Cont: Deeper than primes - Continuation 2

[realpaladin]

Dessi sure provided the influx of a new breath of comic relief in this 7 year old discussion. Mostly due to the fact that she thinks herself a smart enough cookie not to read back and so being prone to repeating the errors of all that have gone before.

There is a description for that behaviour, but let's not dwell on that. This thread is about Doron's Discoveries.

My prediction (and ok, it is rather a repeat of earlier predictions, all of which have come true for the most part) is that *any* discussion with Doron about this subject will go like this:

A = n00b poster in the thread, B = jsfisher or other veteran, C = Doron

A: Look, C, I am not rude like these others, I offer you logic in formal language X, Y or Z
B: That's no use, we went through all of them over the course of years
A: *pedantic* I am smarter than you guys, look C, here it is, infallible ironclad logic
B: No, not smarter, just more intelligent, there's a difference...
C: *ignore B* Ah, fresh blood... eh... hello welcome newcomer, let me see what you have written...
C: Ah, yes, but if we twist meaning f into slot g then your logic fails you because you do not know how to twist. In fact, that is nowhere to be seen in your so-called logic.
A: Well, then show me how to twist f into g, then I will gladly point out where you went wrong.
C: Ok, if you use a rapuctor to boodlezwam into infinity then all the real numbers take off their plastic coating and become all natural.
A: Wut? You can't use a rapuctor for that! What the heck *is* a rapuctor anyway? Look, real numbers are not the same as natural numbers, here is the ironclad logic, backed up by bulletproof math.
B: Been there, done that, got the hat.
C: *ignore B* You see, that is where you are wrong, your logic simply does not allow you to boodlezwam! And therefore, anything you want to prove in your logic is wrong.
A: *ignore B* Ok, so then show me how you define boodlezwam.
C: Please respond to rapuctor! Show me why it can not beedlebork!
A: Beedlebork? Boodlezwam? That's not even real math!
C: You don't get it! Please respond to Boodlebork!
A: *silently ignores the thread, never to be heard from again*
B: Cheers Doron, here's to another year!

 

[doronshadmi]

..

 

[doronshadmi]

Can you show me the steps involved in your calculation?

Dear Dessi, as long as you think only in terms of serial steps, you have no chance to conclude anything of what I say.

Pretend that I'm not a mathematician, pretend I'm a random person off the street or maybe a student in a high school class. How do you explain "observes the real line from cardinality |N|" so that a layman without any specialized mathematical training could understand it?

Let's say that you wish to build an infinitely long line of curbstones along a trail, such that each curbstone is marked by a unique symbol, for example {1,2,3,...}.

If there is a one worker that puts the curbstones step-by-step, the mission is never accomplished.

If there is a bijection between workers and curbstones, each worker puts exactly one curbstone along the trail together with the rest of the workers in the same time, and the mission is accomplished in one step (this working style is done in parallel).

 

[doronshadmi]

For the naive and the eternally hopeful, I offer this link wherein Doron provides new insights and understandings into Zeno's Paradox, complete with three programming examples.

this link is irrelevant anymore to what is written in http://www.internationalskeptics.com/forums/showpost.php?p=10332081&postcount=110.

 

[doronshadmi]

jsfisher provided one such example

Already answered in http://www.internationalskeptics.com/forums/showpost.php?p=10329187&postcount=78.

 

[Apathia]

Dessi sure provided the influx of a new breath of comic relief in this 7 year old discussion. Mostly due to the fact that she thinks herself a smart enough cookie not to read back and so being prone to repeating the errors of all that have gone before.

There is a description for that behaviour, but let's not dwell on that. This thread is about Doron's Discoveries.

My prediction (and ok, it is rather a repeat of earlier predictions, all of which have come true for the most part) is that *any* discussion with Doron about this subject will go like this:

A = n00b poster in the thread, B = jsfisher or other veteran, C = Doron

A: Look, C, I am not rude like these others, I offer you logic in formal language X, Y or Z
B: That's no use, we went through all of them over the course of years
A: *pedantic* I am smarter than you guys, look C, here it is, infallible ironclad logic
B: No, not smarter, just more intelligent, there's a difference...
C: *ignore B* Ah, fresh blood... eh... hello welcome newcomer, let me see what you have written...
C: Ah, yes, but if we twist meaning f into slot g then your logic fails you because you do not know how to twist. In fact, that is nowhere to be seen in your so-called logic.
A: Well, then show me how to twist f into g, then I will gladly point out where you went wrong.
C: Ok, if you use a rapuctor to boodlezwam into infinity then all the real numbers take off their plastic coating and become all natural.
A: Wut? You can't use a rapuctor for that! What the heck *is* a rapuctor anyway? Look, real numbers are not the same as natural numbers, here is the ironclad logic, backed up by bulletproof math.
B: Been there, done that, got the hat.
C: *ignore B* You see, that is where you are wrong, your logic simply does not allow you to boodlezwam! And therefore, anything you want to prove in your logic is wrong.
A: *ignore B* Ok, so then show me how you define boodlezwam.
C: Please respond to rapuctor! Show me why it can not beedlebork!
A: Beedlebork? Boodlezwam? That's not even real math!
C: You don't get it! Please respond to Boodlebork!
A: *silently ignores the thread, never to be heard from again*
B: Cheers Doron, here's to another year!

Don't forget D! The guy who successfully predicts the debacle. Yes, yes. We have seen them come and go.

And then there's E. The Lurker, who went silent but still watches in morbid fascination whenever new blood tries to engage Doron.

This E. thanks the As, especially the current one, for helping illuminate Doron's frame of thinking.

 

[realpaladin]

Don't forget D! The guy who successfully predicts the debacle. Yes, yes. We have seen them come and go.

And then there's E. The Lurker, who went silent but still watches in morbid fascination whenever new blood tries to engage Doron.

This E. thanks the As, especially the current one, for helping illuminate Doron's frame of thinking.

Thank you for putting me in my place, I needed that/had it coming

 

[realpaladin]

Dear Dessi, as long as you think only in terms of serial steps, you have no chance to conclude anything of what I say.



Let's say that you wish to build an infinitely long line of curbstones along a trail, such that each curbstone is marked by a unique symbol, for example {1,2,3,...}.

If there is a one worker that puts the curbstones step-by-step, the mission is never accomplished.

If there is a bijection between workers and curbstones, each worker puts exactly one curbstone along the trail together with the rest of the workers in the same time, and the mission is accomplished in one step (this working style is done in parallel).

The logic error in this example is of course that this will only accomplish the laying of the curbstones.

It will not tell you how many there are, since no single worker knows how many others there are to the left or to the right of him.
EDIT: actually, the first worker knows that on one side there is nobody there...

They'd need to sound off, like 1, 2, 3... like... oh... for want of a better word... sequentially?

 

[doronshadmi]

Doron can only think of mathematical expressions in terms of a computer program.

Dear Dessi, you are wrong in this case, please do not try to understand me only according to your remarkable Programming Background (
1997: VB5
1998: VB6
1999: HTML
1999: JavaScript
1999: VBScript/Classic ASP
2000: PHP
2001: C++*
2001: Java
2002: Perl*
2003: VB.Net
2004: C#
2006: Python
2007: Delphi
2007: OCaml
2007: F#
)

 

[Dessi]

Also Ruby ^_^

 

[doronshadmi]

Also Ruby ^_^

Great!

Please reply to http://www.internationalskeptics.com/forums/showpost.php?p=10333177&postcount=143.

Thank you.

 

[Dessi]

Pretend that I'm not a mathematician, pretend I'm a random person off the street or maybe a student in a high school class. How do you explain "observes the real line from cardinality |N|" so that a layman without any specialized mathematical training could understand it?

Let's say that you wish to build an infinitely long line of curbstones along a trail, such that each curbstone is marked by a unique symbol, for example {1,2,3,...}.

If there is a one worker that puts the curbstones step-by-step, the mission is never accomplished.

If there is a bijection between workers and curbstones, each worker puts exactly one curbstone along the trail together with the rest of the workers in the same time, and the mission is accomplished in one step (this working style is done in parallel).

If an infinite number of workers placing an infinite number of stones completes the mission, can I say that one worker who places an infinite number of stones infinitely fast also completes the mission? I think so. Are an infinite number of workers equivalent to a single infinitely productive worker? Seems like it.

Does it make a difference whether we set all stones in the set simultaneously, or set stones one after the other at infinite speed? No, not really. It's hard for me to see the difference.

Is my thinking here correct?

--

Also, out of curiosity can you explain how one " observes the real-line is observed from |R| cardinality", in layman-friendly terms?

 

[Dessi]

A: *silently ignores the thread, never to be heard from again*

I not generally invested in threads for very long anyway.

Actually, I am rarely invested in online communities longer than a year either. ISF is a very exceptional case, it's active and interesting. I never thought I'd have more than a few dozen posts after I joined.

 

[Apathia]

Thank you for putting me in my place, I needed that/had it coming

Well, you're certainly not the only one who has played the D role in this fine Human interest story. There's Zooterkin and others.

And there are better Es who have more sense than to post in this thread.

 

[realpaladin]

I not generally invested in threads for very long anyway.

Actually, I am rarely invested in online communities longer than a year either. ISF is a very exceptional case, it's active and interesting. I never thought I'd have more than a few dozen posts after I joined.

And here you are, over 2.5k posts...

Btw, I see that you are mostly into the garbage collected languages?
(I count Bjarne's concoction not to the bare metal languages; I find it a hideous construct, but that is for another thread).

How about doing some real fun with ASM? Making your code trick the MMU so it fits completely in the L1 Cache and all of it's data in the L2?

As far as I can make out from your online presence, coding is a tool to express your mathematical abilities, not generic problem solving (as in hacking stuff).

But all of that is neither here nor there, we are talking about this 'Deeper than Primes' thingy.

The reason why most people stay away after some time is because Doron has the uncanny ability to trick people in defending their stance that his claim is wrong. He plays 'reductio ad absurdum' all the time.

But this is not the correct scientific way; Doron makes a claim, Doron needs to corroborate it.

The rest of us do not have to prove that he is wrong; he must prove he is right.

 

[realpaladin]

Well, you're certainly not the only one who has played the D role in this fine Human interest story. There's Zooterkin and others.

And there are better Es who have more sense than to post in this thread.

Yep. As I said before, Doron is like having a favourite toothache.

But it would be something if we ever would make *some* progress.

We had unity, Transcendental Meditation, Organic Mathematics, infinity, two islands, Cantor is wrong, Cantor is right, etc...

And I keep asking "ok, what *if* we *all* agreed that you are right, without need for any proof, then what?" and we never get an answer to that...

So my conclusion from the empiric evidence is that Doron's goal is kibitzing and nought else.

 

[jsfisher]

Direct perception is still my favorite. How can you go wrong with direct perception?

If Doron thinks it true, well, it must be true because that's what Doron perceives it to be...directly. My only regret is the direct perception is inaccessible to the rest of us because of that visual/spatial thing or something. Actually, we just don't get it.

Heck, I'm so backwards I believe the union of the members of {{A}, {B}} to be {A, B} instead of {{A}, {B}}....

 

[doronshadmi]

Does it make a difference whether we set all stones in the set simultaneously, or set stones one after the other at infinite speed? No, not really. It's hard for me to see the difference.

Dear Dessi,

First, please look again at http://www.internationalskeptics.com/forums/showpost.php?p=10330277&postcount=102.



In terms of process, infinite sequential (step-by-step) speed is equivalent to moving all stones simultaneously (in parallel, by one step).

So in both cases the keyword is one step, or on other words: "mission is accomplished by one step", which means that there is no room for the notion of process of more than one step among the considered subject.

Again, infinite sequential (step-by-step) speed is actually one and only one step, or in other words, the notion of more than one step (for example: step-by-step) is not satisfied.

So the parallel model is better than the serial model as an explanation method for layman, because it is naturally lack of any potential illusion of process of more than one step among the considered subject.

Here is a concrete example of wrong conclusions by a person that is definitely not a layman, if she observes infinite collections only in terms of serial (step-by-step) observation: http://www.internationalskeptics.com/forums/showpost.php?p=10326945&postcount=66.

If you fail because you are using only step-by-step observation of infinite collections, it is clear that your only step-by-step observation is not a useful point of view to explain |N| to a given layman.

Once again, the cardinality of the natural numbers is |N| and this size is known in one step, no matter what complexity is involved among the natural numbers, as demonstrated, for example, in the following diagram:

Also, out of curiosity can you explain how one " observes the real-line is observed from |R| cardinality", in layman-friendly terms?

Since the considered subject here is related to process in terms of one step (no processes of more than one step is used) one easily follows after one step |R| and one step |N| of the real-line, by using the fact that |N|<|R|, and this is exactly what I am doing in http://www.internationalskeptics.com/forums/showpost.php?p=10332081&postcount=110.

Dear Dessi, using ∞ in order to deduce conclusions in terms of infinity is not accurate enough, simply because it does not use the accurate observation of |N| < |P(N)| < |P(P(N))| < |P(P(P(N)))| < |P(P(P(P(N))))| < ... different levels of infinity, where each one of them is achieved in no more than one step.

 

[Dessi]

And here you are, over 2.5k posts...

Btw, I see that you are mostly into the garbage collected languages?
(I count Bjarne's concoction not to the bare metal languages; I find it a hideous construct, but that is for another thread).

How about doing some real fun with ASM? Making your code trick the MMU so it fits completely in the L1 Cache and all of it's data in the L2?

But I can't even see the metal while floating 30,000 ft on my Haskell cloud.

As far as I can make out from your online presence, coding is a tool to express your mathematical abilities, not generic problem solving (as in hacking stuff).

I'm a professional software engineer who tinkers with Arduino and functional programming ^_^

I prefer to express mathematical concepts using established, accepted mathematical notation. Unless I were specifically explaining how to encode certain concepts in code, like an implementation of a specific graphing algorithm, I would almost never use a source code to express a mathematical concept.

The snippet of pseudocode in this post is not meant to illustrate a mathematical concept. That piece of code was authored by Doron, not myself, in his paper on Zeno's paradox. I did a quick peer review and noticed his paper incorrectly states that the program models an infintely long race, when in fact in models a 1 second long race.

The snippet of code in this post is not meant to illustrate a mathematical either. I provided it to support my personal speculation on how Doron arrives at concepts like "different instantiations of 2". I hypothesize that, if this concept is meaningful to Doron, it must be because he is a Java programmer, and he generalizes the quirks in Java's type system (where "different instantiations of 2" is a meaningful statement) as an inherent feature in mathematics.

But all of that is neither here nor there, we are talking about this 'Deeper than Primes' thingy. [ . . . ]

But this is not the correct scientific way; Doron makes a claim, Doron needs to corroborate it.

Doron can correct me if I'm wrong, but I gather from his posts that he's a programmer with an interest in mathematics.

I hypothesize that Doron interprets mathematical notation as a kind of source code. Mathematics is a kind of programming language with its own unique and flexible syntax. Computation is, conceptually, the result of executing mathematical source code on a computer. His comments actually make a lot of sense in this context:

• The distinction between "serial-computation" and "parallel-computation". Obviously a computer program would never halt on inputs involving actual infinities, so we need to optimize its execution. Parallelization is the most straightforward optimization. Doron agrees that an infinitely fast serial process is an acceptable and equivalent optimization.
  
  
• He presumably makes a distinction between "different instantiations of 2". This is the exact same verbiage that object-oriented programmers use to explain how different instances of a class/type may contain same value, but are not referentially equal because they are stored at different addresses in memory. Evidently numeric values and variables in a mathematical expressions imply allocating memory and new'ing up instances of the Number class.
  
  
• On a computer, 0.999... not exactly equal to 1, because they have a different pattern of bits. 0.999... and 1 can't be equal because they are not bitwise equal.
  
  
• 0.000...1 is defined to be the smallest interval between 0.999... and 1. This number serves the same purpose as machine episilon, which is the upperbound relative error in floating point arithematic on computers.
  
  
• He wrote a paper analyzing Zeno's paradox. But, instead of using the standard mathematical notation of series and recurrence relations, he literally wrote source code in a BASIC-like pseudocode, complete with loops and mutable variables. Code is code, right? It should be readable. The dense and ugly syntax of mathematics, APL, or Perl, is almost never preferable to readable pseudocode.
  
  
• He insists that parallel-thinking is not a "process", not an "operator", it's not really anything that can be expressed in mathematical notation. It's a different way of thinking about the objects modeled in code, it's a programming paradigm.

In this mindset, quirks and gotchas in computer arithmetic are inherent features in mathematics more generally.

That's just my hypothesis. I'm happy to be corrected if I've misinterpreted Doron entirely.

In the mean time, Doron, you will enjoy reading the evolution of a Haskell programmer

 

[realpaladin]

But I can't even see the metal while floating 30,000 ft on my Haskell cloud.

Jenga... that's why I can teach my students to get into just about any system nowadays

I'm a professional software engineer who tinkers with Arduino and functional programming ^_^

Well coding is a meritocracy where designations mean little; I mean, I managed a company in India for 1.5 years and I got certified PhD guys in software engineering who I had to teach the basics of complexity theory.

I prefer to express mathematical concepts using established, accepted mathematical notation. Unless I were specifically explaining how to encode certain concepts in code, like an implementation of a specific graphing algorithm, I would almost never use a source code to express a mathematical concept.

That's where we would differ; I would use anything that works. If that would mean using a cardboard difference engine or plastic bottles filled with sand, so be it.

The snippet of pseudocode in this post is not meant to illustrate a mathematical concept. That piece of code was authored by Doron, not myself, in his paper on Zeno's paradox. I did a quick peer review and noticed his paper incorrectly states that the program models an infintely long race, when in fact in models a 1 second long race.

Cool. I'll add that to the communities' services rendered to Mr. Shadmi; code reviewing.

The snippet of code in this post is not meant to illustrate a mathematical either. I provided it to support my personal speculation on how Doron arrives at concepts like "different instantiations of 2". I hypothesize that, if this concept is meaningful to Doron, it must be because he is a Java programmer, and he generalizes the quirks in Java's type system (where "different instantiations of 2" is a meaningful statement) as an inherent feature in mathematics.

I rather have him pegged as a (Turbo)Pascal user who now migrates to Java.

Doron can correct me if I'm wrong, but I gather from his posts that he's a programmer with an interest in mathematics.

I hypothesize that Doron interprets mathematical notation as a kind of source code. Mathematics is a kind of programming language with its own unique and flexible syntax. Computation is, conceptually, the result of executing mathematical source code on a computer. His comments actually make a lot of sense in this context:

[*] The distinction between "serial-computation" and "parallel-computation". Obviously a computer program would never halt on inputs involving actual infinities, so we need to optimize its execution. Parallelization is the most straightforward optimization. Doron agrees that an infinitely fast serial process is an acceptable and equivalent optimization.

Which is essentially correct. But he needs to get his analogies right, that is why I mentioned the weighing versus counting; weighing is basically a one-step parallel addition of all the weights, as opposed to weighing one stone after another and adding all their respective weights together.

[*] He presumably makes a distinction between "different instantiations of 2". Obviously that means 2 instances which are not referentially equal, they happen to be the same value which are stored at different addresses in memory.


[*] On a computer, 0.999... not exactly equal to 1, because they have a different pattern of bits. 0.999... and 1 can't be equal because they are not bitwise equal.

I think that one is rather his 'intuitive feeling that something is rotten in Kislev'... if the most significant digit is different then the numbers must be different. Something like that.

[*] 0.000...1 is defined to be the smallest interval between 0.999... and 1. This number serves the same purpose as machine episilon, which is the upperbound relative error in floating point arithematic on computers.

But you do know that in mathematics, there is no smallest interval in a limit.

[*] He wrote a paper analyzing Zeno's paradox. But, instead of using the standard mathematical notation of series and recurrence relations, he literally wrote source code in a BASIC-like pseudocode, complete with loops and mutable variables. Code is code, right? It should be readable. The dense and ugly syntax of mathematics, APL, or Perl, is almost never preferable to easy-to-read pseudocode.

Try doing that in Brainf*ck (which, as you know, *is* a programming language)...

[*] He insists that parallel-thinking is not a "process", not an "operator", it's not really anything that can be expressed in mathematical notation. It's a different way of thinking about the objects modeled in code, it's a programming paradigm.[/list]
In this mindset, quirks and gotchas in computer arithmetic are inherent features in mathematics more generally.

That's just my hypothesis. I'm happy to be corrected if I've misinterpreted Doron entirely.

You've done pretty well.

The part that is missing is his intentions; at one point everyone in the thread agreed with him for the sake of finally moving on.

Then we got to the two islands thought experiment and he got tangled up; since then he supposedly ignores me, but keeps reacting (not responding, mind you) to my posts.

As Apathia stated; the pattern repeats and repeats; whatever happens, his joy is in the discussing of something and not in the achieving of something.

In the mean time, Doron, you will enjoy reading the evolution of a Haskell programmer

Yes, now there is some bliss when you have known the horrors of COBOL...

EDIT: I kind of mangled the layout somewhat... too lazy to fix properly