Plentyoffish dating forums are a place to meet singles and get dating advice or share dating experiences etc. Hopefully you will all have fun meeting singles and try out this online dating thing... Remember that we are the largest free online dating service, so you will never have to pay a dime to meet your soulmate.
     
Show ALL Forums  > Science/philosophy  >      Home login  
 AUTHOR
 scorpiomover
Joined: 4/19/2007
Msg: 98
view profile
History
1=1 Is it a fact a theory or both?Page 7 of 8    (1, 2, 3, 4, 5, 6, 7, 8)
RE Msg: 95 by SomethinDifferent:
I've been reading through all these posts and noticed something kind of odd. The original question was "Does 1 always equal 1". Nobody has disproved that yet. All of the math in here keeps showing that other things can ALSO equal 1, but there has not been an instance that shows that 1 does not equal one.
1 rock does NOT equal 1 sweet.
 JustDukky
Joined: 7/8/2004
Msg: 99
1=1 Is it a fact a theory or both?
Posted: 11/21/2009 10:27:35 AM

1 rock does NOT equal 1 sweet.

I think I can disprove that theorem:

assume: 1 rock (does not equal) 1 sweet

I have 1 piece of rock candy

It's a rock that tastes sweet

Therefore rock = sweet and by the identity axiom wherein 1=1,

we have: 1 rock = 1 sweet contradiction! (and counterexample)

Therefore [1 rock (does not equal) 1 sweet] is false (which completes the disproof).
 scorpiomover
Joined: 4/19/2007
Msg: 100
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/21/2009 12:21:31 PM
RE Msg: 150 by JustDukky:
I think I can disprove that theorem:

assume: 1 rock (does not equal) 1 sweet

I have 1 piece of rock candy

It's a rock that tastes sweet

Therefore rock = sweet
That's true for rock candy, and would be true for all rocks and all sweets, if all rocks were only ever rock candy, and all sweets were nothing but rock candy. But that's never been true. Most rocks aren't sweets, and most sweets aren't rocks. Further, it doesn't even matter what most are. All we need to prove that 1 = 1 is not always true, is ONE counterexample. A single simple granite rock will suffice.

But it was fun watching the attempt.
 scorpiomover
Joined: 4/19/2007
Msg: 101
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/21/2009 12:59:30 PM
RE Msg: 152 by Thorb:
1=1 ... only if the 1's are not different ones
[taking for granted you would understand that means apples and oranges]
But 2 apples are not the same either, and 2 oranges are not the same either.
 JustDukky
Joined: 7/8/2004
Msg: 102
1=1 Is it a fact a theory or both?
Posted: 11/21/2009 1:15:59 PM

it was fun watching the attempt.

I do something for a joke and you take it seriously? At least try to be funny & entertaining about it, or are you that determined to play the straight man to my "loony tune"?
The joke's wearing thin, so I won't bother to point out the flaw that shows your refutation of my (only moderately humorous) refutation to be fallacious and invalid. Besides, nobody else would be interested if we wasted their time in a dull trivial argument.
 scorpiomover
Joined: 4/19/2007
Msg: 103
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/21/2009 1:43:17 PM
RE Msg: 154 by JustDukky:

it was fun watching the attempt.
I do something for a joke and you take it seriously? At least try to be funny & entertaining about it, or are you that determined to play the straight man to my "loony tune"?
I was trying to make my post a bit light-hearted with that.

But I've been told that I have a warped sense of humour. People used to say that there are 3 types of humour: "funny ha-ha", "funny peculiar", and "funny sick", and my sense of humour is "funny sick". It's not to everyone's taste.

The joke's wearing thin, so I won't bother to point out the flaw that shows your refutation of my (only moderately humorous) refutation to be fallacious and invalid. Besides, nobody else would be interested if we wasted their time in a dull trivial argument.
OK. No need to bite my head off. Anyway, my liver tastes much better, especially with a nice bottle of Chianti.
 JustDukky
Joined: 7/8/2004
Msg: 104
1=1 Is it a fact a theory or both?
Posted: 11/22/2009 7:41:50 AM

The issues are not easy to understand and the best minds in math and philosophy seem to have much trouble grappling with them, so I suppose the ordinary person should not be surprised if they find the same.

Which brings us to this thread (BTW - good post Greg)
Here we find ordinary people basically on the same footing as the ivory tower elite. Who's right, who's wrong? Will we ever know? What is mathematics anyway? The deepest and most profound questions about math have been locked in the ivory tower long enough. Time to give Joe Blow a shot at it. Who knows how many Srinivasa Ramanujans are shuffling about invisibly in the milling throng, unable to be heard over the din? Besides, it's a beautiful view from the tower. Everybody should be able to go up there and enjoy it from time to time.
 DartmouthRunner
Joined: 3/5/2009
Msg: 105
1=1 Is it a fact a theory or both?
Posted: 11/22/2009 7:54:20 AM

What is mathematics anyway?


Simply, it's a language. Well that's what a Dean told me when I was getting my pre-reqs in line for grad school and needed to get another full credit in a language. Math counts.

Seemed off at first. However, when you think about it, he's correct. Math isn't a science per-say, but the tool that scientists and other fields use to explain events that they observe, like Physics. The fun thing is that it is an ever-evolving language adding more and more to it.


Everybody should be able to go up there and enjoy it from time to time.


Anybody can. However, it's a beast that requires a person to understand each step before they can even move onto the next one. I wouldn't even bother trying to explain integrals to a person who hasn't heard of derivatives. Wow, just mentioning those sent a cold chill up my spine.
 JustDukky
Joined: 7/8/2004
Msg: 107
1=1 Is it a fact a theory or both?
Posted: 11/22/2009 9:19:34 AM
I have a problem with people equating "theory" with "hypothesis".

The problem is that many people do. Hence we have "pseudo-science" where any old hypothesis can be advanced as a "theory" to the masses and often believed by those who feel it "makes sense to them" (only because they lack the background to critically assess a hypothesis).

Math is a language...and it's a philosophy...and it's a science (in a sense).
There are however differences in the similar nomenclature between science and math that many people don't pick up on.

For instance in science, facts are accumulated by observation of nature.When compiled they often pose a question, tentatively answered with a hypothesis, which is tested empirically for veracity. If it passes such tests, it becomes a theory. The theory may never be proved, because in most cases to do so, one would have to examine the entire universe to rule out a possible counterexample, a clearly impossible task. (So I always laugh at the ignorant arguers who say "That's only a theory!")

What is "the process" in mathematics? A mind poses itself a question (a conjecture or hypothesis) and tries to answer it within the confines of the rules of the game (or language, if you prefer). If through manipulations within the language the conjecture results in the derivation through logic of an unambiguous answer, we have a "theorem", which is a proved statement that answers the original question. It gets added to the language, and if it is consistent (within some domain of math) it may answer many more questions, possibly unrelated to the original. In that sense math is a growing language based on propositional logic and therefore a philosophy also, in that it seeks to know more about itself. Notice the difference from science; we go from fact to hypothesis to proof (where's the theory?), where science goes from facts to hypothesis to theory (where's the proof?) It becomes important for anyone not to get the progression of the two disciplines mixed up. There are theories in math and there are proofs in science, but they are uncommon in both cases and left out to avoid confusion.

Poppers example of white crows comes to mind as an empirical proof: If you examine every bit of your back yard and find no white crows in it, you have proved empirically that there are no white crows in that domain and have given some (little) evidence in support of your theory that white crows don't exist. You'll still have a lot more to examine before anybody will take your theory seriously, so at this level, one can still (for all intents and purposes) consider it a hypothesis.

The Goldbach conjecture has proved true (empirically) well into the trillions. Most scientists might say "Enough already! - It's probably true" and consider it a scientific theory (which it now becomes by virtue of the empirical testing and confirmation within a very large "domain") The numerical analysts, engineers and scientists probably now have enough to work with "as though" the conjecture is true, but the "theoretical" (or "pure") mathematician isn't happy; he'll settle for nothing less than either a proof (turning conjecture into a theorem), or a counterexample ("Throw the conjecture in the trash with the other ones, willya?").
 scorpiomover
Joined: 4/19/2007
Msg: 108
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/22/2009 9:04:14 PM
RE Msg: 158 by SexStoreGuy:
I'd just like to point out that, in the scientific context, theory and fact aren't two opposite concepts.
That's because they are two entirely different things.

The theory of gravitation is a fact.
Which one? Newtonian or Einsteinian?

It's a FACT that if I drop an apple from mid-air, that it almost always falls to the ground. It's also a fact that gliders can just ride around in the air for ages, without coming down.

Newton had a theory about it. Einstein had a theory about it. Both are supported by the evidence. Einstein's is supported more by the evidence. But to be honest, we cannot state for sure that either is definitely true. You might come up with an even better theory. Or, some evidence might be found that contradicts both, and you might come up with a theory that is as good as either on the facts we already know, and isn't contradicted by the new facts. That's the beauty of science. Theories can always be improved, because they are never taken to be 100%, unlike facts.

I have a problem with people equating "theory" with "hypothesis".
It might help you to understand why we follow a given theory, and how that relates to the nature of what we might call a hypothesis, even though both can be replaced instantly.

As far as 1=1 goes, so far, it's observable that it seems to be true. But like JustDukky pointed out with the Goldbach Conjecture, that just makes it a Conjecture. If it ever gets proved that in ALL contexts of mathematics, that 1=1, then it becomes a Theorem. But either way, it wouldn't be a fact OR a theory. Those are scientific terms. Different language entirely for maths, because maths deals with truths in an entirely different manner than science.

Conjecture = Seems to be true. But we have no proof that it might not be wrong in some situations.
Theorem = Proof that it can never be wrong under the conditions of the theorem.
 JustDukky
Joined: 7/8/2004
Msg: 109
1=1 Is it a fact a theory or both?
Posted: 11/22/2009 9:14:23 PM
Sheesh!...Until I re-read my post I was unaware of how much I was getting to be like ol' Abe Simpson, with long-winded irrelevant "war stories" & all.

My apologies to the group. I'll try to restrain my babbling rambles & rambling babble in the future.
I'm really not like that when I'm sober, but that's only once in a blue moon.
 JustDukky
Joined: 7/8/2004
Msg: 111
1=1 Is it a fact a theory or both?
Posted: 11/24/2009 3:58:28 AM
This is where this "proof" goes WRONG.

Sorry, no cigar:

sqrt(a x a) = sqrt(a) x sqrt(a) = plus OR minus a, NOT abs(a) (& not plus AND minus a)

Bukk showed everyone where the proof goes wrong.

The "proof" was a sneaky way to show everyone why 1 = 1 and not 1 = -1 by hiding it in a square to prove that it "is".
 scorpiomover
Joined: 4/19/2007
Msg: 112
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/24/2009 2:45:19 PM
RE Msg: 164 by JustDukky:
sqrt(a x a) = sqrt(a) x sqrt(a) = plus OR minus a, NOT abs(a) (& not plus AND minus a)

Bukk showed everyone where the proof goes wrong.

The "proof" was a sneaky way to show everyone why 1 = 1 and not 1 = -1 by hiding it in a square to prove that it "is".
Seriously? Anyone BOUGHT that? Sheesh! That must be the first thing we learned about square roots, that they could be positive OR negative. If I'd got that wrong in maths class, I would have been told to write out the square roots of every number from 1 to 200.
 JustDukky
Joined: 7/8/2004
Msg: 113
1=1 Is it a fact a theory or both?
Posted: 11/24/2009 2:52:29 PM

I would have been told to write out the square roots of every number from 1 to 200.

Gee...That's pretty heartless. I only would've told you to write the square root of two to the last decimal place.
 JustDukky
Joined: 7/8/2004
Msg: 115
1=1 Is it a fact a theory or both?
Posted: 11/24/2009 2:57:56 PM

It relates to everything else.

Why do you suppose that is?
 scorpiomover
Joined: 4/19/2007
Msg: 116
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/26/2009 9:54:22 AM
RE Msg: 166 by JustDukky:

I would have been told to write out the square roots of every number from 1 to 200.
Gee...That's pretty heartless. I only would've told you to write the square root of two to the last decimal place.
Your teacher sounds more heartless. Even I know that would take forever. You'd still be doing that now.
 JustDukky
Joined: 7/8/2004
Msg: 117
1=1 Is it a fact a theory or both?
Posted: 11/26/2009 11:15:16 AM
Your teacher sounds more heartless. Even I know that would take forever. You'd still be doing that now.

I was speaking as (though) YOUR teacher. I would've given you only one thing that took forever... not several. (I thought I was being a nice guy in reducing your work for you!)
 scorpiomover
Joined: 4/19/2007
Msg: 118
view profile
History
1=1 Is it a fact a theory or both?
Posted: 11/26/2009 12:05:48 PM

I was speaking as (though) YOUR teacher. I would've given you only one thing that took forever... not several. (I thought I was being a nice guy in reducing your work for you!)
My teacher would have expected me to only write them out to a fixed number of decimal places. If he didn't specify, and I didn't ask, then when he asked for the homework, he'd probably tell me that I should just hand in what I did, and that next time, I should remember that square roots have an infinite number of decimal places, and to ask to how many decimal places.
 JustDukky
Joined: 7/8/2004
Msg: 121
1=1 Is it a fact a theory or both?
Posted: 12/8/2009 7:50:12 AM

The first being the Piraha, an Amazonian tribe that has been studied by linguistic anthropologist Daniel Everett. Their language is different in that, among other things (lack of color words, lack of recursion), it lacks numbers.

I've often wondered what we'd be like (and how it would affect us) if we never learned math. I'll have to read up on these guys. Thanks for mentioning them.
 AtomicGogol
Joined: 4/4/2008
Msg: 123
view profile
History
1=1 Is it a fact a theory or both?
Posted: 12/10/2009 3:07:12 PM
I think an amusing article about this subject can be found here:

http://qntm.org/?destroy#sec5

Proving that 1=0.

If 1 did indeed equal 0, so it is reasoned, then since there is 1 Earth, there must be 0 Earths... so, if one could prove it, the Earth would cease to exist. This is specious logic. Finding a proof in mathematics does not magically change a fact from being false to being true. It merely verifies rigorously as true a fact that always was true. Thus, if 1=0 could be proved, then it would always have been true and the Earth should never have existed. But Earth is still here. QED.

In fact it would be impossible for there to even exist a universe in which 1 was equal to 0. For any mathematical system in which 1=0, it is extremely trivial to prove, in addition, that 1=2, 2=3, and in fact that every number is equal. Or, in other words, the mathematical system has only one number in it, 0. In a universe which obeyed such laws, there would be nothing at all.
 JustDukky
Joined: 7/8/2004
Msg: 124
1=1 Is it a fact a theory or both?
Posted: 12/10/2009 3:11:34 PM

In a universe which obeyed such laws, there would be nothing at all.

If mathematics is just a language, what does a mathematical statement have to do with a physical reality, like the universe? Why should there be any correspondence at all? How do we know there is?
 AtomicGogol
Joined: 4/4/2008
Msg: 125
view profile
History
1=1 Is it a fact a theory or both?
Posted: 12/10/2009 3:14:34 PM
I know what you're saying, Just. The correspondence is that mathematics is a language to describe the reality we're in. Obviously, if we didn't have mathematics, the reality would still be there, albeit undescribed.
 JustDukky
Joined: 7/8/2004
Msg: 126
1=1 Is it a fact a theory or both?
Posted: 12/10/2009 3:55:23 PM

if we didn't have mathematics, the reality would still be there, albeit undescribed.

...or described differently.
 AtomicGogol
Joined: 4/4/2008
Msg: 127
view profile
History
1=1 Is it a fact a theory or both?
Posted: 12/10/2009 4:05:21 PM
Touche, Senor J. I like your style. :)
 AtomicGogol
Joined: 4/4/2008
Msg: 128
view profile
History
1=1 Is it a fact a theory or both?
Posted: 12/13/2009 11:34:36 PM
I assume you bowed to the author, since I didn't actually write that. :) I just agree with it.


Philosophically, it means if I understand it correctly, if something is "gone" through fire or erosion etc, there will always be something else to take its place. In nature, voids are always filled.


I think you're referring to it scientifically, and it's simple conservation of matter/energy that prohibits anything from completely going away. Therefore, there isn't any true void or empty space as we would think because something is always present, even in interstellar space. I apologize if I misunderstood you; let me know.
Also, I wasn't sure why you concluded that the only number is zero. Could you explain?
Show ALL Forums  > Science/philosophy  >