Cont: Deeper than primes - Continuation 2

[Hevneren]

Ok, we'll add some context then:

I do not accept reasoning and its results, which are derived from separately using one's visual brain skills | symbolic brain skills, exactly as you do at this very moment, ...

You don't accept valid reasoning and correct results because of how you think I'm using my brain? Why not study the results and the logic that leads to them? Everybody's different, and I don't think you can expect anyone to think like you.

As for the second diagram, it's not very relevant. I'm fine with all the orange figures having the same length if that's what you're trying to say, but I'm still not fine with your not accepting the sum of infinite geometric series.

 

[doronshadmi]

You don't accept valid reasoning and correct results because of how you think I'm using my brain?

Valid reasoning is the result of using the natural ability to combine visual AND symbolic brain skills among any human being.

Invalid reasoning is the result of blocking the natural ability to combine visual AND symbolic brain skills among any human being.

Why not study the results and the logic that leads to them?

Why not study how to naturally combine visual AND symbolic brain skills among any human being, in order to get valid results?

Everybody's different, and I don't think you can expect anyone to think like you.

Everybody's different in infinitely many ways, and I don't think you can expect everyone to be restricted to some fixed result of infinitely many things, just because symbolic-only skillers | visual-only skillers restrict the actual richness of infinity into fixed values.

As for the second diagram, it's not very relevant. I'm fine with all the orange figures having the same length if that's what you're trying to say,

You repeat once again on your fundamental mistake about infinitely many things.

The term "all" is wrongly related to infinitely many things, in order to grasp them in terms of finitely many things, and such wrong treatment is derived form artificially blocking the natural connection among our visual brain skills AND our symbolic brain skills, which provides the illusion of restraining infinity into some fixed limit, some fixed cardinality like |N|, etc.

but I'm still not fine with your not accepting the sum of infinite geometric series.

Because you are still under illusions which are the results of being trained (by your teachers of mathematics) not to naturally combine your visual brain skills AND symbolic brain skills during your mathematical work.

 

[Hevneren]

Valid reasoning is the result of using the natural ability to combine visual AND symbolic brain skills among any human being.

And I suppose you're the only one who has that ability, or the only one who uses it? Because AFAIK no one has ever agreed with anything you've said about math in all these years.

Invalid reasoning is the result of blocking the natural ability to combine visual AND symbolic brain skills among any human being.

Maybe sometimes, often it's not.

Why not study how to naturally combine visual AND symbolic brain skills among any human being, in order to get valid results?

One could do that, but valid results are still valid no matter how you arrived at them. The same goes for invalid results.

Everybody's different in infinitely many ways, and I don't think you can expect everyone to be restricted to some fixed result of infinitely many things, just because symbolic-only skillers | visual-only skillers restrict the actual richness of infinity into fixed values.

That's just insane. Different people can find the answers to math problems in different ways, but the correct answers are obviously the same for everybody.

You repeat once again on your fundamental mistake about infinitely many things.

No, there aren't infinitely many orange figures in your diagram. So this time I get to say "all".

 

[doronshadmi]

And I suppose you're the only one who has that ability, or the only one who uses it? Because AFAIK no one has ever agreed with anything you've said about math in all these years.

Agreement that is based on not using the natural abilities to combine our visual AND symbolic brain skills during mathematical work, are resulted by forcing the finite in order to define the infinite.

Maybe sometimes, often it's not.

Exactly the opposite.

One could do that, but valid results are still valid no matter how you arrived at them. The same goes for invalid results.

Valid or invalid results are deeply related of how we are able to understand them, and understanding is deeply related of how we are using our brain skills, in order to establish agreements (including mathematical agreements) among us.

That's just insane. Different people can find the answers to math problems in different ways, but the correct answers are obviously the same for everybody.

That's just insane. Agreements (including mathematical agreements) among different people, are deeply related of how they are able to combine their natural brain skills in order to really understand both challenges (you call it problems) and their useful (real life-supporting) answers.

No, there aren't infinitely many orange figures in your diagram. So this time I get to say "all".

There are 4 variables in (a+b+c+d+...) and yet you had no problems to understand this expression as a tool that represents infinitely many things.

The same holds about the endless Koch's fractal diagram, both visually AND symbolically.

Once again you "succeed" to understand http://www.internationalskeptics.com/forums/showpost.php?p=11708547&postcount=2451 in finite-only terms.

I wonder why, maybe it is deeply related of how you the combination among your visual AND symbolic brain skills?

 

[doronshadmi]

Ok, please look at the diagram in http://www.internationalskeptics.com/forums/showpost.php?p=11708547&postcount=2451.

By using both your visual AND symbolic brain skills, it is easy to understand that no endless number of projected bent orange figures (with the same constant value X>0) upon the top straight orange figure (that also has the same constant value X>0), enable to define along it endless number of 2(a+b+c+d+...) sub-figures that actually can be added up into constant value X>0.

The endless smaller added positive sub-figures in that diagram are simply not restricted by the Archimedean property (https://en.wikipedia.org/wiki/Archimedean_property) where this mathematical fact is easily known in case that we using both our visual AND symbolic brain skills.

This natural ability is already within any healthy human being, and enable real natural agreements (including mathematical agreements) among us.

Traditional mathematicians wrongly accept the artificial restrictions of the Archimedean property exactly because they define their mathematical frameworks by artificially separating between their visual and symbolic brain skills during their mathematical work.

Because of this artificial separation, they are missing the fact that any attempt to by related to the 0 value at the bottom of the diagram, is involved with finite jump from some arbitrary bent orange figure with constant X>0 into 0 value, where this finite jump is done over infinitely many smaller added positive sub-figures that are simply not restricted by the Archimedean property.

Because of the involvement of a finite jump from some arbitrary bent orange figure with constant X>0 into 0 value (at the bottom of the diagram) traditional mathematician's artificial reasoning can't comprehend the right result of the projected endless number of bent orange figures (with the same constant value X>0) upon the top straight orange figure (that also has the same constant value X>0), which can't be but positive constant value X > endless added positive values 2(a+b+c+d+...) that can't have a fixed positive sum (which is an essential property that is related to infinitely many added positive sub-figures of the considered diagram).

A similar nonsense of traditional mathematicians about the "result" of multiplying endless (0,1] members with each other, is seen in http://www.internationalskeptics.com/forums/showpost.php?p=11678072&postcount=2336 and http://www.internationalskeptics.com/forums/showpost.php?p=11677266&postcount=2330, exactly because they are using the Archimedean property restrictions, which is a direct result of the artificial separation between visual AND symbolic natural human brain skills.

 

[doronshadmi]

Some researches about combining brain skills as the optimal basis for doing mathematics:

https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/

http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0148981&type=printable

https://www.omicsgroup.org/journals...-and-learning-2168-9679-1000325.php?aid=80807

http://download.springer.com/static...7c2ebada8a3a041a66ea3878f61de2a9c4e8369efa4c0

http://bernhard-hommel.eu/Effectiveness of visual and verbal prompts.pdf

http://www.mitpressjournals.org/doi/abs/10.1162/089892903321107819#.WKCDlYVOIeE

 

[doronshadmi]

Thus infinitesimals, so strongly denied by Cantor, are a natural consequence of Hilbertian formalism. While we should still honour Cantor for putting mathematical analysis on a rigorous basis by defining the real numbers as a complete ordered field, we now realise that he did not eliminate infinitesimals at all. They simply lie in a larger mathematical structure that can be defined formally, manipulated symbolically, and visualised perceptually.

https://arxiv.org/ftp/arxiv/papers/1401/1401.1468.pdf , page 24.

http://www.internationalskeptics.com/forums/showpost.php?p=11712656&postcount=2465 is a result of formally using visual AND symbolic brain skills during mathematical work, where this formalism is not restricted to symbolic-only | visual-only reasoning.

 

[doronshadmi]

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.

What I mean is this:

and if you are really using your visual AND symbolic brain skills, you actually understand the the fact that 2X>X√2 is inseparable of the fact that 2X>2(a+b+d+...), and no symbolic-only or visual-only reasoning can change this inseparable fact.

 

[MetalPig]

the fact that 2X>2(a+b+d+...),

Except that's not really a fact.

If 2X > 2(a+b+d+...), please tell us the difference.

 

[Hevneren]

Except that's not really a fact.

If 2X > 2(a+b+d+...), please tell us the difference.

Seconded

 

[doronshadmi]

Except that's not really a fact.

Please prove your claim.

I claim that it is guaranteed that any given proof that you provide, will be based on symbolic-only reasoning.

Please show that my claim is wrong.

If 2X > 2(a+b+d+...), please tell us the difference.

You still to not comprehend the real nature of infinitely many added a+b+c+d+... in the considered diagram.

They are not added up into a single fixed value like X, and so is the case about 2X and 2(a+b+c+d+...), there is no fixed value for this difference, and the best that can be provided is that it is > 0, exactly because 2X > 2(a+b+c+d+...) is inseparable of the fact that 2X > X√2, in the considered diagram.

Generally, you do not comprehend the real nature of infinitely many ever smaller added positive values, as given by the considered diagram, and no symbolic-only | visual-only reasoning can change this real nature.

2X = 2(a+b+c+d+...) only by using a finite jump over infinitely many ever smaller positive values, right to 2X, similarly as already shown in http://www.internationalskeptics.com/forums/showpost.php?p=11712656&postcount=2465.

 

[Hevneren]

Please prove your claim.

I claim that it is guaranteed that any given proof that you will provide, is based on symbolic-only reasoning.

Please show that my claim is wrong.

What about my fridge? It's 1 meter away from me. I could express that distance as half the distance plus half of the rest plus half of the rest ad infinitum. The fridge is still 1 meter away. And there are no symbols involved here. Neither is there a "finite jump".

You still to not comprehend the real nature of infinitely many added a+b+c+d+... in the considered diagram.

They are not added up into a single fixed value like X, and so is the case about 2X and 2(a+b+c+d+...), there is no fixed value for this difference, and the best that can be provided is that it is > 0, exactly because 2X > 2(a+b+c+d+...) is inseparable of the fact that 2X > X√2, in the considered diagram.

Generally you do not com,prehend the real nature of infinitely many ever smaller added positive values, as given by the considered diagram, and no symbolic-only | visual-only reasoning can change this real nature.

2X = 2(a+b+c+d+...) only by using a finite jump over infinitely many ever smaller positive values right to 2X, similarly as already shown in http://www.internationalskeptics.com/forums/showpost.php?p=11712656&postcount=2465.

You haven't proved anything yet, Doron, neither with symbolic nor visual reasoning. Or any combination of those. You just keep repeating a false claim. But it isn't too late for you yet.

 

[MetalPig]

Please prove your claim.

I claim that it is guaranteed that any given proof that you provide, will be based on symbolic-only reasoning.

Nope. It's obvious from your picture as well.

 

[doronshadmi]

Nope. It's obvious from your picture as well.

Please support in details your claim by using the considered diagram (http://www.internationalskeptics.com/forums/showpost.php?p=11719386&postcount=2468).

 

[doronshadmi]

What about my fridge? It's 1 meter away from me. I could express that distance as half the distance plus half of the rest plus half of the rest ad infinitum. The fridge is still 1 meter away. And there are no symbols involved here. Neither is there a "finite jump".

If X=1 and infinitely many sub positive values are involved, exactly as seen in my two diagrams, then the case that X=1 does not eliminate the fact that ever smaller added infinitely many sub positive values are permanently < X, unless a given finite jump to X is done over ever smaller added infinitely many sub positive values, in the considered diagrams.

You haven't proved anything yet, Doron, neither with symbolic nor visual reasoning. Or any combination of those. You just keep repeating a false claim. But it isn't too late for you yet.

You just keep using the dichotomy between your visual and symbolic barin skills, as the basis of your "reasoning", by also ignore http://www.internationalskeptics.com/forums/showpost.php?p=11716498&postcount=2467 or http://www.internationalskeptics.com/forums/showpost.php?p=11713929&postcount=2466.

By your own evidence, which is:

I just wanted to stir the pot a bit myself, while at the same time brushing up my English writing.

you do not actually wish to learn anything that does not fit to the dichotomy between your visual and symbolic barin skills.

 

[MetalPig]

If X=1 and infinitely many sub positive values are involved, exactly as seen in my two diagrams, then the case that X=1 does not eliminate the fact that ever smaller added infinitely many sub positive values are permanently < X,

Please tell us the difference between X and the sum of the infinitely many values.

 

[Hevneren]

If X=1 and infinitely many sub positive values are involved, exactly as seen in my two diagrams, then the case that X=1 does not eliminate the fact that ever smaller added infinitely many sub positive values are permanently < X, unless a given finite jump to X is done over ever smaller added infinitely many sub positive values, in the considered diagrams.

Evidence?

You just keep using the dichotomy between your visual and symbolic barin skills, as the basis of your "reasoning", by also ignore http://www.internationalskeptics.com/forums/showpost.php?p=11716498&postcount=2467 or http://www.internationalskeptics.com/forums/showpost.php?p=11713929&postcount=2466.

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

By your own evidence, which is:

you do not actually wish to learn anything that does not fit to the dichotomy between your visual and symbolic barin skills.

Stirring the pot is part of my motivation for posting here, yes. But I'm still right and you're still wrong. I would love to learn something from you, though I'm not very optimistic at this point.

 

[doronshadmi]

Please tell us the difference between X and the sum of the infinitely many values.

Please read http://www.internationalskeptics.com/forums/showpost.php?p=11719572&postcount=2471 in order to really comprehend it.

At the moment that you comprehend it, you immediately understand that there is no such thing like unique (or fixed) positive difference between X and ever smaller added infinitely many sub positive values.

Moreover, you immediately understand that there is no such thing like the sum of ever smaller added infinitely many sub positive values.

Also this time please reply to http://www.internationalskeptics.com/forums/showpost.php?p=11719640&postcount=2474.

 

[MetalPig]

Please read http://www.internationalskeptics.com/forums/showpost.php?p=11719572&postcount=2471 in order to really comprehend it.

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

At the moment that you comprehend it, you immediately understand that there is no such thing like unique (or fixed) positive difference between X and ever smaller added infinitely many sub positive values.

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.

Moreover, you immediately understand that there is no such thing like the sum of ever smaller added infinitely many sub positive values.

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

 

[doronshadmi]

I would love to learn something from you, though I'm not very optimistic at this point.

Let's see...

And there are no symbols involved here.

An example of you using visual-only reasoning.

So, NO, you would not love to learn something from me.

More important, you would not love to learn something from your own natural abilities to combine your visual AND symbolic brain skills during your mathematical activity.