Does 1+1=3?

[Myself]

http://dsc.discovery.com/news/2009/06/11/w...-engine-02.html

The real question is not whether a warp drive, which by Cleaver's estimate is hundreds of years away, will be stable or not. It's about the fundamentals of the universe; do we live in a universe where 1 plus 1 equals 2 or 3? Until scientists can answer that question, there will be significant limitations on scientific models of the universe.

Is anybody here familiar enough with the state of modern physics to explain why this is even a question? I find it amazing that physicists are debating whether 1+1=2. I can't believe it.

I don't understand.

[Juxtys]

Why physicists are doing it? Yes, 1+1 equal more than 2, but only in mating...

[sanjavalen]

I AM NOT A PHYSICS EXPERT.

I see it as one of two possibilities.

1) The author of the piece is misrepresenting what the scientists are actually debating; perhaps, in order to make it more understandable to a layman, they put it in those terms, but in terms that the professionals can understand it is actually non-contradictory. I have to say that'd be a poor metaphor though, precisely for the reason that it seems contradictory on the face of it.

2) These particular scientists interviewed have gone bonkers and are actively interpreting data they get in an irrational manner.

[AlexL]

I see it as one of two possibilities.

1) The author of the piece is misrepresenting what the scientists are actually debating...

I looked at what I believe to be the article in question and I think that your first hypothesis is the correct one: the author probably misunderstood what the reviewer said.

The authors of the article submitted for publication write that they could perform the calculations for "1 + 1 dimensions", that is for a simplified model with only one spatial and one temporal dimension. The authors note that for "3 + 1 dimensions" (that is for the real case of three spatial dimensions) one has to resort to numerical calculations, and that the result could be qualitatively different.

The article does not question the result of the addition 1+1.

Alex

Edited June 14, 2009 by AlexL

[Myself]

The article does not question the result of the addition 1+1.

Thanks for the explanation.

That article was misleading in the extreme and made me question the sanity of the scientists involved. I'm surprised that no one on the editorial staff noticed such a blatant error.

I wonder how many people read that article and either concluded that theoretical physics was irrational, or worse, that 1+1=2 was a legitamate question that scientists hadn't solved.

Edited June 14, 2009 by Myself

[Thomas M. Miovas Jr.]

I read that article a few days ago and realized what some scientists do is to mentally play with the fundamentals of what it means to have a universe. They weren't questioning if 1+1=2 in our universe, but rather projecting what would be possible if 1+1=3 in some hypothetical universe. It's kind of like fantasizing what it would be like to be able to walk through solid walls, as in science fiction. In a universe in which 1+1=3, the mathematics would be different, leading to a solution for a mathematical problem that can't be solved in our universe where 1+1=2. By projecting this, it wouldn't take the entire matter / energy of Jupiter to be able to form a stable warp drive.

I think this is a bizarre methodology, and I think this disconnects the scientist's mind from reality -- that is, it is a form of rationalism. Kind of a rationalistic form of science fiction.

[D'kian]

There's an old math joke: 2+2>4 for very large values of 2

[Steve D'Ippolito]

There's an old math joke: 2+2>4 for very large values of 2

Or (alternative phrasing) 2+2 = 5 for sufficiently large values of 2.

I am told that the very earliest FORTRAN compilers would generate code that could be "tricked" into changing the values of numerical constants, so that people debugging the code would check everything and see no problem. "X is still 2, so I don't understand it!" "Yes, X is still 2, but 3 isn't 3 anymore!"

[John McVey]

Adding two and two to get five is an old trick with spreadsheets and calculators. It works by the precision of the number in calculaton being higher than the precision of the number as displayed. 2.4 + 2.4 = 4.8, but when the figures are rounded to whole figures for display purposes it looks like 2+2=5.

*prick*TSSSSSsssss....* "awwwww...."

JJM

[D'kian]

I am told that the very earliest FORTRAN compilers would generate code that could be "tricked" into changing the values of numerical constants, so that people debugging the code would check everything and see no problem. "X is still 2, so I don't understand it!" "Yes, X is still 2, but 3 isn't 3 anymore!"

I never used FORTRAN, but in Pascal variables had to be defined at the start of the program. It was common to break into someone else's programs and screw up the variables.

As to spreadsheets, Mr. McVey, they still plague us with hidden decimals. I've seen people spend two or three hours hunting down an error only to find they entered 5.455 instead of 5.45 in some cell displaying only two decimals.

[John McVey]

As to spreadsheets, Mr. McVey, they still plague us with hidden decimals. I've seen people spend two or three hours hunting down an error only to find they entered 5.455 instead of 5.45 in some cell displaying only two decimals.

I never experienced it myself, but apparently in the 90's there was a bad batch of Intel CPU's that had dodgy floating-point subunits. It must have sent people needing to calculate with big mantissas bonkers. A certain chant was later reworded and pressed into service:

"We are Pentium of Borg. Precision is futile. You will be approximated."

JJM

[D'kian]

I never experienced it myself, but apparently in the 90's there was a bad batch of Intel CPU's that had dodgy floating-point subunits. It must have sent people needing to calculate with big mantissas bonkers.

I recall reading something about it. I really don't like doing complex stuff on a spreadsheet anyway. Spreadsheets have no memory, after all, and don't keep track of movements and changes to them. You should see the trouble I had keeping an inventory in one (I reworked the inventory in a dedicated program instead, a lot easier).

A certain chant was later reworded and pressed into service:

"We are Pentium of Borg. Precision is futile. You will be approximated."

Cute. I'd like to know of any software or hardware glitch that can't be attributed to the Borg

BTW back in the 90s I made a few Borg taglines. These are the funniest:

"I am Droopy of Borg. You know what? You will be assimilated."

"Pinky, are you pondering what I'm pondering?

I think so, Brain. But what if the Borg won't wear the nylons?"

[John McVey]

Spreadsheets have no memory, after all, and don't keep track of movements and changes to them.

Excel has a track-changes option in it - at least from 2003 onwards. I haven't used it, though, so I don't know if it would suit your needs (I have used it in Word and found it helpful).

JJM

[D'kian]

Excel has a track-changes option in it - at least from 2003 onwards. I haven't used it, though, so I don't know if it would suit your needs (I have used it in Word and found it helpful).

I dind't know that. Anyway, I used it for inventory around 2001 and I don't think that PC ever went beyond Office 97. I inherited the spreadsheet from someone else. The problem came if I made an error and everything went out of whack. Tracking down the error took hours. With the dedicated program it took a minute, 90 seconds at most.

I use Excell a lot these days, but for other things that don't require keeping track of changes.

[aleph_0]

So this, too, will be off-topic, and it's an oldie but a goodie:

Let A = B, then

A^2 = AB ==>

A^2 - B^2 = AB - B^2 = (A+B )(A-B ) = B(A-B ) ==>

A+B = B = 2B ==>

2 = 1.

Edited August 20, 2009 by aleph_0

[Rudmer]

So this, too, will be off-topic, and it's an oldie but a goodie:

Let A = B, then

A^2 = AB ==>

A^2 - B^2 = AB - B^2 = (A+B )(A-B ) = B(A-B ) ==>

A+B = B = 2B ==>

2 = 1.

Exhibit A in the case for why dividing by zero is not okay.

[Thomas M. Miovas Jr.]

So this, too, will be off-topic, and it's an oldie but a goodie:

Let A = B, then

A^2 = AB ==>

A^2 - B^2 = AB - B^2 = (A+B )(A-B ) = B(A-B ) ==>

A+B = B = 2B ==>

2 = 1.

I think it is a case of rationalism, and it doesn't say that 2=1, it says that both A and B are zero. The second line A^ -B^2 would be equal to zero, since A=B, so (A+(A- indicates that both A and B are zero. So the last line says Zero +Zero = Zero, and any number multiplied by Zero is Zero; so you might as well have said 500B and not just 2B, and then rationalistically said that 500=1.

I'm reminded of discussions with The Maverick Philosopher who loved modal logic and never brought his thinking down to earth.

Added on Edit: On second thought A+B = B solved for A is A = 0, so B = 0.

So, you really haven't said anything, except for the fact that you can do abstract addition using zero as a number.

Edited August 20, 2009 by Thomas M. Miovas Jr.

[Jake_Ellison]

(A+B )(A-B ) = B(A-B )

If A-B does not equal zero, then you can divide both sides with (A-B ), and you will get A+B=B ==> A=0.

If A-B = 0, then you get A=B.

What you can't do is divide both sides of the equasion by zero, and then claim that the product of your mistake is the correct result. This example was devised by someone who failed math in highschool, because he didn't bother learning about solving equasions.

[aleph_0]

As Jake pointed out in a long-winded way, and Rudmer pointed out in a brief way, A = B (so they're not both zero, they're just equal). That was in the initial set-up. And so you can't divide by A - B = 0. This has nothing at all to do with rationalism and I don't see an out-right problem with modal logic. It's consistent and provably complete for many of its axiom systems, so it's a pretty fun tool.

[Jake_Ellison]

As Jake pointed out in a long-winded way, and Rudmer pointed out in a brief way, A = B (so they're not both zero, they're just equal). That was in the initial set-up. And so you can't divide by A - B = 0. This has nothing at all to do with rationalism and I don't see an out-right problem with modal logic. It's consistent and provably complete for many of its axiom systems, so it's a pretty fun tool.

I'm not sure what you mean, all I did was explain why this statement, from your post, written as if it's correct, is in fact wrong:

(A+B )(A-B ) = B(A-B ) ==>

A+B = B

The correct version of that is:

(A+B )(A-B ) = B(A-B ) and A-B <> 0 ==>

A+B = B

It's not some type of higher mathematics everyone is missing, it's an attempt at very basic mathematics, but done incorrectly. It proves nothing, and is relevant to nothing, except the fact that its author is bad at basic math. It is rationalism: whoever came up with that set out to prove that 1=2, and did it without any understanding of what he is doing, instead of trying to investigate what the truth is, without bias.

Edited August 20, 2009 by Jake_Ellison

[aleph_0]

We all know it's wrong. You identified why with many words, Rud identified it with few, that's all I was pointing out.

It is not rationalism since no rationalist (or at least, no non-amateur rationalist) believes you can divide by zero. Descartes, if you'll remember, was the foremost rationalist and one of the greatest mathematicians in history.

The person who made it up was not trying to prove a contradiction, I am almost sure of it. The person who came up with it was more likely trying to give a test to make people see what went wrong. In fact, this is how it was delivered to me. Someone wrote the proof and said, "So what's wrong with it?" The point is to train the reader to become good at spotting invalid moves in mathematics. There are many such "proofs".

Another less tricky one: 1 = (1)^(1/2) = ([-1][-1])^(1/2) = (-1)^(1/2) * (-1)^(1/2) = -1 ==> 1 = -1. You're not supposed to be convinced by this, you're supposed to find the error.

[Jake_Ellison]

I'm sorry, I misunderstood. You're right about the rationalism thing too, I actually meant to write rationalizing. Sorry, I should've payed more attention.

[Thomas M. Miovas Jr.]

I'm sorry, I misunderstood. You're right about the rationalism thing too, I actually meant to write rationalizing. Sorry, I should've payed more attention.

It wouldn't be rationalizing, because that means trying to justify an emotion using pseudo-logic*. Rationalism means basically having mental functioning without referencing reality. Maybe the error is that one cannot divide by zero, but A + B = B only works for A = Zero, which means B is also Zero, is what I was getting at. You're saying the mistaken step was the one before that.

Modal logic takes a premise (sometimes abstractly) and assumes it is true and comes to a conclusion. The Maverick Philosopher brought up a syllogism similar to this:

All pigs can fly

George is a pig

Therefore George can fly

Even assuming "pig" means the animal and not a fat slob, it doesn't make sense because pigs cannot fly, even though it is a valid syllogism. That is the crucial difference between how modal logicians handle logic and how Objectivism handles logic. If logic is the art of non-contradiction, and a statement can contradict the facts, then saying all pigs can fly is a contradiction, and is therefore not logical.

Added on edit: A rationalization would be something like you feel angry, and therefore someone must have done you an injustice. Instead of checking your premises to see if someone did commit an injustice to you. It's primacy of emotions instead of primacy of the facts and their relation to you.

Edited August 20, 2009 by Thomas M. Miovas Jr.

[aleph_0]

That's a pretty rough characterization of rationalism which I don't think any rationalist would acquiesce to.

As for modal logic, not just modal logicians but EVERY logician would agree that that syllogism is false but valid. That's just from what the word "valid" means. It means that, assuming true premises, the conclusion follows from them. The word valid has no other meaning in logic, and so the syllogism is in fact valid. The word "false" means something different than valid, and here the argument is false because of false premises. That's not modal logic. That's standard logic. And the adjective "logical" is not something formally defined in logic--it's a colloquial term, so I have no idea what you mean by it in this context.

Whether this account is Objectivist logic, I don't know, I'd be surprised if anyone said there was such a thing as Objectivist logic--but perhaps many Objectivists dislike this concept of validity, which I think would be unfortunate since it is a good distinction to show a person what is wrong with his argument and what he should be careful of in future arguments.

[Thomas M. Miovas Jr.]

Yes, but a rationalist or a full modal logician will not look at the facts of reality to verify his mental processing. The argument I have heard regarding modal logic is that the conclusion must be true if the premises are true and if it is a valid syllogism. However, they don't think true means in compliance with reality, and they don't think false means it contradicts the facts of reality. In other words, the statement "All pigs can fly" is certainly not true, but a modal logician leaves it at that and doesn't realize (at least not fully) that it is not true because it contradicts the facts of reality. That point doesn't enter his head -- it is either true or false to him, but he considers a contradiction to be between two opposite statements and not a false statement contradicting reality. That's the crucial point.

A die-hard rationalist loves to do mental processing not grounded in the facts of his subject in the premises. Often, he does the mental processing on a definition alone, without taking all of the facts into account; thus he considers his conclusion to be true if there are no false statements or contradictory statements in his premises. As an example, take the following syllogism:

Matter does not have free will

Man is comprised of matter

Therefore man does not have free will

The first premise contradicts the facts of reality if you know that man is comprised of matter and yet he has free will, so the rationalist will not consider the first premise to contradict the facts, and he holds it as true because many things comprised of matter do not have free will and they don't even have a consciousness -- i.e rocks, tables, spoons, grass, dirt, etc. are not aware of anything and have no consciousness, let alone free will. So, a rationalist usually over-generalizes, goes strictly by definitions, and does not consider the facts included or subsumed under the premises.