## Search found 896 matches

- Mon Feb 10, 2020 12:49 am
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

Yes it's the standard definition in the computer science curriculum. And that would be dandy, but I side-stepped academia. I am an autodidact. I understand computer science (engineering?) by having done it for 20+ years. Now that I am reading the theory, I am joining all the dots to the practice. Ok.

- Mon Feb 10, 2020 12:41 am
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

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 defi...

- Mon Feb 10, 2020 12:35 am
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

- Mon Feb 10, 2020 12:13 am
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

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 ...

- Mon Feb 10, 2020 12:08 am
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

- Mon Feb 10, 2020 12:03 am
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

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.

- Sun Feb 09, 2020 11:38 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

- Sun Feb 09, 2020 11:03 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

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-intra...

- Sun Feb 09, 2020 10:47 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

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 o...

- Sun Feb 09, 2020 10:39 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

No algorithm takes infinite time. I think you are confused about basic computer science. Pi has no "last digit" An algorithm that outputs "all the digits of pi one by one" cannot come to an "end". There is no such point on the time line that you can label "after the algorithm halted" I can't talk y...

- Sun Feb 09, 2020 10:34 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

Ok. Then call it tracticably computable and we have no difference of opinion. But then what of 1/3? How do you handle that objection? Or do you regard 1/3 as tracticably noncomputable? We don't have a difference of opinion once we assume infinities as intractable. An algorithm that takes infinite t...

- Sun Feb 09, 2020 10:31 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

Turing's view misses out on tractability, so it falls short of my needs. Engineer here. Tractability matters. Ok. Then call it tracticably computable and we have no difference of opinion. But then what of 1/3? How do you handle that objection? Or do you regard 1/3 as tracticably noncomputable? And ...

- Sun Feb 09, 2020 10:28 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

I am trying to figure out my axioms. In as much as it's becoming obvious to me - what I am doing is far closer to reverse mathematics. https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf If you want to use a different definition, call it quasi-computable or Skepdick-computable so that people ...

- Sun Feb 09, 2020 10:22 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

I think what we are disagreeing here is the definition of "halt". The general, human intuition for "halting" is that "it gives a final, definite answer in finite time". Your definition conflicts with that of Turing and the entire computer science profession. We need not go back and forth on this, y...

- Sun Feb 09, 2020 10:11 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: √5 and Phi
- Replies:
**132** - Views:
**1270**

### Re: √5 and Phi

Why it's intuitive to me is "Everything implementable on a classical computer is algebraic". But of course this is false. Pi is computable, as is e, as is every well-known transcendental constant. If it halts, it's either polinomial time, or polinomial space. That's also of course completely false ...