Cont: Deeper than primes - Continuation 2

[Hevneren]

You claimed that any proof for 2X = 2(a + b + c + d +...) would be "based on symbolic-only reasoning". You were wrong.

 

[doronshadmi]

Evidence?

Clearly given by the diagrams if visual AND symbolic brain skills are used.

No, I don't care about your dichotomy. You're the one who keeps mentioning it. I only care about the results.

Results (mathematical or not) are comprehended by using our brain skills, and this is not my dichotomy, but it is exactly the dichotomy that is deeply involved in your brain, during your mathematical activity.

 

[doronshadmi]

You assert that the difference is > 0, but offer no proof, or even evidence.

I offer you to use your visual AND symbolic brain skills abut the issue at hand.

Why is that difference not fixed? X has a specific value

In finite terms.

and the sum has a specific value. There really should be a specific difference.

Only in case of finite terms.

Symbolic tells me there is, and visual tells me there is. Why should that change if I use symbolic and visual?

Please simultaneously use your visual AND symbolic brain skills in order to understand the considered diagram, in order to provide the answer to your question.

 

[doronshadmi]

You claimed that any proof for 2X = 2(a + b + c + d +...) would be "based on symbolic-only reasoning". You were wrong.

Evidence?

 

[Hevneren]

Evidence?

The fridge evidence. That wasn't based on any symbols.

 

[Hevneren]

Why is that difference not fixed? X has a specific value and the sum has a specific value. There really should be a specific difference.

Doron probaby won't admit this, but he seems to think there's an ongoing, never-ending process of adding smaller and smaller line pieces, so the difference will get smaller for each small piece you add. I think this is his fundamental error. He can't see the X line as a whole.

 

[doronshadmi]

The fridge evidence. That wasn't based on any symbols.

Your fridge "evidence" does not distinguish between infinite addition and finite addition.

Moreover, it artificially separates what actually have in the considered diagrams, exactly because it uses visual-only reasoning.

Furthermore, by writing "based on symbolic-only reasoning" (seen in the beginning of http://www.internationalskeptics.com/forums/showpost.php?p=11719572&postcount=2471) I am talking about the traditional mathematical stuff about the issue at hand.

If you disagree with me then please provide traditional mathematical stuff about the considered diagrams that deduce them by using both visual AND symbolic reasoning.

 

[doronshadmi]

Doron probaby won't admit this, but he seems to think there's an ongoing, never-ending process of adding smaller and smaller line pieces, so the difference will get smaller for each small piece you add. I think this is his fundamental error. He can't see the X line as a whole.

X line is a non-composed positive thing if taken on its own.

If it is measured by positive sub-things along it, then finitely many positive sub-things cover it, but do not have its own non-composed property.

If it is measured by ever smaller infinitely many positive sub-things along it, then infinitely many positive sub-things do not cover it AND do not have its own non-composed property.

He can't see the X line as a whole.

Your fundamental mistake is that you take X line as a collection of positive things AND you also do not distinguish between finite collections and infinite collections along the non-composed X line.

X line on its own is a positive non-composed thing, which is a notion that your collection-oriented reasoning of X, can't comprehend.

Also you avoid http://www.internationalskeptics.com/forums/showpost.php?p=11719762&postcount=2487 and http://www.internationalskeptics.com/forums/showpost.php?p=11713929&postcount=2466 and http://www.internationalskeptics.com/forums/showpost.php?p=11716498&postcount=2467.

Moreover, you ignored http://www.internationalskeptics.com/forums/showpost.php?p=11712656&postcount=2465 (and what is written there about Archimedean property (which is definitely not used in my framework)).

 

[Hevneren]

Your fridge "evidence" does not distinguish between infinite addition and finite addition.

Moreover, it artificially separates what actually have in the considered diagrams, exactly because it uses visual-only reasoning.

Furthermore, by writing "based on symbolic-only reasoning" (seen in the beginning of http://www.internationalskeptics.com/forums/showpost.php?p=11719572&postcount=2471) I am talking about the traditional mathematical stuff about the issue at hand.

If you disagree with me then please provide traditional mathematical stuff about the considered diagrams that deduce them by using both visual AND symbolic reasoning.

I could easiy do that, but I have already tried to explain this to you using visual, symbolic, AND combined lines of thought. You just keep rejecting whatever I say. It's your turn to prove your stuff now, not just repeating you false claims. You are totally out of line with mathematics here, so the burden of proof is upon you.

 

[Hevneren]

X line is a non-composed positive thing if taken on its own.

If it is measured by positive sub-things along it, then finitely many positive sub-things cover it, but do not have its own non-composed property.

If it is measured by ever smaller infinitely many positive sub-things along it, then infinitely many positive sub-things do not cover it AND do not have its own non-composed property.


Your fundamental mistake is that you take X line as a collection of positive things AND you also do not distinguish between finite collections and infinite collections along the non-composed X line.

Rubbish. I take X as a line of some length, AND I know the sum of an infinite geometric series. Collections don't enter into it.

X line on its own is a positive non-composed thing, which is a notion that your collection-oriented reasoning of X, can't comprehend.

It's in fact you that don't seem to get this.

Also you avoid http://www.internationalskeptics.com/forums/showpost.php?p=11719762&postcount=2487 and http://www.internationalskeptics.com/forums/showpost.php?p=11713929&postcount=2466 and http://www.internationalskeptics.com/forums/showpost.php?p=11716498&postcount=2467.

Moreover, you ignored http://www.internationalskeptics.com/forums/showpost.php?p=11712656&postcount=2465 (and what is written there about Archimedean property (which is definitely not used in my framework)).

Link spamming to you own posts won't get you anywhere. You haven't explained or proved anything at all in your previous posts, so why link to them? If you have some evidence, please just provide it.

 

[doronshadmi]

I could easiy do that

So do that, please provide traditional mathematical stuff about the considered diagrams that deduce them by using both visual AND symbolic reasoning.

 

[doronshadmi]

Rubbish. I take X as a line of some length, AND I know the sum of an infinite geometric series. Collections don't enter into it.

Please show me an infinite geometric series that is not a collection of infinitely many things.

It's in fact you that don't seem to get this.

On the contrary, you actually have no clue what is actually X line as a non-composed thing of its own, which is independent of how we measure it (you still do not comprehend what is written at the beginning of http://www.internationalskeptics.com/forums/showpost.php?p=11719779&postcount=2488).

EDIT: Moreover, please provide a traditional mathematical stuff which according to it X line is a non-composed thing.

Link spamming to you own posts won't get you anywhere. You haven't explained or proved anything at all in your previous posts, so why link to them? If you have some evidence, please just provide it.

You ignore the links in those links (which are not my works), exactly because they do not fit to your reasoning.

 

[Hevneren]

So do that, please provide traditional mathematical stuff about the considered diagrams that deduce them by using both visual AND symbolic reasoning.

Sorry, but no It's your turn. **** or get off the pot.

 

[doronshadmi]

Sorry, but no It's your turn. **** or get off the pot.

So, you can't do that.

Now please try http://www.internationalskeptics.com/forums/showpost.php?p=11719830&postcount=2492.

 

[MetalPig]

I offer you to use your visual AND symbolic brain skills abut the issue at hand.

Exactly. You offer no proof, or even evidence. That's what I said and youseem to confirm.

In finite terms.
<...>
Only in case of finite terms.

Are you saying the sum of infinitely many numbers can not have a specific value?

Please simultaneously use your visual AND symbolic brain skills in order to understand the considered diagram, in order to provide the answer to your question.

Why don't *you* give me the answer?
Symbolic tells me the sum exists, and visual tells me the sum exists. Why should that change if I use symbolic AND visual skils?


Take some length X. Make it into 2 halves. Call one of the halves a and put it aside. Take the remaining part and make it into two halves. Call one of the halves b and put it aside. Take the remaining part and make it into two halves. Call one of the halves c and put it aside.
Repeat infinitely many times (inventing new letters as you go). At no point in the process do I throw anything away, so the sum of the infinitely many bits I end up with must be X.

You can visualize the process or put it into symbols or both. The sum will always be X.

 

[doronshadmi]

Exactly. You offer no proof, or even evidence. That's what I said and youseem to confirm.

Once again you do not use your visual AND symbolic brain skills in order to realize that in the considered diagram the fact that 2X>X√2 is inseparable of the fact that 2X>2(a+b+d+d+...). The diagram is the proof of this inseparability only if you are actually simultaneously using both your visual AND symbolic brain skills during its observation.

Are you saying the sum of infinitely many numbers can not have a specific value?

What I say is that there is no sum to the added positive values in the considered diagram.

Why don't *you* give me the answer?

Because the right answer about the considered diagram is deeply related of how *you* are actually simultaneously using both your visual AND symbolic brain skills during the considered diagram observation.

Symbolic tells me the sum exists, and visual tells me the sum exists. Why should that change if I use symbolic AND visual skils?

Because this is the whole point, *your* brain can't comprehend the diagram unless *you* simultaneously observe it by using *your* visual AND symbolic brain skills.

As long as *you* search for a string of symbols that is observed by *you* as a mathematical proof about the considered diagram, *you* are using *your* symbolic-only brain skills, which actually prevent the actual understanding of the considered diagram.

Take some length X. Make it into 2 halves. Call one of the halves a and put it aside. Take the remaining part and make it into two halves. Call one of the halves b and put it aside. Take the remaining part and make it into two halves. Call one of the halves c and put it aside.
Repeat infinitely many times (inventing new letters as you go). At no point in the process do I throw anything away, so the sum of the infinitely many bits I end up with must be X.

You can visualize the process or put it into symbols or both. The sum will always be X.

Look how *you* actually observe X separately of how it is actually visually AND symbolically defined in the following diagram:

FACT 1: No infinitely many staircases with constant value 2X are equal to X√2 (written as 2X>X√2).

FACT 2: a+b+c+d+... is the result of the intersections of the diagonal black lines on the peaks of the infinitely many staircases, with the 2X sides of the diagram.

FACT 3: The interactions along the 2X sides are inseparable of FACT 1.

FACT 4: By FACT 3, one realizes that no infinitely many 2(a+b+c+d+...) are equal to 2X ( written as 2X>2(a+b+c+d+...) ).

FACT 5: No infinitely many 2(a+b+c+d+...) have a fixed sum, exactly because 2X>X√2 AND 2X>2(a+b+c+d+...) are inseparable in the considered diagram.

FACT 6: FACTS 1 to 5 are known only if one actually simultaneously using both his\her visual AND symbolic brain skills during his\her observation of the considered diagram.

 

[Hevneren]

FACT 1: No infinitely many staircases with constant value 2X are equal to X√2 (written as 2X>X√2).

True. Nobody disagrees.

FACT 2: a+b+c+d+... is the result of the intersections of the diagonal black lines on the picks of the infinitely many staircases, with the 2X sides of the diagram.

OK.

FACT 3: The interactions along the 2X sides are inseparable of FACT 1.

What do you mean by inseparable? This isn't clear.

FACT 4: By FACT 3, one realizes that no infinitely many 2(a+b+c+d+...) are equal to 2X ( written as 2X>2(a+b+c+d+...) ).

Maybe "one" does, but then "one" is wrong. This has been expained to you many times.

FACT 5: No infinitely many 2(a+b+c+d+...) have a fixed sum, exactly because 2X>X√2 AND 2X>2(a+b+c+d+...) are inseparable in the considered diagram.

False. The sum is 2X.

FACT 6: FACTS 1 to 6 are known only if one actually simultaneously using both his\her visual AND symbolic brain skills during its observation of the considered diagram.

It doesn't matter what skills were used when the results are wrong.

I think you may have observed that the black diagonals approach length X√2 as the staircase steps grow smaller, and it may look like some paradox that the staircase has constant length 2X while it looks more and more like a straight line as the steps get smaller. Geometry is a fascinating subject, but your answers are still wrong. Now try to disprove the following (it should be easy if you are right):

S = 1/2 + 1/4 + 1/8 + 1/16 + ...
2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 ...

2S-S= 1 + 1/2 + 1/4 + 1/8 + 1/16 ...
- 1/2 - 1/4 - 1/8 - 1/16 + ...

S=1

Yes, this is symbolic only, but since you master both kinds of reasoning so superbly, it can't be too difficult.

 

[doronshadmi]

Yes, this is symbolic only, but since you master both kinds of reasoning so superbly, it can't be too difficult.

http://www.internationalskeptics.com/forums/showpost.php?p=11720090&postcount=2496 simply evolved beyond the artificial limitations of *your* symbolic-only | visual-only dichotomy.

and it may look like some paradox that the staircase has constant length 2X while it looks more and more like a straight line as the steps get smaller.

There is no paradox of any kind here, and exactly because there is not paradox FACTS 1 to 6 hold.

 

[Hevneren]

http://www.internationalskeptics.com/forums/showpost.php?p=11720090&postcount=2496 simply evolved beyond the artificial limitations of *your* symbolic-only | visual-only dichotomy.

I guess it did. Any comments on my proof?

 

[doronshadmi]

What do you mean by inseparable? This isn't clear.

It is clear as a noon sun.

No infinitely many staircases are "settled down" into X√2, and since 2(a+b+c+d+...) is the result of the intersections of the diagonal black lines on the peaks of these infinitely many staircases with the 2X sides of the diagram, 2(a+b+c+d+...) can't be "added up" into 2X.