√5 and Phi

[wtf]

Guy, I am not trying to ruffle your feathers - I am not trying to start a fight,

I am merely pointing out that an approximation of pi is not pi.

Pi is Pi.

To compute pi on a real-world computer requires infinite time.

I agree completely. But that's not the definition of computability in the field of computer science. And you didn't answer me about 1/3 = .333333.... Is that an intractable number too?

[Skepdick]

I agree completely. But that's not the definition of computability in the field of computer science.

You are treating "the field of computer science" as some homogenous group. In as much as having worked at Google, Amazon and a few other places full of "computer scientists" there has been shared understanding.

We part ways when it comes to symbolic and numeric methods, and that's OK.

And you didn't answer me about 1/3 = .333333.... Is that an intractable number too?

With the "..." then yes. It's intractable.
If you are happy with an approximation - then no, it's obviously tractable.

In as much as it matters to engineers/pragmatists - it's a range-precision trade-off.

I see it as a choice-function.

[wtf]

I see it as a choice-function.

That's not what a choice function is. That phrase already has a standard meaning in math. It's a function that picks out one element out of each of a collection of nonempty sets.

I'll let you have the last word. I'm done here.

ps -- If 1/3 = .3333... is Skepdick-intractable, what about if you write it in base three, 1/3 = .1.

Does Skepdick-intractability only refer to the representation and not the number itself? Have you actually thought through your own idea?

[Skepdick]

That's not what a choice function is. That phrase already has a standard meaning in math. It's a function that picks out one element out of each of a collection of nonempty sets.

*sigh* That is exactly the definition I am using.

I am just in the habbit of turning things into questions. What degree of precision do I desire for the answer to 1/3 (or x/y) ?

The answer to that question is a choice in the Integer domain. Is it not?

As long as the answer is not "infinity", I can implement that choice function on a physical computer.

And by Curry-Howard-Lambek that's "proving my choice function".

Does Skepdick-intractability only refer to the representation and not the number itself?

Yes. This is an astute observation. One that Ed Nelson makes too.

I treat Mathematics as strictly representational.

[wtf]

Yes. This is an astute observation.

I'll let you ass toot on your own. And shame on you for invoking the good name of the late Ed Nelson to promote your crackpot ideas.

[Skepdick]

I'll let you ass toot on your own. And shame on you for invoking the good name of the late Ed Nelson to promote your crackpot ideas.

Dude, quit being an asshole. I am literally quoting Ed Nelson - his own words.

Confessions of an Apostate Mathematician

Page 7

And mathematics is slowly beginning to become non-representational. Slowly in departments of mathematics, but quickly in computer
science departments. Those who do computer science know that they
are inventing and not discovering, and they are making beautiful and
deep results concerning the nature of feasible computations. If we who
are in traditional departments don’t want to miss the boat, it behooves
us to saddle a formalist horse pronto.

In as much as I can't determine if I am treating Mathematics as "representational" or "non-representational", or you are using those words exactly inversely to the way I do - call it a bit-flip error.

[wtf]

Dude, quit being an asshole.

Uh, yeah, fuck you too. Congratulations. You hijacked the thread and got a rise out of me. Pretty clever to start out with sensible mathematical questions about algebraic numbers, then subtly change the subject. Troll grate A-. Not bad at all.

[Skepdick]

Uh, yeah, fuck you too. Congratulations. You hijacked the thread and got a rise out of me. Pretty clever to start out with sensible mathematical questions about algebraic numbers, then subtly change the subject. Troll grate A-. Not bad at all.

It was not my intent to get a rise out of you. For all it's worth - sorry.

Carry on with your life, I appreciate you taking the time.

[wtf]

It was not my intent to get a rise out of you. For all it's worth - sorry.

Carry on with your life, I appreciate you taking the time.

You serious? Am I genuinely misconstruing you? Ok. My mistake then.

[Skepdick]

You serious? Am I genuinely misconstruing you? Ok. My mistake then.

And I understand why. Your prior is skewed, and that's totally my fault.

[wtf]

You serious? Am I genuinely misconstruing you? Ok. My mistake then.

And I understand why. Your prior is skewed, and that's totally my fault.

I'm simply using the standard definitions. Instead of you saying, "Pi isn't computable because it never ends," why not just say, "Pi is Turing-computable but not Skepdick-computable because I use a different definition." That would show some intellectual honesty. But it's my fault for engaging in the first place. Like I said, your transition from sanity to insanity was subtle and I got caught up in it.

[Skepdick]

I'm simply using the standard definitions. Instead of you saying, "Pi isn't computable because it never ends," why not just say, "Pi is Turing-computable but not Skepdick-computable because I use a different definition."

Because I don't know what the "standard definitions" are; or what my "definitions" (axioms) are. My intuition comes from practice - I learned from experience, not definitions.

Which is why it seems to me that what I am doing is closer to reverse mathematics - I have theorems (truths), I am looking for axioms (foundations).

That would show some intellectual honesty.

I am being as transparent as I best know how. It's why I refuse to give any "definitions" to anything.

I have no idea! I've never had to define my axioms. I operate on intuition.

But it's my fault for engaging in the first place. Like I said, your transition from sanity to insanity was subtle and I got caught up in it.

The thing is, you think that there was a "transition". From where I am looking - what I said was consistent with my world-view.

And so my theory as to what's going on is your "mathematics" and my "reverse mathematics" are clashing.

I literally think backwards to the way you do. Is why I seem like a "crackpot". Is all an act FYI.

[wtf]

ow what the "standard definitions"; or what my "definitions" (axioms) are.

Didn't you claim to have read Turing 1936? So when you say you don't know the standard definition of a computable number, you are, shall we say, dissembling.

[Skepdick]

Didn't you claim to have read Turing 1936? So when you say you don't know the standard definition of a computable number, you are, shall we say, dissembling.

I have read it. You have quoted it. I have that definition committed to memory.

In 2020 is that still what you refer to as "the standard definition"? Because there are other models of computation...

It still doesn't address my 2nd point. Every definition I read looks like a definition I might agree with, and I am still no closer to telling you which definition I am using.

I am probably using all of them at different times.

[wtf]

Didn't you claim to have read Turing 1936? So when you say you don't know the standard definition of a computable number, you are, shall we say, dissembling.

I have read it. You have quoted it. I have that definition committed to memory.

In 2020 is that still what you refer to as "the standard definition"? Because there are other models of computation...

Yes it's the standard definition in the computer science curriculum.