Freethought & Rationalism Archive

Shake · 04-07-2004, 11:02 AM

A big, hearty, "Thank you," goes to Mike Rosoft for perhaps the best response to this silliness yet. If it hadn't been so long since I'd worked with set theory, I might have beat you to it.

Good one, Mike!

Chimp · 04-08-2004, 10:09 PM

Quote:

Originally Posted by Mike Rosoft

The Universal Set is the set of all that exists.

A set of all sets that exist can not exist in any self-consistent set theory. This is why:

One of the axioms of the set theory is that for every set X there exists a set Y which is composed of all elements of X for which f is true where f is any statement. (Note that in a set theory every element of a set is a set itself.) Suppose that a set U such that for every set x: x is an element of U. (By definition, U is an element of U.) Statement f is "x is not an element of x" (i.e., of itself). This means that a set U' exist which is composed of all sets that are not an element of themselves. Is U' an element of itself? If so, then by definition of U' it is not an element of itself, and if not, then it is an element of itself. Since both options lead to a contradiction, the set U can not exist.

(I could rewrite this proof in formal language, but there are not enough characters in the ASCII.)
Mike Rosoft

Let 2^x = x

then 2^[2^x] = x

2^[2^[2^x]] = x

2^[2^[2^[2^x]]] = x

etc.

Dr. Math replies to my question:

Quote:

As russ wrote to Dr. Math
On 04/03/2004 at 05:43:34 (Eastern Time),
>[Question]
>The equation 2^x = x .
>
>2^x = x
>
>then
>
>2^(2^x) = x
>
>2^2^(2^x) = x
>
>2^2^2^(2^x) = x
>
>2^2^2^2^2^2^2^2^ ... 2^(2^x)_n
>
>How can this equation be solved symbolocally?
>
>
>[Difficulty]
>
>
>[Thoughts]
>2^x = x
>
>2 = x^[1/x]
>
>x^[1/x]- 1 - 1 = [2^x]/x ...

Dear Russ,
What is the scope of your investigation? Are you
looking for
answers or methodology? Are you interested in complex
solutions or
only real numbers?
I'm sending under separate cover a graph of x^1/x.
Its maximum
value is e^(1/e)=1.44, so it never comes close to 2.
For negative
values of x, the interpretation of x^(1/x) is
promblematic.
Your thoughts about an infinite series, raising x
to the power x to
the power x are astute, and could be one way to look
for a solution.
There are other methods as well, but none that
involves only a finite
number of calculations. The only solutions to this
kind of equation
are as a limit to an infinite process.
You may be interested in this chapter from our
archives:
http://www.mathforum.org/library/drmath/view/53229.html
- Doctor Mitteldorf, The Math Forum

The "Universal Set" can be defined as a recursion.

Goliath · 04-08-2004, 10:34 PM

Quote:

Originally Posted by Chimp

Let 2^x = x

then 2^[2^x] = x

2^[2^[2^x]] = x

2^[2^[2^[2^x]]] = x

etc.

No, you are wrong again. If X is any set, then X can never equal 2^X.

Quote:

The "Universal Set" can be defined as a recursion.

No, there is no such thing as a "Universal Set", as there is no such thing as the set of all sets. The poor sod that answered your question wasn't aware that you were talking about sets and not functions of a real or complex variable. Why the dishonesty?

No, Chimp, you are beaten.

Why do you persist? You aren't fooling me into believing that you have the slightest idea as to what you're talking about. Please, do both of us a favor and learn some mathematics before continuing with your "argument".

Try to obtain and read a copy of Halmos' Naive Set Theory.

Sincerely,

Goliath

Chimp · 04-08-2004, 11:00 PM

Quote:

Originally Posted by Goliath

Why do you persist? You aren't fooling me into believing that you have the slightest idea as to what you're talking about. Please, do both of us a favor and learn some mathematics before continuing with your "argument".

Try to obtain and read a copy of Halmos' [i]Naive Set Theory[/b].

Sincerely,

Goliath

Thanks for the book reference Goliath. Now it becomes abundantly clear, that you are one, who has "zeroth" imagination, to be so utterly and hopelessly pedantic...

Goliath · 04-08-2004, 11:08 PM

Quote:

Originally Posted by Chimp

Thanks for the book reference Goliath. Now it becomes abundantly clear, that you are one, who has "zeroth" imagination,

Was that an insult? An insult usually needs to make sense in order to be effective. "zeroth"? Is that some kind of alien photocopy machine?

Sincerely,

Goliath

(edit - I'm just picturing an ad in my head....a freaky looking alien appears and says "Is the photocopier in your Intergalactic Office of Terror working too slowly? Is your human shredder broke down? Then get the new Zeroth 2700X. It makes 5,000 copies per minute, and includes a human shredder! Not only that, but the Zeroth 2700X recycles your shredded humans to make more paper for photocopies! And in the current intergalactic market, recycling is important. For a no-obligation informational download to your datapad, dial 1-800-GRGRFLRFGZZGRGH!!! That's 1-800-GRGRFLRFGZZGRGH!!!" LOL)

Chimp · 04-08-2004, 11:15 PM

Quote:

Originally Posted by Goliath

Was that an insult? An insult usually needs to make sense in order to be effective. "zeroth"? Is that some kind of alien photocopy machine?

Sincerely,

Goliath

(edit - I'm just picturing an ad in my head....a freaky looking alien appears and says "Is the photocopier in your Intergalactic Office of Terror working too slowly? Is your human shredder broke down? Then get the new zeroth 2700X. It makes 5,000 copies per minute, and includes a human shredder! Not only that, but the Zeroth 2700X recycles your shredded humans to make more paper for photocopies! And in the current intergalactic market, recycling is important." LOL)

:notworthy :notworthy :notworthy

http://en.wikipedia.org/wiki/Zeroth

Quote:

Zeroth
From Wikipedia, the free encyclopedia.

The zeroth item is the initial item of a sequence, if that sequence is numbered beginning from zero rather than one. This kind of numbering is common in computer systems, and so hackers and computer scientists often use zeroth where others might use first, and so forth.

In computer science, zero is the smallest natural number, and the base case for many kinds of numerical recursion. Thus, proofs and other sorts of mathematical reasoning in computer science often begin with zero. Zero is also the lowest unsigned integer value, one of the most fundamental types in programming and hardware design. For these reasons, computer science scholars are accustomed to count from zero rather than one.

Goliath · 04-08-2004, 11:16 PM

Quote:

Originally Posted by Chimp

...to be so utterly and hopelessly pedantic...

Yep, you've made it more clear that you know nothing about mathematics. First of all, a large degree of pedantry is necessary in mathematics. Defined terms must be defined precisely (and axioms for undefined terms must be laid down precisely). Proofs must be done rigorously. Again, look at Naive Set Theory

Sincerely,

Goliath

Goliath · 04-08-2004, 11:17 PM

I'll be damned...and I thought it was spelled "zeroeth".

Oh well, you learn something new every day.

("zeroth" still looks weird, though).

Sincerely,

Goliath

PS Your mocking " :notworthy "s have not gone unnoticed, and they do not change the fact that your argument fails miserably.

Goliath · 04-08-2004, 11:27 PM

By the way, shouldn't that be "zero" imagination, and not "zeroth" imagination? Your attempt at an insult still doesn't make sense.

Sincerely,

Goliath

Chimp · 04-08-2004, 11:29 PM

Quote:

Originally Posted by Goliath

I'll be damned...and I thought it was spelled "zeroeth".

Oh well, you learn something new every day.

("zeroth" still looks weird, though).

Sincerely,

Goliath

PS Your mocking " :notworthy "s have not gone unnoticed, and they do not change the fact that your argument fails miserably.

Here is the "latest" argument:

Here is the definition of "algorithm":

http://en.wikipedia.org/wiki/Algorithm

Quote:

"Algorithm

From Wikipedia, the free encyclopedia.

Broadly-defined, an algorithm is an interpretable, finite set of instructions for dealing with contingencies and accomplishing some task which can be anything that has a recognizable end-state, end-point, or result for all inputs. (contrast with heuristic). Algorithms often have steps that repeat (iterate) or require decisions (logic and comparison) until the task is completed."

DNA is an algorithm, a finite set of instructions, which can construct a carbon based life form.

The life form physically contains the DNA and the DNA contains the life form in an "abstract" sense.

At a fundamental level of existence, it is postulated that "nature" could be constructed of tiny strings, and those strings, loops, or branes, could even be constructed of string "bits".

These bits could encode information, analogous to the universe's "DNA"? A set of instructions built into the fabric of space/time and mass/energy?

Quote:

"If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? I answer without hesitation that there is, in my opinion, a right way, and that we are capable of finding it. I hold it true that pure thought can grasp reality, as the ancients dreamed." (Albert Einstein, 1954)

http://www.blc.arizona.edu/Molecular...TML#Components

Quote:

DNA is a polymer. The monomer units of DNA are nucleotides, and the polymer is known as a "polynucleotide." Each nucleotide consists of a 5-carbon sugar (deoxyribose), a nitrogen containing base attached to the sugar, and a phosphate group. There are four different types of nucleotides found in DNA, differing only in the nitrogenous base. The four nucleotides are given one letter abbreviations as shorthand for the four bases.
A is for adenine
G is for guanine
C is for cytosine
T is for thymine

AGCT looks like code to me... DNA? = information?

Physicist Stephen Hawking writes:

Quote:

DNA is the basis of all life on Earth. It has a double helix structure, like a spiral staircase...
[...]

There are four bases in DNA: adenine, guuanine, thymine, and cytosene. The order in which they occur along the spiral staircase carries the genetic information that enables the DNA to assemble an organism around it and reproduce itself...

At the most fundamental length scales, the fundamental paticles, called "strings", could be constructed of even more basic units i.e. bits? analogous to a computer code?

1010100010...etc.

Universal algorithms?

This assumption seems to hint for a designed universe, or even stranger still, a universe that is a type of life form...???

Some interesting ideas on "string bits":

http://xxx.lanl.gov/PS_cache/hep-th/...07/9607183.pdf

http://xxx.lanl.gov/PS_cache/hep-th/...07/9707048.pdf

Quote:

Introduction

In string-bit models, string is viewed as a polymer molecule, a bound system of point-like constituents which enjoy a Galilei invariant dynamics. This can be consistent with Poincar´e invariant string, because the Galilei invariance of string-bit dynamics is precisely that of the transverse space of light-cone quantization. If the string-bit description of string is correct, ordinary nonrelativistic many-body quantum mechanics is the appropriate framework for string dynamics. Of course, for superstring-bits, this quantum mechanics must be made supersymmetric.

According to string theory, the uncertainty in position is given by:

Dx < h/Dp + C*Dp

Which points towards a type of "discrete" spacetime?

Interesting...

It seems that the probabilities become more "exact" [deterministic?] as the number of trials increase? As a simplistic example, if a coin is tossed n number of times, then the greater the n, the greater the correspondence to the probability of 1/2 heads and 1/2 tails.

An infinite number of coin tosses points towards the exact 50% probability?

It would appear that "randomness" is bound within parameters, set by the algorithms? That is to say IF the statistical algorithms correspond to the real universe...

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04-07-2004, 11:02 AM	#81
Shake Contributor Join Date: Jan 2001 Location: Folding@Home in upstate NY Posts: 14,394	A big, hearty, "Thank you," goes to Mike Rosoft for perhaps the best response to this silliness yet. If it hadn't been so long since I'd worked with set theory, I might have beat you to it. Good one, Mike!

04-08-2004, 11:17 PM	#88
Goliath Banned Join Date: Mar 2001 Location: Fargo, ND, USA Posts: 1,849	I'll be damned...and I thought it was spelled "zeroeth". Oh well, you learn something new every day. ("zeroth" still looks weird, though). Sincerely, Goliath PS Your mocking " :notworthy "s have not gone unnoticed, and they do not change the fact that your argument fails miserably.

04-08-2004, 11:27 PM	#89
Goliath Banned Join Date: Mar 2001 Location: Fargo, ND, USA Posts: 1,849	By the way, shouldn't that be "zero" imagination, and not "zeroth" imagination? Your attempt at an insult still doesn't make sense. Sincerely, Goliath

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