10 etc. As for the second question, I'm not sure. What do you think? R [ October 03, 2003: Message edited by: Rosie Nelson ]
I guess what is important is how one deals with questions like this, and not necessary absolute correctness. By the way I'm not sure there is "fact" in mathematics.
Joined: Oct 08, 2001
I said that 1 + 1 = 2 is based on underlying axioms and assumptions 1.e. the number system we are using is decimal, and so therefore the result is open to interpretation because in base 2, or binary, 1 + 1 = 10 etc. As for the second question, I'm not sure. What do you think? You gave a good answer, and in fact, it covers both questions. If "1+1=2" is open to interpretation, it ceases to be a simple fact, doesn't it?
I think facts are open to interpretation when all the facts about the question are not provided. For example, if the question was stated.. Is it a fact that 1 + 1 = 2 using the decimal system. Then THAT question is not up for interpretation. If someone said, Is it a fact that it is the year 2003. That fact is wide open for interpretation. The jewish calendar puts us at like 5xxx some odd date (I'm not jewish and I don't know, I just know it is way ahead of ours). So I just think it depends. I'm sure someone could find some alternate interpretation of any fact. But I think there are some that are not interpretable.
I remember one math class i took, where we spent the whole semester "developing" the real number system. at one point, we did "prove" that 1 + 1 does indeed equal 2. BUT... we started off with and inherent knowledge of what a "set" was, and what it meant for an element to be "contained in a set". Then, we took 5 axioms. These are statements that are supposed to be so obvious, everyone accepts them to be true. (see http://mathworld.wolfram.com/PeanosAxioms.html). If you accept these 5 statements, then yes, 1+1 does equal 2. But since nobody has proved them, the whole set of logic up to that point it up to interpretation. This is how we ended up with Non-Euclidean Geometry. [ October 03, 2003: Message edited by: fred rosenberger ] [ October 03, 2003: Message edited by: fred rosenberger ]
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Is it a fact that 1 + 1 = 2? Usually. Are facts open to interpretation? Many are. Some are more open than others, and in many cases such interpretation may just be a waste of time. Other times it's critical to bridging communcation gaps or "thinking outside the box". I think the "best" answer here would depend on what sort of jobs you're interviewing for, and what sorts of traits they're looking for. Are they interested in finding someone with a good background in formal logic and number theory? Or are the interested in finding people who can communicate effectively in normal conversation without digressing into irrelevant side issues? They might be looking for both - can you go into formal logic mode without becoming pedantic and unable to comunicate with normal people, or feeling compelled to crush your opposition with the correctness of your arguments? I'd favor an answer like "It's usually a fact. Would you like me to discuss it in terms of number theory?" Don't jump headfirst into Full Geek Mode™, but let them know you're awayre there are complexities that can be further discussed.
Originally posted by Rosie Nelson: Are facts open to interpretation?
A fact - or say a REAL fact, which is true with out any assumptions, can not be interpreted. 1 + 1 = 2 is not a fact, its a statement based on a number of assumptions or standards. Now only if someone can give me an example a real fact!
Are facts open to interpretation I'd say properties of facts, which is their meaning, significance etc, are open to interpretation. If we start to doubt facts themselves, the first thing we must do is to demote them to "statements" and not to call them "facts" anymore, for not to spread confusion. Speaking about 1 + 1, it's not a fact, it's a representation of such in certain notation. In one notation it will be 2, in another 10, in yet another "+" symbol can get totally different meaning. For more details search for "Peirce's triad" or "The semiotic triangle". -------------------- "It's getting really babylonic here" -- Chris Baron