Cont: Deeper than primes - Continuation 2

[doronshadmi]

Any comments on my proof?

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

Exactly as MetalPig, you observe it separately of the considered diagram, and this is the bast of what your symbolic-only | visual-only dichotomous reasoning actually achieves.

So the answer is: you have no proof whatsoever.

I just wanted to stir the pot a bit myself, ...

Still in deep sleep.

What about my fridge?

Still in deep freeze.

 

[jsfisher]

Exactly as MetalPig, you observe it separately of the considered diagram, and this is the bast of what your symbolic-only | visual-only dichotomous reasoning actually achieves.

That doesn't make it wrong. The proof stands. Mathematical rigor does not yield to your misinterpretation of simple diagrams nor to your self-proclaimed superior reasoning methods.

The mathematical fact that 1/2 + 1/4 + 1/8 + ... is 1 follows directly from definitions; your insistence otherwise has no impact.

Mathematics doesn't care if you don't understand.

 

[MetalPig]

No infinitely many staircases are "settled down" into X√2,

Nobody disputes this. 2 > √2 , we know.

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.

Maybe you can't add them up, but it can be proven symbolically, and it's visually obvious from your diagram that they add up to 2X.

Somehow doing it "symbolically and visually" prevents you from getting to the correct answer. Sad.

 

[doronshadmi]

jsfisher, MetalPig and Hevneren,

http://www.internationalskeptics.com/forums/showpost.php?p=11720522&postcount=2500 is exactly the right result about the considered diagram.

No reasoning that is based on the artificial dichotomy between *your* natural abilities to combine *your* visual AND symbolic brain skills, is going to change that right result.

Moreover, ignoring http://www.internationalskeptics.com/forums/showpost.php?p=11713929&postcount=2466, http://www.internationalskeptics.com/forums/showpost.php?p=11716498&postcount=2467 and http://www.internationalskeptics.com/forums/showpost.php?p=11712656&postcount=2465 (including the rejection of the Archimedean property) actually put you in an obsolete state with respect to the actual fundamental developments of Maths that are deeply rooted in researches of the human brain.

Now days mathematics is an aggregation of frameworks that even contradict each other, exactly because of the lack of Unity consciousness among human beings.

Mathematics, together with more scientifically developed methods, is going to play a main factor in developing Unity consciousness among human beings, where drafts in this direction are seen in http://www.internationalskeptics.com/forums/showpost.php?p=11700724&postcount=2342 and http://www.internationalskeptics.com/forums/showpost.php?p=11706920&postcount=2438.

 

[Hevneren]

Oh no, I'm obsolete. Still not looking forward to the day when all humans have Doron's consciousness

 

[jsfisher]

jsfisher, MetalPig and Hevneren,

http://www.internationalskeptics.com/forums/showpost.php?p=11720522&postcount=2500 is exactly the right result about the considered diagram.

And yet, it isn't. Perhaps if you stopped pretending your diagrams showed what you want to be true and stopped fighting basic definitions in Mathematics, you might actually figure out your diagrams prove nothing while suggesting the opposite of your baseless beliefs.

 

[zooterkin]

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

Still stuck with your insistence on enumerating every member of the sequence in order to arrive at the sum?

 

[doronshadmi]

Still stuck with your insistence on enumerating every member of the sequence in order to arrive at the sum?

Traditional Mathematics can't deal with the simple fact that a series of infinitely many ever smaller positive values (as given in the considered diagram) does not have a fixed sum (where in the considered diagram this fact is notated as 2X>2(a+b+d+...)).

 

[doronshadmi]

Perhaps if you stopped pretending your diagrams showed what you want to be true and stopped fighting basic definitions in Mathematics,

Perhaps if you stopped pretending your symbolic-only reasoning showed what you want to be true and stopped forcing it as if it is really basic for actual definitions in Mathematics, you might actually figure out my diagrams prove that 2X>X√2 AND 2X>2(a+b+c+d+...) are inseparable in the considered diagram, despite of your baseless symbolic-only beliefs.

The near future of real mathematics is inseparable of human brain research (as briefly given in http://www.internationalskeptics.com/forums/showpost.php?p=11721126&postcount=2504) and the tradition of symbolic-only reasoning is going to vanish.

 

[Hevneren]

Traditional Mathematics I can't deal with the simple fact that a series of infinitely many ever smaller positive values (as given in the considered diagram) does not in some cases has a fixed sum (where in the considered diagram this fact is notated as 2X>=2(a+b+d+...)).

FTFY, you're welcome

 

[Hevneren]

The near future of real mathematics is inseparable of human brain research (as briefly given in http://www.internationalskeptics.com/forums/showpost.php?p=11721126&postcount=2504) and the tradition of symbolic-only reasoning is going to vanish.

So this is the dawning of the age of doronetics? We're certainly living in interesting times.

 

[doronshadmi]

So this is the dawning of the age of doronetics?

No, this is the dawn of the age of the science of human consciousness development into Unity consciousness, and mathematics is going to play a main role in this development.

 

[jsfisher]

...your symbolic-only reasoning...

Is this supposed to be meaningful in some way?

Logical reasoning follows a set of rules to draw its conclusions. Got anything like that?

 

[doronshadmi]

Logical reasoning follows a set of rules to draw its conclusions. Got anything like that?

Logical reasoning follows a set of rules based on both visual AND symbolic brain skills in order to draw its conclusions. Got anything like that (for example http://www.internationalskeptics.com/forums/showpost.php?p=11721126&postcount=2504)?

 

[doronshadmi]

FTFY, you're welcome

Typical result of dichotomous visual | symbolic brain skills that is going to vanish simply because real mathematics is done by naturally using both visual AND symbolic brain skills.

A concrete example about the fundamental concept of set, which is based on the natural activity of visual AND symbolic brain skills, is already given in http://www.internationalskeptics.com/forums/showpost.php?p=11706920&postcount=2438.

 

[jsfisher]

Logical reasoning follows a set of rules

This part is correct.

based on both visual AND symbolic brain skills in order to draw its conclusions.

This part is incorrect. It does nothing but get us back to the direct perception nonsense you tried to peddle once before.


Be that as it may, if you do have a set of rules for reasoning (based on whatever you imagine it to be based on), please, tell us all about these rules. I'm sure they will be fascinating.

 

[doronshadmi]

This part is incorrect. It does nothing but get us back to the direct perception nonsense you tried to peddle once before.


Be that as it may, if you do have a set of rules for reasoning (based on whatever you imagine it to be based on), please, tell us all about these rules. I'm sure they will be fascinating.

Since you simply unable to realize that your responses are based on your visual AND symbolic brain skills, lets make it more easy for you.

The axiom of mathematics:

Given X, no sub-X is X.

In order to really understand this string of symbols both your visual AND symbolic brain skills are simultaneously used, whether you aware of it, or not.

So the useful state of mind is to be aware of it during your mathematical work, and this awareness is the mathematical basis for the development of Unity consciousness among human beings.

What is already given in http://www.internationalskeptics.com/forums/showpost.php?p=11721126&postcount=2504)? is done by being aware of it during mathematical work, which in turn becomes a useful tool for the development of Unity consciousness among human beings.

 

[jsfisher]

The axiom of mathematics:

Given X, no sub-X is X.

This is not an axiom of Mathematics.

In order to really understand this string of symbols both your visual AND symbolic brain skills are simultaneously used, whether you aware of it, or not.

This is a bare assertion. You do a lot of assertion, but never go beyond that.


Be that as it may, what, I ask again, are your rules for your version of reasoning? They do not correspond to those of mathematical logic, so it would be helpful those playing along at home trying to follow your line of reasoning if they knew what your rules were.

 

[doronshadmi]

This is not an axiom of Mathematics.

I agree with you, because this is The axiom of Mathematics:

Given X, no sub-X is X.

No assertion of any kind, and it is extremely useful by naturally using both our visual AND symbolic brain skills, as already given in http://www.internationalskeptics.com/forums/showpost.php?p=11721126&postcount=2504)?

From now on I will reply to you by using The axiom of Mathematics, any attempt from you to ignore it will be a clear sign that you do not really wish to discuss with me about Mathematics and its further development.

Now about this axiom, it simply says that that no expressions that may emerge from X, are X, simply because X is non-composed by definition that is known both visually AND symbolically.

 

[jsfisher]

I agree with you, because this is The axiom of Mathematics:

Given X, no sub-X is X.

You are re-asserting the same falsehood. Got anything to show otherwise?

No assertion of any kind

It certainly was an assertion. That is a simple truth by the very nature of your statement. It question was was it a bare assertion. I'll leave it to you to divine the difference.

From now on I will reply to you by using The axiom of Mathematics, any attempt from you to ignore it will be a clear sign that you do not really wish to discuss with me about Mathematics and its further development.

You may leap to whatever conclusions you like; it is only when you attempt to pass them off as fact that you run into trouble.

Be that as it may, you seem more concerned with the past developments in Mathematics, and that misinterpreting some drawing disproves well-established things.