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Riemann Zeta Function


This is why I have a problem with people that consider things intrinsically true in the universe. 2+2 is 4 in an algebra book, but the factual universe does some really weird shit.

gtfo with you’re sorcery.

I still don’t believe it. It’s make no intuitive sense whatsoever.


[quote]Dr. Pangloss wrote:
I still don’t believe it. It’s make no intuitive sense whatsoever.[/quote]

You can say the same for basically all of modern physics.

Sometimes I wish I became a physicist lol.

The part I don’t get is 2*S. They add them together but shift it…

[quote]Dr. Pangloss wrote:
I still don’t believe it. It’s make no intuitive sense whatsoever.[/quote]

This is not an intuitive process, and this article is very misleading. This sum is indeed accurate, but it is not the only value that can be assigned to the sum of natural numbers. Under the standard axioms applied to the field of real numbers, this sum is indeed divergent, which is what would be intuitive to most people since the field axioms as applied to real numbers are what are taught in primary, secondary, and post-secondary classes up until complex numbers and other things become a factor. This means that it approaches some kind of infinite value, or the limit in some other way does not exist. In this case it is one form of an infinitely positive value.

The problem is that people are taught these topics without it ever being explained to them that this is not the only way to do things mathematically. Things like addition and multiplication (which when applied to real numbers using the standard field axioms are the exact same thing) are taught as pure, unalterable facts to people and by people who do not understand that the reason that these are true are because we are following arbitrary rules made up by mathematicians for a specific purpose and they can be altered or thrown out altogether under certain circumstances. For example, the field axioms applied to real numbers and the operations that arise from them do not apply at all to imaginary numbers (which, despite the name, are very much real. Now, when we apply the field axioms to other, more complicated groups and fields and such we get new definitions of operations like addition and multiplication and we can define things like the Riemann Zeta function, or Ramanujan summation which we can apply to sum the set of natural numbers and get -1/12 and other values like 1/4 (which is also a valid convergent value for the sum of natural numbers under some conditions) both of these are extremely useful to physicist like myself.

Dr. Matt is the coolest

[quote]csulli wrote:
Dr. Matt is the coolest[/quote]

Thank you very much!

[quote]Dr.Matt581 wrote:

[quote]Dr. Pangloss wrote:
I still don’t believe it. It’s make no intuitive sense whatsoever.[/quote]

This is not an intuitive process, and this article is very misleading. This sum is indeed accurate, but it is not the only value that can be assigned to the sum of natural numbers. Under the standard axioms applied to the field of real numbers, this sum is indeed divergent, which is what would be intuitive to most people since the field axioms as applied to real numbers are what are taught in primary, secondary, and post-secondary classes up until complex numbers and other things become a factor. This means that it approaches some kind of infinite value, or the limit in some other way does not exist. In this case it is one form of an infinitely positive value.

The problem is that people are taught these topics without it ever being explained to them that this is not the only way to do things mathematically. Things like addition and multiplication (which when applied to real numbers using the standard field axioms are the exact same thing) are taught as pure, unalterable facts to people and by people who do not understand that the reason that these are true are because we are following arbitrary rules made up by mathematicians for a specific purpose and they can be altered or thrown out altogether under certain circumstances. For example, the field axioms applied to real numbers and the operations that arise from them do not apply at all to imaginary numbers (which, despite the name, are very much real. Now, when we apply the field axioms to other, more complicated groups and fields and such we get new definitions of operations like addition and multiplication and we can define things like the Riemann Zeta function, or Ramanujan summation which we can apply to sum the set of natural numbers and get -1/12 and other values like 1/4 (which is also a valid convergent value for the sum of natural numbers under some conditions) both of these are extremely useful to physicist like myself.

This means that it approaches some kind of infinite value, or the limit in some other way does not exist [/quote]

I’m wondering where you’ve been when I’ve been ridiculed for saying arrhythmic is an invented convention for specific application and not a universal truth.

I even posted that 2+2=22 and challenged anyone to prove otherwise without reference to the physical world and got nothing (other than mocked).

[quote]DoubleDuce wrote:

I’m wondering where you’ve been when I’ve been ridiculed for saying arrhythmic is an invented convention for specific application and not a universal truth.

I even posted that 2+2=22 and challenged anyone to prove otherwise without reference to the physical world and got nothing (other than mocked).[/quote]

I have been really busy with moving to Norway (I have to learn the language really fast so that I can lecture in Norwegian). I am sorry that I missed that thread; if I had seen the discussion I would have chimed in and helped out.

-1/12

[quote]Dr.Matt581 wrote:

[quote]Dr. Pangloss wrote:
I still don’t believe it. It’s make no intuitive sense whatsoever.[/quote]

This is not an intuitive process, and this article is very misleading. This sum is indeed accurate, but it is not the only value that can be assigned to the sum of natural numbers. Under the standard axioms applied to the field of real numbers, this sum is indeed divergent, which is what would be intuitive to most people since the field axioms as applied to real numbers are what are taught in primary, secondary, and post-secondary classes up until complex numbers and other things become a factor. This means that it approaches some kind of infinite value, or the limit in some other way does not exist. In this case it is one form of an infinitely positive value.

The problem is that people are taught these topics without it ever being explained to them that this is not the only way to do things mathematically. Things like addition and multiplication (which when applied to real numbers using the standard field axioms are the exact same thing) are taught as pure, unalterable facts to people and by people who do not understand that the reason that these are true are because we are following arbitrary rules made up by mathematicians for a specific purpose and they can be altered or thrown out altogether under certain circumstances. For example, the field axioms applied to real numbers and the operations that arise from them do not apply at all to imaginary numbers (which, despite the name, are very much real. Now, when we apply the field axioms to other, more complicated groups and fields and such we get new definitions of operations like addition and multiplication and we can define things like the Riemann Zeta function, or Ramanujan summation which we can apply to sum the set of natural numbers and get -1/12 and other values like 1/4 (which is also a valid convergent value for the sum of natural numbers under some conditions) both of these are extremely useful to physicist like myself.

[/quote]

And this is also why we engineers don’t let physicists actually design mechanical objects.

[quote]Dr.Matt581 wrote:

[quote]DoubleDuce wrote:

I’m wondering where you’ve been when I’ve been ridiculed for saying arrhythmic is an invented convention for specific application and not a universal truth.

I even posted that 2+2=22 and challenged anyone to prove otherwise without reference to the physical world and got nothing (other than mocked).[/quote]

I have been really busy with moving to Norway (I have to learn the language really fast so that I can lecture in Norwegian). I am sorry that I missed that thread; if I had seen the discussion I would have chimed in and helped out.
[/quote]

I even challenged everyone to define addition in an absolute context (so I could disprove it in practical application) but didn’t get any takers.

As an engineer I’ve learned not to think of math and it’s answers as right or wrong. I now only really see it as useful or not. They are just tools. Things like infinity and i aren’t really numbers so much as useful concepts. The same goes for things like addition or integers to String theoryâ??s dozen dimensions.

[quote]thethirdruffian wrote:

[quote]Dr.Matt581 wrote:

[quote]Dr. Pangloss wrote:
I still don’t believe it. It’s make no intuitive sense whatsoever.[/quote]

This is not an intuitive process, and this article is very misleading. This sum is indeed accurate, but it is not the only value that can be assigned to the sum of natural numbers. Under the standard axioms applied to the field of real numbers, this sum is indeed divergent, which is what would be intuitive to most people since the field axioms as applied to real numbers are what are taught in primary, secondary, and post-secondary classes up until complex numbers and other things become a factor. This means that it approaches some kind of infinite value, or the limit in some other way does not exist. In this case it is one form of an infinitely positive value.

The problem is that people are taught these topics without it ever being explained to them that this is not the only way to do things mathematically. Things like addition and multiplication (which when applied to real numbers using the standard field axioms are the exact same thing) are taught as pure, unalterable facts to people and by people who do not understand that the reason that these are true are because we are following arbitrary rules made up by mathematicians for a specific purpose and they can be altered or thrown out altogether under certain circumstances. For example, the field axioms applied to real numbers and the operations that arise from them do not apply at all to imaginary numbers (which, despite the name, are very much real. Now, when we apply the field axioms to other, more complicated groups and fields and such we get new definitions of operations like addition and multiplication and we can define things like the Riemann Zeta function, or Ramanujan summation which we can apply to sum the set of natural numbers and get -1/12 and other values like 1/4 (which is also a valid convergent value for the sum of natural numbers under some conditions) both of these are extremely useful to physicist like myself.

[/quote]

And this is also why we engineers don’t let physicists actually design mechanical objects.[/quote]

Lol. We take the physics, simplify the structure as a beam and the beam as a line and the line as a point, run the calculations, then multiply by a safety factor of four. Then we build it and run physical testing to verify.

[quote]Dr.Matt581 wrote:

[quote]DoubleDuce wrote:

I’m wondering where you’ve been when I’ve been ridiculed for saying arrhythmic is an invented convention for specific application and not a universal truth.

I even posted that 2+2=22 and challenged anyone to prove otherwise without reference to the physical world and got nothing (other than mocked).[/quote]

I have been really busy with moving to Norway (I have to learn the language really fast so that I can lecture in Norwegian). I am sorry that I missed that thread; if I had seen the discussion I would have chimed in and helped out.
[/quote]
Even your explanations for your absences are cool.

[quote]csulli wrote:
Dr. Matt is the coolest[/quote]

He’s so cool that patients go see him when they’re healthy and stay out of his sight when they’re ill because they know they’re not good enough for him. He’s so cool that he has patients despite not being a MD. He’s so cool that he’s a MD anyway. He’s cool that numerical constructs are his patients.

I watched the video again.

I got so mad I had to lay down.

[quote]spar4tee wrote:

[quote]csulli wrote:
Dr. Matt is the coolest[/quote]

He’s so cool that patients go see him when they’re healthy and stay out of his sight when they’re ill because they know they’re not good enough for him. He’s so cool that he has patients despite not being a MD. He’s so cool that he’s a MD anyway. He’s cool that numerical constructs are his patients.[/quote]

LOL, I would never have chosen MD as a profession. I never wanted to take up a trade, but if I had decided on a trade I would have accepted the commission I was offered by the Russian Army (officer training was required for most university students in the Soviet Union and continued for the first years of the Russian Federation, and I excelled at my military studies but my grandfather would have been really disappointed if I joined the military). Academia is where I belong and I could not imagine myself as happy as I am now in any other career.