• Security incident: ISF was recently accessed by intruders. Please change your password, and change it anywhere else you used it. Read more

Cont: Deeper than primes - Continuation 2

Status
Not open for further replies.
Last edited:
doronshadmi said:
No, you don't.

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=11705863&postcount=2400.
Click to expand...
I can see 5 different staircases in the diagram. One with 32 steps, one with 16 steps, one with 8 steps, one with 4 steps, and one with only 2 steps. For each of them it's easy to add the lengths of the steps (yes, all of them) and end with 2X as you requested. One can easily imagine additional staircases with even more steps: 64, 128, 256, 512 and so on. It will still be easy to add the lengths and get 2X.

If you're looking for a different kind of answer, please guide me.
 
While I'm waiting for step 2, please allow me to take a slight detour into language and culture.

In my country the children sometimes say, "Onker'n min er pollti!" Literally translated it means "my uncle is a policeman", but the phrase is frequently heard from children whose uncles aren't police officers, or who don't even have an uncle.

The actual meaning of the phrase is "I'm running out of arguments, so I'm going to say something big and impressive so I won't lose face". Does the term "visual AND symbolic reasoning" have a similar function in your culture? I ask because you keep using it that way.
 
Last edited:
Hevneren said:
I can see 5 different staircases in the diagram. One with 32 steps, one with 16 steps, one with 8 steps, one with 4 steps, and one with only 2 steps. For each of them it's easy to add the lengths of the steps (yes, all of them) and end with 2X as you requested. One can easily imagine additional staircases with even more steps: 64, 128, 256, 512 and so on. It will still be easy to add the lengths and get 2X.

If you're looking for a different kind of answer, please guide me.
Click to expand...
Please do not deal only with finite cases and use visual AND symbolic reasoning.
 
Hevneren said:
While I'm waiting for step 2, please allow me to take a slight detour into language and culture.

In my country the children sometimes say, "Onker'n min er pollti!" Literally translated it means "my uncle is a policeman", but the phrase is frequently heard from children whose uncles aren't police officers, or who don't even have an uncle.

The actual meaning of the phrase is "I'm running out of arguments, so I'm going to say something big and impressive so I won't lose face". Does the term "visual AND symbolic reasoning" have a similar function in your culture? I ask because you keep using it that way.
Click to expand...
Hevneren, all you need in order to understand exactly what I mean is already found in my reply to you in http://www.internationalskeptics.com/forums/showpost.php?p=11705884&postcount=2404 (including the links there).

Actually you still do not ask yourself "Why I do not use both my visual AND symbolic brain skills in order to understand the issue at hand?"

Can you do that (if you do that, the answer to step 2 is immediately known to you)?
 
Last edited:
jsfisher said:
Proofs are proofs. Proof methods don't result in different conclusions unless you are doing them wrong.


There is a lot of assertion there; no proof, though.
Click to expand...
Still you try to comprehend visual AND symbolic reasoning by symbolic-only reasoning.
 
doronshadmi said:
Please do not deal only with finite cases and use visual AND symbolic reasoning.
Click to expand...
OK. What cases should I deal with, and what is the correct line of reasoning? I need you to be a bit specific. "Visual AND symbolic reasoning" apparently doesn't mean what I thought it means.
 
doronshadmi said:
Do you understand that 2X is a constant > X√2 in the considered diagram, no matter how many staircases of 2X there are in it?
Click to expand...
Yes, if 2X>X√2 then 2X>X√2, regardless of the number of staircases. How could that ever not be the case? And 2X is in fact greater than X√2 in your diagram.

I feel more than ready for step 2 now.
 
doronshadmi said:
Still you try to comprehend visual AND symbolic reasoning by symbolic-only reasoning.
Click to expand...

As I said, proofs are proofs, and the proof method is immaterial. Since the value of the series in your diagram follows directly from a few definitions, there isn't much to prove.

Your scorn for the proof method and for the underlying definitions matter not at all. The proof stands. Your assertions to the contrary fail.
 
Hevneren said:
Yes, if 2X>X√2 then 2X>X√2, regardless of the number of staircases. How could that ever not be the case? And 2X is in fact greater than X√2 in your diagram.

I feel more than ready for step 2 now.
Click to expand...
Correction: It's step 3 I'm waiting for, not step 2.
 
doronshadmi said:
By using visual AND symbolic reasoning about the considered diagram, one immediately understands that 2X > X√2 exactly because there is no fixed amount of infinitely many staircases, and since a+b+c+d+... is inseparable of 2X>X√2, then X>a+b+c+d+... (or 2X>2(a+b+c+d+...)).
Click to expand...
2X > X√2 because 2 > √2 and X > 0. That has nothing to do with staircases. Or, using visual reasoning: We can easily see that the two X catheti of a triangle together form a longer path than the X√2 hypotenuse alone.

What do you mean by "inseparable of", by the way? That part is still a bit unclear, though you mention it a lot.
 
Last edited:
Hevneren said:
Yes, if 2X>X√2 then 2X>X√2, regardless of the number of staircases. How could that ever not be the case? And 2X is in fact greater than X√2 in your diagram.

I feel more than ready for step 2 now.
Click to expand...
You say it (using your symbolic brain skills) but don't see it (you do not use also your visual brain skills).

If 2X>X√2 in my diagram AND a+b+c+d+... is an infinite series, then 2X>2(a+b+c+d+...) regardless of the infinitely many numbers of that series.

The inseparability in 2X>X√2 and 2X>2(a+b+c+d+...) in my diagram is exactly the inequality (notated by ">") of the two expressions, and it can be known only if one actually using visual AND symbolic brain skills.

Hevneren said:
"all the horizontal components of the steps will add up to X, and all the vertical components of the steps will add up to X"
Click to expand...
There is no such thing like all in a+b+c+d+... , and you are able to know it only if you are using your visual AND symbolic brain skills in order to really understand the following diagrams:

http://www.internationalskeptics.com/forums/showpost.php?p=11702679&postcount=2343
 
Last edited:
jsfisher said:
As I said, proofs are proofs, and the proof method is immaterial.
Click to expand...
The term "immaterial" is given by persons that get visual brain skills as "material".

By using visual AND symbolic brain skills, one enables to move beyond the artificial separation of symbolic-only | visual-only brain skills.
 
doronshadmi said:
You say it (using your symbolic brain skills) but don't see it (you do not use also your visual brain skills).

If 2X>X√2 in my diagram AND a+b+c+d+... is an infinite series, then 2X>2(a+b+c+d+...) regardless of the infinitely many numbers of that series.

The inseparability in 2X>X√2 and 2X>2(a+b+c+d+...) is exactly the inequality (notated by ">") of the two expressions.
Click to expand...
Yes, I can see that the bloody hypotenuse is shorter than the catheti combined. Even a child can see that. Next step, please. I hope that's the one where you explain your "inseparability" of the two inequalities.

BTW, if a+b+c+d+... represents X(1/2 + 1/4 + 1/8 + 1/16 + ...) the second inequality is incorrect. The expression is equal to X, not less than X. That's a well-proven fact, not an illusion.
 
Hevneren said:
BTW, if a+b+c+d+... represents X(1/2 + 1/4 + 1/8 + 1/16 + ...) the second inequality is incorrect. The expression is equal to X, not less than X. That's a well-proven fact, not an illusion.
Click to expand...

Hevneren said:
"all the horizontal components of the steps will add up to X, and all the vertical components of the steps will add up to X"
Click to expand...
Hevneren said:
That's a well-proven fact, not an illusion.
Click to expand...
This is exactly the illusion that is caused by using symbolic-only | visual-only brain skills.

There is no such thing like all in a+b+c+d+... , and you are able to know it only if you are using your visual AND symbolic brain skills in order to really understand the following diagrams:

http://www.internationalskeptics.com/forums/showpost.php?p=11702679&postcount=2343

Also see http://www.internationalskeptics.com/forums/showpost.php?p=11706565&postcount=2417.
 
Last edited:
doronshadmi said:
Hevneren said:
If you mean that all the horizontal components of the steps will add up to X, and all the vertical components of the steps will add up to X, no matter how small you make the steps, then yes. X + X = 2X, and 2X > X√2. That never changes.
Click to expand...
This is exactly the illusion that is caused by using symbolic-only | visual-only brain skills.

There is no such thing like all in a+b+c+d+... , and you are able to know it only if you are using your visual AND symbolic brain skills in order to really understand the following diagrams:
Click to expand...

I wasn't talking about a+b+c+d+..., I was talking about the steps in each staircase. Please study your own diagram, Doron. There's one staircase with 2 steps a wide and a tall, one staircase with 4 steps b wide and b tall etc. The combined horizontal and vertical lengths for each staircase will add up to 2X, no matter how small you make each step. Or are you trying to say that at some point the sum will be smaller than 2X, because we've somehow reached infinity? It's difficult to follow you here. To prove me wrong, you have to present a coherent argument. It's not sufficient to tell me that my reasoning is wrong. That doesn't make you right. And I would be happy to know how you are using your visual AND symbolic brain skills to get the results you do. Please show us mortals how to reason like a master, so we can try to emulate you. The fate of humanity may depend on it.
 
Status
Not open for further replies.

Share this page

ISF - Join now!

Every member here is approved by hand. No bots, no spam, just people who care about evidence and honest debate.

Membership is free!

Create your free account

Back
Top Bottom