Is the number 2 simpler than the number 1?

@markr,

Quote:

"the number 2 implies a system with three choices"

Not always - the binary system (base 2) is made up of ones and zeros.

The binary system is a system with two choices. Incidentally there is no number "2" in the binary system. I think you make Cyclo's point nicely.

(Or maybe the number 10 implies 3 choices)

1 Reply

@Francis,

Our hostess may be on the right track after all>

Quote:

Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function, defined by ζ(s) = 1 + 1/2s + 1/3s + 1/4s + ... . He also formulated a conjecture about the location of these zeros, which fall into two classes: the "obvious zeros" -2, -4, -6, etc., and those whose whose real part lies between 0 and 1

http://www.claymath.org/millennium/Riemann_Hypothesis/1859_manuscript/
> something really weird happens in the space between 0 and 1. The higher numbers, like 2, 3, and so on, are in that sense easier to understand; now if we only could prove Riemann's (and Pentacle Queen's, who finds herself in august company) hypothesis, we would not only win $1m (see above link) but also untold additional $$$$ by providing truly unbreakable prime number encryption codes.

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@High Seas,

PS the really infuriating part in all this (to me) is that after you've done all the research work you find that some Greek proved whatever you're looking for in some century BC:

Quote:

Every integer can be written as a product of primes in an essentially unique way. Euclid also showed that if the number (2**n) - 1 is prime then the number (2**n-1)*((2**n) - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to show that all even perfect numbers are of this form. It is not known to this day whether there are any odd perfect numbers. In about 200 BC the Greek Eratosthenes devised an algorithm for calculating primes called the Sieve of Eratosthenes.

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html

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@High Seas,

Greeks are infuriating dudes, aren't they? Mr. Green

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@Francis,

Well, the same goes for Gauss, de la Vallee Poussin, von Neumann, and many others with fundamental proofs in prime numbers.... none of them Greek, far as I know Smile

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@Francis,

Francis, flowers just make me sneeze.
Seriously (sort of), ONE is both more complex (because it refers to everything) and more simple (because there is nothing outside of UNITY).
I'm thinking, of course, of the perspective--as I understand it--of mysticism

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With integers many theorists break all positive whole numbers into one of four types--0, 1, prime, and composite (product of prime).

Since 2 is a prime, it is one of an infinite number of primes. However, 2 is the only even prime--so it is unique.

1, though is the multiplicative identity. It starts and ends as a unique number with very unique properties.

So if I were to arbitrarily pick a simpler number, it would be 2--no 1, no make that 2, er 1.

There that should put an end to that Piaget psychobabal.

Rap

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I've seen Fellini's Amarcord a few times and I eventually found that it revolved around the number 2 and powers of 2.

So much so that when some guy threw a bunch of papers out of a fast moving car I would have bet there were 256 or 512 or 1,024 blowing in the wind.

That is one exceptional movie. If they do make them like that anymore I have yet to figure them out.

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@ebrown p,

"The binary system is a system with two choices. Incidentally there is no number "2" in the binary system. I think you make Cyclo's point nicely.

(Or maybe the number 10 implies 3 choices) "

No, the number 10 implies as many choices as the base, which in the case of the binary system, is two. I don't think I'm making Cyclo's point at all. "2" happens to be the representation of the number two in bases greater than tw0. The fact that there is no number "2" in the binary system doesn't negate the fact that it is base two and offers two choices.

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@raprap,

raprap wrote:

.....1, though is the multiplicative identity. It starts and ends as a unique number with very unique properties. ....

"VERY" unique?! VERY?? Unique is a Y/N proposition, not a matter of degree, Rap - it may be the Piaget psychobabble here is contagious.

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@raprap,

Quote:

There that should put an end to that Piaget psychobabal.

Piaget psychobabble??? Hrmmph.

We are having a three page discussion--- allegedly about math-- revolving around the term "simpler". No one has offered anything close to a mathematical definition of what "simple" means.

I would argue that every post in this discussion is "psychobabble".

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@ebrown p,

That just ain't so - both Francis and I discussed Riemann's hypothesis. Hardly "psychobabble", Piaget-related or otherwise.

For reasons based on number theory I concluded 2 really is simpler than 1, as you'd know if you'd read the links.

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Yes, but is the number 1 or 2 the psychobabblest?

Rap

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I have a great love for the number 2. It is surely a beautiful number -- the first prime number. But can anything be simpler than 1, the building block of counting? You can make any number just by adding a bunch of them together. Any number multiplied or divided by it is itself. It practically defines countability. It's the atom, the cell, and the brick.

There's my contribution to the "psychobabble" (though "psychobabal" is a hole 'nother can of worms).

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@High Seas,

You don't need to be defensive.

I am just pointing out that the term "simple" (lacking any mathematical definition) would seem indicate the ability of a human being to understand. In this case any discussion of this term is psychology.

You can't base a question on an undefined term and call it "mathematics".

Your discussion of Riemann's hypothesis has this problem, lacking a key definition of what makes a number "simple", it is impossible to link the two even if for some values Riemann's hypothesis is "really weird" (another phrase with no mathematical definition.

A "mathematical" discussion on whether non-mathematical assertions are true is psychobabble. The addition of mathobabble doesn't change this fact.

You could fix this problem if you provide a mathematical definition of "simple" that didn't involve human perceptions.

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@raprap,

Quote:

Yes, but is the number 1 or 2 the psychobabblest?

One is the loneliest number...

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That's psychobabble, par excellence..

Tell me why is it lonelier than any other number.

Is loneliness a mathematical concept?

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@Francis,

ebrown_p wrote:

One is the loneliest number...

It looks like I owe an apology for this extremely insensitive, inflammatory, provocative and offensive statement. I am sorry by anyone who was hurt by this comment. For example ...

High Seas (on a non-related thread) wrote:

That has been standard operating procedure for [ebrown_p] since he started posting here. When made to confront his scurrilous inanities and outright lies he just runs off the thread and starts over with another topic. I'll post some examples in a moment...

Example 2 (in addition to the one noted by Setanta, above) of crass fabrication by [ebrown_p] , on the subject of mathematics:

[here he links to the very comment I posted above (on this thread)].
...
Further examples abound, but I find this fake, flake, liar, fraud, and accomplice of criminals so sickening that posting them might ruin everyone's St Patrick's day

Realizing there really is no justification for my "sickening" behavior (I take full responsibility for my words) let me at least try to explain the reason for what I did...

You see, "One is the loneliest number" is a popular song by "Three Dog Night" (see http://www.youtube.com/watch?v=bOVb7kGO48I). I assumed (obviously incorrectly) that everyone would get the reference as silly humor, and that in some sick way, people might even chuckle. In hindsight I realize I clearly crossed a line.

Attempts at silly humor on such a serious topic as the philosophic meanings of the number "one" are inexcusable-- and I deserve everything that High Seas said.

I apologize for the pain I have cause him.

1 Reply

@ebrown p,

yes two is twice as simple as one

one is nothing

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@solipsister,

solipsister, you are a troll. "one is nothing"? 1 = 0? What planet did you learn to count on?

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Is the number 2 simpler than the number 1?

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