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19th November 2014, 02:19 PM  #121 
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(I presume from your foto's etc. that you are quite a bit younger than I am).
And *that* is why modern computing is broken! What is wrong with normal black coffee and vi? You see, whenever a 'new and hip paradigm' is discussed, I get passed by all them youngsters, but whenever I enter a competition I hand them their behinds on an epic scale... All you need is the patience to think (and caffeine to stay awake during that process) and the ability to find all the letters on the keyboard in an acceptable timespan. I never needed a debugger or profiler either and still my code runs stable and blazing fast. </old fart mode off> EDIT: ^^^ that is for fun, I am not a *grumpy* old man...(I am not even *that* old ahem) 
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19th November 2014, 02:25 PM  #122 
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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

19th November 2014, 02:43 PM  #124 
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In my model (which is finer and therefore stronger than your model) 0.999... = 1 if the realline is observed from N cardinality, or 0.999... < 1 if the realline is observed from R cardinality, and no intuition is involved in http://www.internationalskeptics.com...&postcount=110.
Moreover, by observing the realline from N cardinality _{0.999...}_{10} is an exact value along the real line that is < value 1 by the exact value 0.000...1_{10}. 
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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

19th November 2014, 02:50 PM  #125 
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It is selfevident if you observe the realline by cardinality R exactly as done in http://www.internationalskeptics.com...&postcount=110.

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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

19th November 2014, 03:05 PM  #126 
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No, it isn't selfevident. I would also say the following statement:
"Exactly as some finite series that is observed from a convergent sequence with N values < some given limit value" requires justification. Your statement implies that the sum S of a series Σ(n = 0, n > ∞) f(n) has a limit L, then S < L. How do you know S < L? Can you show a proof? Let me narrow the scope so we aren't talking about very broad generalities: you agree that S = Σ(n = 0, n > ∞) (9/10)(1/10n) has a limit L = 1, how do you show S < 1? 
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19th November 2014, 03:06 PM  #127 
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You keep saying this as if it were sensible. It isn't. The real number line does not enter the discussion at any point, yet you keep referring to it and you keep accusing others of "observ[ing it] from N cardinality", which no one has done, even if we knew what exactly you meant by that particular confluence of words.
The only thing under consideration is the valuation of Sum(n=1 to infinity, 9/10^n). The valuation of that summation, by the way, is a matter of definition, not point of view. You cannot disprove Mathematics by redefining its terms, although you persist in trying. 
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19th November 2014, 03:13 PM  #128 
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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

19th November 2014, 03:20 PM  #129 
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19th November 2014, 03:38 PM  #130 
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I would like to do that, but however one "observes the real line from cardinality N" is undefined. I just don't know what you are talking about. You comment could be profoundly insightful, or simply gibberish, and I wouldn't know the difference.
Suppose I told you that 0.999... = 1 because its a monad which is a monoid in the category of endofunctors, but I never told you the meaning of any of those words. Suppose you asked me what a monoid is, and I said is a pointset anamorphism on the category of monads, you would not find that helpful. Suppose you asked me to explain what these words meant, explain the meaning of "pointset anamorphism" so that mere mortals could understand it. And I replied that an anamorphism is obviously an injective catamorphism in the disjointunion of topological categories... so what the problem? You might find that unhelpful too. How would you know if my original statement was right? or wrong? or mu? How would you know speaking truthfully or speaking gibberish? That's how I feel right now. Your proof is wrapped up in so much obscure jargon that no one, no matter their mathematical background, understands a word of what you say. I simply don't know what you are describing by the words "observing the realline from cardinality N", I can't even guess at the meaning. I would be most appreciative if you could communicate your thoughts in clear, precise, meaningful language. This isn't an unreasonable request. I would love if you could just clarify and define your jargon, without piling more and more jargon. 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? 
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19th November 2014, 04:47 PM  #131 
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Dessi, a naive question: is it reasonable (or even helpful) to ask for Doron to reproduce a simple living example in code (e.g c# or f#)? I'm thinking this would give us some insight into the process by eliminating the jargon.
Edit: no disrespect to Doron is intended, I'm just trying to get my head around what he's trying to communicate. 
19th November 2014, 05:19 PM  #132 
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It certainly couldn't hurt. I'd also recommend MathNet.Numerics.FSharp for arbitrary precision arithmetic.

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19th November 2014, 05:47 PM  #133 
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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.

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19th November 2014, 06:24 PM  #134 
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When I observe from the realline from N cardinality, I find 0.999... = 1.
Clearly I've made a mistake, or maybe you have. Can you show me the steps involved in your calculation? I read the post you linked and could not understand a word of it, so I would appreciate if you could provide a laymanfriendly description for my benefit. I also could not define any function f(x) = 0.000...1. How would you define f(x), using a laymanfriendly description? 
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19th November 2014, 06:38 PM  #135 
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19th November 2014, 06:43 PM  #136 
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19th November 2014, 07:50 PM  #137 
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This post nails it: Doron can only think of mathematical expressions in terms of a computer program. I am not at all surprised his analysis of Zeno's paradox involves an algorithm in pseudocode.
That said, I notice an error in Doron's analysis of Case B, in which he tries to determine Achille's position as the sum of shorter and shorter time intervals: Code:
Position X1 = 0 Position X2 = 10 Achilles Speed = Aspeed = 10 Tortoise Speed = Tspeed = 1 Time = 1 Do Loop K from 1 to ∞ Achilles position = position X1 + distance ( = Aspeed * Time) Tortoise position = position X2 + distance (= Tspeed * Time) Position X1 = Achilles position Position X2 = Tortoise position If X1 ≥ X2 then STOP Time = Time / Aspeed (Achilles Speed = Aspeed = 10) Next Loop K Total Time = t_{n} + t_{n1}/ASpeed, t_{1} = 1. Total Time = 1 + 1/10 + 1/100 + 1/1000 + . . . Total Time = Σ(k = 0, k > ∞) 1*(1/10^{k}) Total Time = (1 / (1  1/10) ) [ see this identity ] Total Time = 1 / (9/10) Total Time = 10/9 Doron's article says "The Race continues forever", but that's not true. After infinite iterations of his loop, about 1 second of the race has actually elapsed, falling short of forever by a considerable margin. The program runs indefinitely only by accident, because Achilles is just too slow to overtake the tortoise in such a small interval of time. If ASpeed = 11 and the program maintains the loop invariant t_{k} = t_{k1} / ASpeed, the program halts:  Total elapsed time = Σ(k = 0, k > ∞) 1*(1/11^{k}) = 1 / (1  (1/11) ) = 11/10 seconds  Achille's position = start position + speed * elapsed duration = 0 + 11 * 11/10 = 121/10 units  Tortoise position = start position + speed * elapsed duration = 10 + 1 * 11/10 = 100/10 + 11/10 = 111/10 units In fact, the program is guaranteed to halt for any ASpeed > 10. 
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19th November 2014, 08:26 PM  #138 
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Yup. Always a process. Even his imaginary parallel summation is a process, albeit a process of just one nondeterministic step.
In addition to process, notation is important. Doron had maintained that 1/4 and 0.25 were different numbers (though he may have finally abandoned that absurdity). There is also something of a concrete instance requirement the peeks out now and then. According to Doron, 2 is not a member of {2}, apparently because those must be different instantiations of 2. Curiously, too, at the very beginning of his Zeno paper, Doron explicitly states that 1 + 1/2 + 1/4 + 1/8 + ... = 2. That is in stark contrast to his stated position, here, regarding 0.111... in base2. Contradiction is no stranger to Doron. 
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19th November 2014, 10:38 PM  #139 
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I am not familiar with Doron's other posts, but if this statement is true, it tells me he thinks of mathematical series only in terms of computer programs, and apparently thinks of programs only in terms of Java.
This deserves an explanation: a handful of builtin types in Java are not objects, but are primitives. For example, Java has an int primitive, but it also has an Integer class which is a wrapper around ints. This wrapper class exists to makes Java's implementation of parametric polymorphism / generics work. Normally, Java's autoboxing usually makes the distinction between primitives and their object wrappers fairly transparent. Usually. There are exceptions: Code:
Integer smallX = 10; Integer smallY = 10; if (smallX == smallY) System.out.println("smallX equals smallY"); else System.out.println("smallX does not equal smallY"); Integer bigX = 1000; Integer bigY = 1000; if (bigX == bigY) System.out.println("bigX equals bigY"); else System.out.println("bigX does not equal bigY"); // output: // smallX equals smallY // bigX does not equal bigY In a mental model where mathematics and Java programs are "one and the same", it completely makes sense that the numeric value in '2' and '{2}' are different instances of the same type: they point to different addresses in memory. Obviously 
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19th November 2014, 11:30 PM  #140 
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Please support you claim (which according to it, when I deal with infinity, I am using only stepbystep (serial) thinking style) according to what is written in http://www.internationalskeptics.com...&postcount=110.

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20th November 2014, 12:34 AM  #141 
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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 socalled 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! 
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20th November 2014, 01:16 AM  #142 
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..

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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

20th November 2014, 01:25 AM  #143 
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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 stepbystep, 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). 
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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

20th November 2014, 01:29 AM  #144 
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this link is irrelevant anymore to what is written in http://www.internationalskeptics.com...&postcount=110.

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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

20th November 2014, 01:46 AM  #145 
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Already answered in http://www.internationalskeptics.com...7&postcount=78.

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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

20th November 2014, 03:20 AM  #146 
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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. 
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20th November 2014, 03:24 AM  #147 
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"All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually"  Doron Shadmi "But this means you actually have nothing."  Realpaladin  

20th November 2014, 03:30 AM  #148 
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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? 
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"All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually"  Doron Shadmi "But this means you actually have nothing."  Realpaladin  

20th November 2014, 03:34 AM  #149 
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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# ) 
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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

20th November 2014, 08:20 AM  #151 
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That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. 

20th November 2014, 08:29 AM  #152 
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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 realline is observed from R cardinality", in laymanfriendly terms? 
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20th November 2014, 09:20 AM  #153 
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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. 
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20th November 2014, 10:41 AM  #154 
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20th November 2014, 11:52 AM  #155 
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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. 
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20th November 2014, 11:58 AM  #156 
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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. 
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"All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually"  Doron Shadmi "But this means you actually have nothing."  Realpaladin  

20th November 2014, 03:04 PM  #157 
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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}}.... 
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21st November 2014, 07:06 AM  #158 
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Dear Dessi,
First, please look again at http://www.internationalskeptics.com...&postcount=102. In terms of process, infinite sequential (stepbystep) 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 (stepbystep) speed is actually one and only one step, or in other words, the notion of more than one step (for example: stepbystep) 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 (stepbystep) observation: http://www.internationalskeptics.com...5&postcount=66. If you fail because you are using only stepbystep observation of infinite collections, it is clear that your only stepbystep 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: 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 realline, by using the fact that N<R, and this is exactly what I am doing in http://www.internationalskeptics.com...&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. 
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21st November 2014, 09:03 AM  #159 
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But I can't even see the metal while floating 30,000 ft on my Haskell cloud.
Quote:
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.
Quote:
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:
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 
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>^.^< 

21st November 2014, 10:53 AM  #160 
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Join Date: Apr 2007
Posts: 2,585

Jenga... that's why I can teach my students to get into just about any system nowadays
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. 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. Cool. I'll add that to the communities' services rendered to Mr. Shadmi; code reviewing. I rather have him pegged as a (Turbo)Pascal user who now migrates to Java. 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 onestep parallel addition of all the weights, as opposed to weighing one stone after another and adding all their respective weights together. 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. But you do know that in mathematics, there is no smallest interval in a limit. Try doing that in Brainf*ck (which, as you know, *is* a programming language)... 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. 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 
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"All is needed (and it is essential to my definitions) is to understand the actuality beyond the description, for example: Nothing is actually"  Doron Shadmi "But this means you actually have nothing."  Realpaladin  

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