Aleph Not, Aleph Shaday

[Huiou_Theou]

I have been having a mathematical (and therefore philosophical) conversation on a physics website about the idea of “infinities” beyond “infinities”, or Aleph One, Two, and so forth.
Of course, if I mention God There – my thread will be locked; and now I find myself being threatened with having a thread locked by someone who may have a serious conflict of interest when I am speaking about something purely mathematical but which was first given to me in High School in a movie which made comments about the pope, God, and how this aleph thing is tied up in a proof or another. I sometimes wonder if it is the Stalinist concept of God… or whatever.

This is one of those conversations I would normally have with my brother, John, for he is formally trained in those subjects.

But, I wonder sometimes if it is a sign from God that they chose the first letter of the Hebrew Alphabet for this particular subject. I forget the German’s name who attempted to name the first infinity “Aleph Not (0)” אֵ ; For that letter happens to be the “alpha” of “THE” alpha and the Omega; in Hebrew it just means “The”;

I recall thinking El-Shadday was “God almighty” – but it is really just “THE almighty” in literal translation.

Spock of Star Trek does a live long and prosper hand gesture which is HALF the letter “Shin” for “Shadai” – as in, “Almighty” in the blessings of Jewish Rabbis.
So, here I am having a conversation with something of a bully on a physics website about whether or not I can count all the real numbers. I think I can, I have been more than kind in listing out where an issue might be – and I find myself threatened to prematurely reveal the answer; when if the man was more patient I might even have given him a better answer; By now, those on this website know I don’t joke, and I don’t try to be cruel. But I really wonder, should I give this fellow a partial answer this early or not?

His exact words to me were: (one sentence, no copyright infringement possible – Google does know about it already…)
“Please give the algorithm in the next post or this thread will be locked. Don’t play games with us. micromass.”

St. Thomas, did, indeed argue about the existence of God and infinities. Could this be a sign I should demolish something like Aleph not? (No god, poly god, what god?)

But, aleph not – I think – really will be replaced by Aleph shadai; it’s just a matter of when. Perhaps leaving God out of it for the moment, (though I am no atheist…) is the appropriate approach, but what do you think, should I give this simple method to him right NOW to count every possible decimal number, or should I refine it first?
Is it appropriate to be bullied by someone and give the lesser of an answer when a better one might be yet found? (I am looking for friendship – and he is acting like a bully.)

Here is how I would count all the possible reals using counting numbers:
(Next post, so the proof will be here – uneditable except by CAF – first.
Google is sure to find it though… )

 

[Alberti_Devoveo]

I have no idea what you are saying here. I Googled that line and found the PhysicsForum website and I have a vague idea of what you are saying there.

As far as I know, there is no way to list all real numbers because there is an effective infinite (it is not truly infinite since an actual infinity cannot exist in reality, only in potentiality) number of decimal places between 0 and 1.
And even if you could express an algorithm that would write down all the real numbers, you would never be able to (a) write the numbers down or (b) finish writing all the numbers before the universe would end. If there is an effective infinite number of decimal places between 0 and 1, then there is an equal number of decimal places between 1 and 2. Moving onwards, there is an effective infinite number of real numbers, from 0 on up to the largest number possible before infinity.

Unless I have completely misunderstood your above rambling and your PF comments, you have lost the bet here, my friend.

 

[Alberti_Devoveo]

Also, it is not called “aleph not,” it is called “aleph naught.”

 

[Huiou_Theou]

Do you have background in the ideas of “infinity”, “God”, Aleph Not?

A discussion of the ideas is something I expected to have on the physics forum before delivering my findings. (Although, there, I would not discuss God directly, here I am free to do so.)

It is this very discussion (which I would use to seek friends on that site) that is being denied. eg: A member of the site (micromass) is attempting to force me into a destroy or be destroyed position, rather than opting to have a discussion first or deal with the falsifiability of the proposition at hand – which is the appropriate way to proceed.

At this time, I would say, I am studying (not playing with, tricking, or trying to hurt) people on the physics forum with regard to questions that I originally learned about in the Thomistic/Scholastic/Systematic theology traditions. Since the actions of some PF members have a high correlation with unethical behavior based on knowledge they OUGHT to have, I have decided to begin defensive manouvers the same as I have done here on CAF in the distant past. Let us hope my anxieties are avoided and wisdom of communication begin to prevail on PF as it often does here, now, on CAF. Even moderators can learn…

(continued in next post…)

 

[Huiou_Theou]

How to count ALL real numbers, by a real man. (No joke, just pun).
אל שדי !!

Step 1) Inform others that you can’t possibly write all numbers down on one page, or even computer, so that you must use a shorthand.

Why? because:
In mathematics http://cdn.mathjax.org/mathjax/late...ts/HTML-CSS/TeX/png/Main/Regular/085/0030.png carries the idea of a 1:1 mapping of counting numbers to any other set of things.

Statement #1: Not all counting numbers can be written down, some are simply too big – but it is generally accepted in the mathematics community that they exist. For every counting number written out there is a “next” one (n+1).

This infinite set (counting numbers) is taken to be a metric of “infinity” by which other sets of things may be measured for “size”.(God vs. god vs. Stalin comes to mind…)

(Conjecture) Statement #2: The decimal representation of the real numbers is sufficient to represent all possible real numbers by a signature. It may be possible that for numbers which terminate in a sequence of all zeroes, eg: 1.79000000000000, that a second representation of the same number may exist: vis. 1.6899999999999… where the ellipsis represent unwritten digits, in this case it is only the digit “9”.
By convention people often omit repeating zeroes without ellipsis or bars; eg: it would be permissible to write 1.79, to mean 1.790…, 1.790[0bar]; Hence the ellipsis now indicate a continuous repetition of zeros.

Conjecture (Statement #3) When the signature between two decimal representations is the same (including conventionally unwritten zeroes) at every place such that there is a (1:1 correspondence) between every digit; then these two decimal representations are identical and represent the same thing. They therefore map to one, and EXACTLY ONE, unique real number.

Axiom (Statement #3) irrational numbers, which by definition can not have an unending repetition of "0’ or “9” digits in the trailing positions are never affected by Statement #2.

Step 2: Ignore all refinements since the audience became agitated.
Possible Step 3: List a very simple example of how to organize all reals that can be converted into an algorithm.

Count #: real number’s signature
index 1: 1.0
index 2: 2.0
index 3: 3.0
… etc
Or more compactly:
0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 0.1, 1.1, 2.1, 3.1, 4.1, 5.1, 6.1, 7.1, 8.1, 9.1, 0.2, …, 9.2, 0.3, …, 9.3, 0.4, …, 9.4, …, …, …, 9.9, 10.0, 11.0, 12.0, … , … etcetera. ]

Many similar mapping, listing, or conversion algorithms can be developed; for the key idea involved is to prevent the “war” of counting from having two “fronts” at the same time; eg: to have an infinite list going “down” and another going “up”; (<–up— 10000, vs, 0.000001–down–>)

What I am doing is combining “smaller” with “larger” so that a single index will encompass both.

Alternate Step 3: Provide a python program which converts from a decimal representation into a unique counting number.

---

Step 4: don’t take over the world, let others do it.

My quest, is in part, about communication with very narrow minded “scientific” types; How ought the subject be approached?

Apologetics isn’t about winning every battle, or gambling (more than once), or even “playing” with people in a cruel way. Nor, I hope, is mathematics about that; though it does often seem that way.

So; What are your thoughts on the philosophy of communication of difficult subjects, and the seeking of a consensus and friendship among people caught in the middle of an ideological warfare zone, much like this one at CAF (but FAR less mature…) ?

– The subject itself has stumped many bright minds for 100’s of years.
– A counter example, with falsifiable premise established, will destroy many careers based on the premise that Aleph 1, and higher exist.
– A0 has already been tied to religion, and those religious implications will come up in the future, even if I do not talk about them in the slightest on the physics forums. This of course gives them a reason to ban me at will whether or not I talk about “God”.
– I was (and still am) looking for people willing to talk (more than argue) in the physics forums, and it is clear that the structure of the site (and many physics sites like it) tends to destroy any attempt at honest communication and collaboration.
– The counter example, I have to offer, of course may be flawed – but I have been as careful as I know how, and it still appears to work. Hence, I have to accept that others are incredulous (reasonably so), and yet they fail to give me normal human courtesy because they believe I will be discredited. Hence, I have two questions I am pondering right now:

1. Given that I succeed (against all “odds”), how do I teach others a lesson (but not an brutalization memorization – if possible) regarding having better communication skills in the future, vs. grinding them into the ground emotionally in a revenge type action into the the hall of “faux pa” shame?
2. Given that I fail (or am trampled by swine, micromass excluded) or even if the counter-example is vindicated in the distant future !!! ------> How do I leave a lasting commentary that will be read by future generations that will lead them toward wisdom?
   Sometimes a failure (like MLK’s jailing) will ultimately prove the tool necessary to correct a problem; it is the triump of a “Cross” WELL PLACED.

 

[Alberti_Devoveo]

I know infinity and God, but you will have to excuse my ignorance of aleph naught. And your notation of counting
0, 1.0, 2.0, … , 9.0, 0.1, …
seems extremely strange and hokey to me.

I do not see any point in trying to map an infinite set of numbers, since you will never get there. David Hilbert proved this conjecture (that actual infinities do not exist) long ago, so you may want to forgive people for not believing you that you can write an algorithm to write an infinite set.

Also, I would avoid using python for any programming, it is okay for writing some quick scripts, but for actual calculations, even using scipy, it is terrible compared to Fortran and/or C/C++.

 

[DaveBj]

Just a minor correction, but the hand-sign for “live long and prosper” shows the whole shin, with the thumb being one vertical line, the index and middle fingers being the middle vertical, and the ring and little fingers being the third vertical.

Decades ago I either heard or read an interview with Leonard Nimoy telling about how the Jewish service on Yom Kippur (if I am remembering correctly) had a part where everyone would turn around so they could not see the rebbe, who would then pronounce a blessing (again, if I am remembering correctly). One year he turned around and sneaked a peek, and the rebbe was holding his hand up in the now familiar gesture. When Nimoy was playing Spock, he decided to use that gesture for the “live long and prosper” gesture.

And thanks, Houiou Theou, for correcting the spelling of Shaddai. Saved me the trouble.

 

[Jaaanosik]

Huiou Theou,
Aleph-naught is a symbol representing something.
Whatever you are going to write down (algorithm, program, …) it’s going to be a ‘symbol’ (just much longer one ).
If you don’t make a mistake then Aleph-naught is going to be equal to your algorithm but they are both just symbols.
If you make a mistake then they are not equal and whatever you wrote is who knows what.

If you try to run your ‘correct’ program and count then it’s not going to happen. You’ll will not be able to actually count what these symbols represent.
Why do you need the new longer symbol? To study psychology?

 

[Huiou_Theou]

I have no idea what you are saying here. I Googled that line and found the PhysicsForum website and I have a vague idea of what you are saying there.

As far as I know, there is no way to list all real numbers because there is an effective infinite (it is not truly infinite since an actual infinity cannot exist in reality, only in potentiality) number of decimal places between 0 and 1.

We can count them in potentiality; that is all I need to show in my count-er example.

And even if you could express an algorithm that would write down all the real numbers,

I believe I can.
It is simple to write down an algorithm to express all the counting numbers in the decimal system. Eg: add one to the “present” count. Inductively, for any count I have an algorithm to represent (n+1), and iteratively (or recursively) list all counting numbers.

you would never be able to (a) write the numbers down or (b) finish writing all the numbers before the universe would end. If there is an effective infinite number of decimal places between 0 and 1, then there is an equal number of decimal places between 1 and 2. Moving onwards, there is an effective infinite number of real numbers, from 0 on up to the largest number possible before infinity.

Now you are into the argument itself. Exactly. Aleph naught is about doing a 1:1 correspondence between any set and any other. You have just assigned a “size” to infinity between 0 and 1, and 1 and 2. (Equal number). And chosen to make two sets.
But there is a formal way to count items in a set, and your intuition may in fact be wrong.

Unless I have completely misunderstood your above rambling and your PF comments, you have lost the bet here, my friend.

No, I haven’t; but many people will believe I have.
IF there are an equal number of items in set 1 and set 2, then it is clear that for whatever number of items there are in set 1 - simply multiply by 2 and add a most significant digit. Then both sets can be counted.

IF you say, “but you can’t do that, because”… then I simply will point you back to my counting algorithm. It does it. If you have objections, then please – let’s discuss them – because I am not allowed to discuss them on the PF or the thread will be shut down.
So, it is far better to at least DEMONSTRATE the point here, and clean up or improve the idea’s defensibility before going live on PF.

I wouldn’t take the challenge if I didn’t think it possible to win; and yes – I might easily loose; but I won’t go down trivially.

 

[Huiou_Theou]

Just a minor correction, but the hand-sign for “live long and prosper” shows the whole shin, with the thumb being one vertical line, the index and middle fingers being the middle vertical, and the ring and little fingers being the third vertical.

David, I don’t have much time. There is a man by the name of George in St. John’s parish in Rochester, Mn. He travels, but that is his home parish. It was he in a study group, there, which he led – that made the comment concerning it being half of what Jewish rabbi’s do in blessing. Perhaps he was mistaken? If you have some documentation I could point to, I’d love to forward it to him in e-mail; perhaps there is something he knows that others don’t, or v. versa…

Decades ago I either heard or read an interview with Leonard Nimoy telling about how the Jewish service on Yom Kippur (if I am remembering correctly) had a part where everyone would turn around so they could not see the rebbe, who would then pronounce a blessing (again, if I am remembering correctly). One year he turned around and sneaked a peek, and the rebbe was holding his hand up in the now familiar gesture. When Nimoy was playing Spock, he decided to use that gesture for the “live long and prosper” gesture.

And thanks, Houiou Theou, for correcting the spelling of Shaddai. Saved me the trouble.

I do the best with the tools I got…

Yes, I seem to recall some kind of interview with Nimoy – but the playboy magazine and half nude yoga picture stuff in it rather annoyed me into not paying much attention to him. Do you think his comments are credible or acted?

 

[Huiou_Theou]

Also, I would avoid using python for any programming, it is okay for writing some quick scripts, but for actual calculations, even using scipy, it is terrible compared to Fortran and/or C/C++.

I have programmed in C and assembly for well over 25 years. C++ was never quite good enough speed and size wise in the early years, and now it is a mess of conflicting libraries. Since the scientific community is starting to use Python wholesale, and because Python has built in libraries which are extremely good – I have been using it for “quick scripts” that I can share with others on the web.

On the PF you will find examples of Python Code which I am using to study certain mathematical constructs. Under C, C++, the language is tied to the math coprocessor available on the hardware of the system, and that choice causes rounding errors which corrupt perfectly good calculations.

Python is slow, I admit, but it is a VERY easy to do complex operations without having to pre-define variables, and include extremely specialized libraries like Boost in C++. Or mpfr, etc. in C; I just include “decimal” – and I can do million digit arithmetic…

To be blunt:
In 5 to 10 lines of code I can often do what would require two pages in C++.
Python is an ideal calculator replacement.

I am intending to use it to make a calculator for doing chemistry problems, significant figures math, and the like for my sons who are going to college soon. I wish I had more time, for my eldest two boys really need it now; and with the national merit scholar securely in hand for at least one of them – I wish my wife hadn’t pushed them a year ahead of their grade level for deadlines are going to start interfering.

I went into college a year too fast, and it would have been better to wait.
Cest la vie. (sp?)

 

[Alberti_Devoveo]

We can count them in potentiality; that is all I need to show in my count-er example.

I can potentially count to infinity. Twice. It seems moot to discuss potentiality, rather than actuality: you could potentially count to infinity, but you cannot actually do so.

I believe I can.
It is simple to write down an algorithm to express all the counting numbers in the decimal system. Eg: add one to the “present” count. Inductively, for any count I have an algorithm to represent (n+1), and iteratively (or recursively) list all counting numbers.

Effectively, you are saying that all you have to do is write a do-loop (speaking as a Fortran coder) that has no end and that it increments a count by one. It is trivial enough, but impractical because your computer would run out of digits before you got very far. I am unsure about Python, but I know the maximum number allowed with quad precision is around 10[sup]4932[/sup].

Now you are into the argument itself. Exactly. Aleph naught is about doing a 1:1 correspondence between any set and any other. You have just assigned a “size” to infinity between 0 and 1, and 1 and 2. (Equal number). And chosen to make two sets.
But there is a formal way to count items in a set, and your intuition may in fact be wrong.

I understand what you want to do a little bit more, I think. If you can go to the infinity-eth decimal place, then you can map each decimal place in a 1:1 correspondence and have an effective algorithm that reproduces all numbers from 0 to infinity.
Since you do not need to actually calculate this, you may not run into the memory issue I mentioned above, since the algorithm will (effectively) be theoretical.

No, I haven’t; but many people will believe I have.
IF there are an equal number of items in set 1 and set 2, then it is clear that for whatever number of items there are in set 1 - simply multiply by 2 and add a most significant digit. Then both sets can be counted.

Perhaps you have not lost the bet, since all you must do is be able to go to the infinity-eth decimal place for only 0 to 1. Sure it is a computational limit that we have now, but we could get there in 10,000 years.

I have programmed in C and assembly for well over 25 years. C++ was never quite good enough speed and size wise in the early years, and now it is a mess of conflicting libraries. Since the scientific community is starting to use Python wholesale, and because Python has built in libraries which are extremely good – I have been using it for “quick scripts” that I can share with others on the web.

On the PF you will find examples of Python Code which I am using to study certain mathematical constructs. Under C, C++, the language is tied to the math coprocessor available on the hardware of the system, and that choice causes rounding errors which corrupt perfectly good calculations.

Python is slow, I admit, but it is a VERY easy to do complex operations without having to pre-define variables, and include extremely specialized libraries like Boost in C++. Or mpfr, etc. in C; I just include “decimal” – and I can do million digit arithmetic…

To be blunt:
In 5 to 10 lines of code I can often do what would require two pages in C++.
Python is an ideal calculator replacement.

I know what you mean. One of my professors wrote a C code to calculate the integral of the modified Bessel function F[sub]n/sub for n=5/2. It was 118 lines long. I wrote a Python script that did it in 7 lines. But, while my program was short, it was not that great at holding the decimal places and my professor’s code had better precision.
Still, if you want ease, I think Fortran is your guy. C/C++ have some issues with length of program, but I have yet to see my Fortran programs hit the lengths of the C/C++ counterparts. And Fortran has some power behind it in terms of extending decimals.

Good luck!

 

[Huiou_Theou]

I can potentially count to infinity. Twice. It seems moot to discuss potentiality, rather than actuality: you could potentially count to infinity, but you cannot actually do so.

Yes and no; The particular issue on PF is a proof that it is impossible to list all the real numbers by an integer/counting number index. This isn’t a subject I am really interested in (practically), but as there seem to be many who are interested in it – I thought I might trade information in order to make a few friends.

Of course, the theological implications of Aleph1, etc. are things which mildly interest me – and will probably come up in the next few years…

Effectively, you are saying that all you have to do is write a do-loop (speaking as a Fortran coder) that has no end and that it increments a count by one. It is trivial enough, but impractical because your computer would run out of digits before you got very far. I am unsure about Python, but I know the maximum number allowed with quad precision is around 10[sup]4932[/sup].

Yes. You are exactly right; and I agree; it’s not practical to list out all the elements.
However, it is not obvious to the mathematical community that a even a for loop can be constructed that would count all possible real numbers, including the irrational ones, exactly once.

That’s really the only thing I am adding to the conversation – it can be done, and here’s how.

I understand what you want to do a little bit more, I think. If you can go to the infinity-eth decimal place, then you can map each decimal place in a 1:1 correspondence and have an effective algorithm that reproduces all numbers from 0 to infinity.
Since you do not need to actually calculate this, you may not run into the memory issue I mentioned above, since the algorithm will (effectively) be theoretical.

Yes, but I am going to get into an argument – undoubtedly – over something called the axiom of choice, which is a proud little axiom which is causing grief in the mathematical community by introducing contradictions. My understanding (second hand) is that it essentially claims that a finite being (like myself) can pretend to have an infinity all at once and compute with certain “reliable” consequences of this “having”.
Of course, I think it nonsense – but others don’t.

Perhaps you have not lost the bet, since all you must do is be able to go to the infinity-eth decimal place for only 0 to 1. Sure it is a computational limit that we have now, but we could get there in 10,000 years.

Well, the issue is this: people are going to ask me to do things in order to prove I have done what I claim I have done, that simply don’t need to be done. I am simply showing HOW it can be done, and evidence that they will not be able to find a flaw in that I haven’t done it.

To a very large percentage of people who read my algorithm, I will be dismissed because they demand more information than the need or have the right to know.

The counter example is to a diagonalization proof (matrix math?) which claims that it can always compute something not in the matrix of any “list” anyone makes of the real numbers; (I think it was called Cantor’s diagonalization). So – I would appreciate if anyone could look at the PF forums thread (now locked) on Cantor’s proof, and consider with me about how my list algorithm would be plugged into it to demonstrate that a conclusion of the proof is wrong.

I’m only going to spend through tomorrow on it; as this is more about making friends than about an ego trip / proof.
I expect the problem of Cantor’s proof is that it reasons by exclusion; and I could demonstrate the problem of “knowing” by exclusion by something called the prisoner’s dillema. I’m not sure if you’ve heard of this or not?

I know what you mean. One of my professors wrote a C code to calculate the integral of the modified Bessel function F[sub]n/sub for n=5/2. It was 118 lines long. I wrote a Python script that did it in 7 lines. But, while my program was short, it was not that great at holding the decimal places and my professor’s code had better precision.
Still, if you want ease, I think Fortran is your guy. C/C++ have some issues with length of program, but I have yet to see my Fortran programs hit the lengths of the C/C++ counterparts. And Fortran has some power behind it in terms of extending decimals.

Good luck!

You might want to look at the decimal class in python. It allows arbitrary digits – and I have recently used it as a 54, 64, and 110 decimal digit calculator to test some ideas about physics and chemistry. It is the basis of the calculator I am developing for my kids and my own personal use.

Definitely NOT fast, but much faster than me, and would solve many problems in plenty of time even on an exam!

Thanks for the well wishing, it helps me deal with the frustration of the other site.

 

[Huiou_Theou]

Huiou Theou,
Aleph-naught is a symbol representing something.
Whatever you are going to write down (algorithm, program, …) it’s going to be a ‘symbol’ (just much longer one ).

Yes, indeed…

If you don’t make a mistake then Aleph-naught is going to be equal to your algorithm but they are both just symbols.
If you make a mistake then they are not equal and whatever you wrote is who knows what.

If you try to run your ‘correct’ program and count then it’s not going to happen. You’ll will not be able to actually count what these symbols represent.
Why do you need the new longer symbol? To study psychology?

I am actually going to make a program first, that if you give me a real number, will tell you the counting number which it would be found at.
For example, if you send my program the number 0, 0.0, 0.00000, etc. It will tell you that is the “first” number in the list. If you can’t write the entire number down, it will still tell you part of the counting number where what you wrote down will be revealed in the listing.

It is about psychology; the psychology of what people believe about things they can’t see. For example, it is very common for people not to believe a child in the womb is a child because they can’t actually see it – now that ultrasounds allow us to see, there is a change of heart coming about in many people on the issue.

The same issue applies with the nth decimal place of a number (though thankfully without an ethics problem if is deleted…).

And more importantly, the issue applies to the very screen and text you are reading – which doesn’t really allow micromass or others see that I am not a fake login, or a heckler, or …, or someone paid to attack the physics website from Christian Science headquarters – or that I am there just there to make his life more miserable.

But, unlike you – micromass chose to use his power and my invisibility to justify a set of behaviors which are rationalizations at best. He would prefer to abort me from PF, to show his “POWER” over me, rather than discover who I am.

 

[Huiou_Theou]

Here is the actual program I think I will submit, and a test run:
I need to figure out how to download a free python interpreter for windows, and probably include instructions so normal people can cut and paste the program and test it too…

#!/bin/env python
"""
This program dedicated to the public domain.
DDiary 00327.00:
Written for and tested on Python 2.7.1, hopefully works on 2.6.x
Andrew F. Robinson, 2012

The purpose of this algorithm is to show that a 1:1 mapping is 
possible between real numbers and counting numbers via decimal
representation.
This version of the algorithm does not include the sign and other
refinements of the original algorithm, see December 2010 notes
for details.

Extracted from conversations of R3DSolutions owner John J Robinson,
and noted in diary 327.

Remember: Ignorance can be cured, but stupidity is forever.
"""

import re

def SignatureToCount( x ):
    sel,y,eel=None,],None
    if not x: return

    sel=re.match(".]{3,}",x)
    if sel: x=x[sel.end():]
    eel=re.search(".]{3,}$",x)
    if eel: x=x:eel.start()]
    if len( re.findall(".]",x) ) > 1: return

    i,end=re.search(".]",x),len(x)
    i=end-1 if i is None else i.start()-1
    step,carry=2,1
    while True:
        if i>=end and ( eel or i-step<0  ): break
        if i<0  and ( sel or i+step>=end ): break
        if i<0 or i>=end:
            digit,carry = carry,0
        else:
            digit, carry=int( x* )+carry, 0
            if digit==10: digit, carry = 0,1
        y.append( str(digit) )
        i, step=i+(-step if step&1 else step), step+1
    if (sel or eel): y.append("...")
    y.reverse()
    return "".join(y)

def Convert():
   while True:
    x=raw_(name removed by moderator)ut( "Enter a decimal signature:" )
    y=SignatureToCount( x )
    if y is None:
        print "Invalid signature detected, try again"
        print "Valid examples: ...17.0405678, 3.99, 3.141...,...0..."
        continue
    print "The index count is:",y

Convert()

Here is a test run to give an idea of how it works…

toot@darkstar:~$ python
Python 2.7.1 (r271:86832, Jan 26 2012, 09:07:02)
[GCC 4.5.3] on linux2
Type “help”, “copyright”, “credits” or “license” for more information.

import signature
Enter a decimal signature:0
The index count is: 1
Enter a decimal signature:1
The index count is: 2
Enter a decimal signature:2
The index count is: 3
Enter a decimal signature:2.1
The index count is: 13
Enter a decimal signature:3.1
The index count is: 14
Enter a decimal signature:4.1
The index count is: 15
Enter a decimal signature:3.999998
The index count is: 809090909094
Enter a decimal signature:3.1415926…
The index count is: …60209050104014
Enter a decimal signature:3.14…]
Invalid signature detected, try again
Valid examples: …17.0405678, 3.99, 3.141…,…0…
Enter a decimal signature:3.14…
The index count is: …4014

quit()
$

What do you think, is it enough to prove the point?
3.14 could be 3.14159 (or even more) and the program does list the same partial counting number (ellipsis means it is incomplete, because the entered number was incomplete…) but no digits change between the two because of this very fact.

3.1415926… → index# …60,209,050,104,014
3.14…-< index# …4,014

Any criticisms? I know counting only 60 Tera-reals in less than 2 seconds is pretty slow when it comes to counting infinity, but the algorithm is here … none the less.

Hopefully this is clever enough to get the social ball rolling…*

 

[DaveBj]

David, I don’t have much time. There is a man by the name of George in St. John’s parish in Rochester, Mn. He travels, but that is his home parish. It was he in a study group, there, which he led – that made the comment concerning it being half of what Jewish rabbi’s do in blessing. Perhaps he was mistaken? If you have some documentation I could point to, I’d love to forward it to him in e-mail; perhaps there is something he knows that others don’t, or v. versa…

I do the best with the tools I got…

Yes, I seem to recall some kind of interview with Nimoy – but the playboy magazine and half nude yoga picture stuff in it rather annoyed me into not paying much attention to him. Do you think his comments are credible or acted?

I’m not really sure what your informant was referring to, whether he meant that the hand gesture was only half of a shin (it’s not; all you have to do is compare the hand gesture to the printed letter to see the similarity), or that he was talking about “live long and prosper” being half of what the rebbe was saying (Nimoy didn’t touch that in the interview that I remember). That interview could have been in a 1970s Playboy; I did read that magazine regularly in my previous life. I thought his comments were believable at the time. We’d have to bring an observant Jew into the discussion to see if the same ritual is being performed today.

Meanwhile, when I have time I’ll see if I can’t find some references. But not this morning

 

[DaveBj]

Had some time, here ya go, Houiou Theou.

upstel.net/~rooster/v-salute.html

Turns out your informant was more correct than my memory.

 

[Jaaanosik]

Yes, indeed…

I am actually going to make a program first, that if you give me a real number, will tell you the counting number which it would be found at.
For example, if you send my program the number 0, 0.0, 0.00000, etc. It will tell you that is the “first” number in the list. If you can’t write the entire number down, it will still tell you part of the counting number where what you wrote down will be revealed in the listing.

It is about psychology; the psychology of what people believe about things they can’t see. For example, it is very common for people not to believe a child in the womb is a child because they can’t actually see it – now that ultrasounds allow us to see, there is a change of heart coming about in many people on the issue.

The same issue applies with the nth decimal place of a number (though thankfully without an ethics problem if is deleted…).

And more importantly, the issue applies to the very screen and text you are reading – which doesn’t really allow micromass or others see that I am not a fake login, or a heckler, or …, or someone paid to attack the physics website from Christian Science headquarters – or that I am there just there to make his life more miserable.

But, unlike you – micromass chose to use his power and my invisibility to justify a set of behaviors which are rationalizations at best. He would prefer to abort me from PF, to show his “POWER” over me, rather than discover who I am.

This seems as a false statement.
Here is a number: generate a text file with ‘0.0000…01’ (replace three dots with ‘0’ till the file size is 1TB) and use the number in this text file as (name removed by moderator)ut to your program.

You just wrote a symbol/representation/… whatever you want to call it.
Anything actual you calculate is a small subset compared to what it represents.
In other C++ words, you created a method of a class but you cannot instantiate it with any number. The instantiation will fail with numbers bigger than is your computer limit for (name removed by moderator)ut.

 

[Huiou_Theou]

This seems as a false statement.
Here is a number: generate a text file with ‘0.0000…01’ (replace three dots with ‘0’ till the file size is 1TB) and use the number in this text file as (name removed by moderator)ut to your program.

You just wrote a symbol/representation/… whatever you want to call it.
Anything actual you calculate is a small subset compared to what it represents.
In other C++ words, you created a method of a class but you cannot instantiate it with any number. The instantiation will fail with numbers bigger than is your computer limit for (name removed by moderator)ut.

Ok, I’d have to add a 2TB swap file as I don’t have enough physical memory; and then I found out I hit the virtual memory space barrier for my 32 bit machine. But after making a very small modification to the python program – I could get it to run on a file rather than on in system memory (RAM/SIMM/DIMM/dang!);

The result is “100…1” where the dots are close to 2TB worth of zeroes that won’t fit in this post. But it does do it; and the result is a counting number – just a dang big one. I don’t think I’m going to bother giving the modified program to the PF at this time, the one I developed here already gives the basic idea and works to a million digits+.

A comp-sci major could re-write it into C,C++, or as a file processing for Python, or even as a 64 bit application if anyone care to bother (but Python has trouble with strings larger than 100Megabyte, so I doubt it will help until that issue is sorted out).
But, in the end, I think it will be merely reduced to the mathematical symbols used in the attempted proofs of Aleph Naught, and then argued over for quite some time.

But you are right, I made another symbol … didn’t I?

Does the statement still seem false?

I can do this process again and again until my computer fails, or someone invents a computer AKA (DEEP THOUGHT) that can run for a seriously long time. But in potential, I can list as much of the infinity of reals as anyone would like – and in actuality, I can list more of it than is humanly worth having.

The number you gave me would be a very long way into my list, but it is there, and I know how many OTHER numbers would come first before I found it.
Is it sort of difficult to wrap you head around? (so to speak…)

The point is, that anyone who takes the algorithm and example list seriously, will have to actually plug it into the diagonalization proof – and then we will all find out where (if not why) the diagonalization proof is ill defined.

Right now I’m going to study ways to get Python running on my brother’s Win XP box (some windows XP professionals come with it pre-installed, but this one didn’t.). I can then give people simple instructions on how to get a legal, free copy, of Python and run my program or write their own…

How about you ??, are you running on Windows XP, 2000, or Windows 7?

Would you be willing to tinker with the algorithm a little bit today/tomorrow and tell me if my instructions to get it running (soon to follow this post) are any good?

(I told the people on the PF I’d give them the algorithm before, I think Saturday or Saturday’s end, so there isn’t much time left … I did that mostly to put an end point to it’s’ absorbing my limited functional brain time.)

 

[Huiou_Theou]

There are several Python releases; Most Linux releases come with at least a 2.6.x version of Python. I have found the 2.7.x versions enhancements in the math libraries to be very useful, although I am still writing scripts aimed at being compatible with the standard 2.6 releases.

(eg: You shouldn’t need python 2.7.x if you already have 2.6.x – if it doesn’t work, let me know what I broke, and if it’s my mistake, I’ll fix it.)

I assume Linux users just get it from their distribution; Mac OS-X 10.1 and above should already have it installed. So the only inconsistent system is good old Microsoft Windows which often doesn’t.

Python 2.7.x may be found and downloaded here for all mainstream OS’s:

python.org/download/releases/2.7.2/

Direct link to Win/32 bit installer: python.org/ftp/python/2.7.2/python-2.7.2.msi
Direct link to Win/64 bit installer: python.org/ftp/python/2.7.2/python-2.7.2.amd64.msi

After FINISHING downloading, I simply double click on the downloaded package icon to launch the installer. It shows up on my desktop labeled python-2.7.2.

Alternately, if you accidentally downloaded to a hidden location, you can still (in Firefox web-browsers at least – Use ctrl-J to get the download window to come back!!!) you can still double click the install package from the download menu.

Once the program starts the install shield, follow the install instructions (I am just going to click OK at every step which does work…).

The installer could install software with virus potential if you have an unethical ISP between you and the python.org website. I have no control over how this page could be interfered with by third parties; so please – if your computer is run time critical – check the security sums for the download packages against the ones found on the actual python.org webpage.

--------------------- RUNNING PYTHON SCRIPTS MANUALLY ----------------------​

I am running this on windows XP, and this is how it works for me:

To run Python, click Start, Programs, Python 2.7, IDLE (Python GUI)
or in place of IDLE, you can launch command line. I like the command line better as the up-arrow allows me to edit old commands quickly – the other program (IDLE) has a little more mouse based features that will appeal to beginners.

Once the text interpreter is up, one can simply type python commands followed by enter into the window. Here’s a simple session:

Python 2.7.2 (default, Jun 12 2011, 15:08:59) [MSC v.1500 32 bit (Intel)] on win32
Type "copyright", "credits" or "license()" for more information.
>>> import os
>>> os.getcwd()
'C:\\Python27'
>>> dir(os)
KeyboardInterrupt
>>> # This is a comment
>>> # KeyboardInterrupt means I pressed ctrl-C, you can press enter if you like there...
>>> # to quit, I can press hangup eg: ctrl-D
>>> # or I can type quit()
>>> quit()

I typed “import os” to find out operating system information; I mean, I did it because I wanted to find out where to save my scripts so they can be run by python…

Now, to get the script from forums.catholic-questions.org, first I’ll start a word-processor:
start->run->wordpad.exe
press enter, and then bring up this link forums.catholic-questions.org/showpost.php?p=8940613&postcount=15 to copy and paste the Python script I wrote into the word processor; In firefox you can do a control click on the link to bring it up in a separate tab to make referring back to these instructions easier. I don’t know how to do it in IE…

Now, once the old post is up – I simply mouse hilight everything in the “code” box, and I actually drag the mouse below the code box to make it scroll down while hilighting. Once all the code is highlighted, I press control C – or do an “edit–>copy”.

Then I switch to the wordpad text editor, and do an Edit->paste. (Ctrl-V)
After which I do a File–>saveAs
Then I click browse to look for the place Python told me about “C:\Python27”
I type in a file name: sigfig.py
and VERY importantly, I set “Save as type:” to “Text document”
Once that is changed (Python does not use RTF text!!!) I click “Save”
At which point it complains about removing formatting and I say “YES!”

Now my script is saved where python can find it; it is called “sigfig.py” and I can try running it!!!

To run Python (again), click Start, Programs, Python 2.7, IDLE (Python GUI)

Python 2.7.2 (default, Jun 12 2011, 15:08:59) [MSC v.1500 32 bit (Intel)] on win32
Type “copyright”, “credits” or “license()” for more information.

import sigfig
Enter a decimal signature:0
The index count is: 1
Enter a decimal signature:0.000000001
The index count is: 100000000000000001
Enter a decimal signature:3.14…
The index count is: …4014
Enter a decimal signature:

Traceback (most recent call last):
File “<pyshell#0>”, line 1, in
import sigfig
File “C:\Python27\sigfig.py”, line 60, in
Convert()
File “C:\Python27\sigfig.py”, line 52, in Convert
x=raw_(name removed by moderator)ut( “Enter a decimal signature:” )
EOFError: EOF when reading a line

quit()

And that’s all folks !!!