Nice people thread 2 - now even nicer

tomterm8

PasturesNew wrote: »

I could do that. Sitting and thinking. Easy!

Here's the introductiory definitions segment of Alan Turings seminal paper ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE
ENTSCHEIDUNGSPROBLEM to get you started.

Alan_Turing wrote:

1. Computing machines.
We have said that the computable numbers are those whose decimals are calculable
by finite means. This requires rather more explicit definition. No real attempt will

be made to justify the definitions given until we reach

§9. For the present I shall

only say that the justification lies in the fact that the human memory is necessarily
limited.
We may compare a man in the process of computing a real number to a machine
which is only capable of a finite number of conditions q

1, q2, ..., qR which will be

called “

m-configurations”. The machine is supplied with a “tape”, (the analogue of

paper) running through it, and divided into sections (called “squares”) each capable
of bearing a “symbol”. At any moment there is just one square, say the

r-th, bearing

the symbol

S(r) which is “in the machine”. We may call this square the “scanned

square”. The symbol on the scanned square may be called the “scanned symbol”.
The “scanned symbol” is the only one of which the machine is, so to speak,
“directly aware”. However, by altering its

m-configuration the machine can

effectively remember some of the symbols which it has “seen” (scanned)
previously. The possible behaviour of the machine at any moment is determined by
the

m-configuration qn and the scanned symbol S(r). This pair qn, S(r) will be

called the “configuration”: thus the configuration determines the possible behaviour
of the machine. In some of the configurations in which the scanned square is blank
(i.e. bears no symbol) the machine writes down a new symbol on the scanned
square: in other configurations it erases the scanned symbol. The machine may also
change the square which is being scanned, but only by shifting it one place to right
or 1eft. In addition to any of these operations the

m-configuration may be changed.

Some of the symbols written down

{232} will form the sequence of figures which is

the decimal of the real number which is being computed. The others are just rough
notes to “assist the memory”. It will only be these rough notes which will be liable
to erasure.
It is my contention that these operations include all those which are used in the
computation of a number. The defence of this contention will be easier when the
theory of the machines is familiar to the reader. In the next section I therefore
proceed with the development of the theory and assume that it is understood what is

meant by “machine”, “tape”, “scanned”, etc.

2. Definitions.

Automatic machines.

If at each stage the motion of a machine (in the sense of

§1) is completely

determined by the configuration, we shall call the machine an “automatic machine”
(or

a-machine). For some purposes we might use machines (choice machines or

c

-machines) whose motion is only partially determined by the configuration (hence

the use of the word “possible” in

§1). When such a machine reaches one of these

ambiguous configurations, it cannot go on until some arbitrary choice has been
made by an external operator. This would be the case if we were using machines to
deal with axiomatic systems. In this paper I deal only with automatic machines, and
will therefore often omit the prefix

a-.

Computing machines.
If an

a-machine prints two kinds of symbols, of which the first kind (called figures)

consists entirely of 0 and 1 (the others being called symbols of the second kind),
then the machine will be called a computing machine. If the machine is supplied
with a blank tape and set in motion, starting from the correct initial
m

-configuration, the subsequence of the symbols printed by it which are of the first

kind will be called the

sequence computed by the machine. The real number whose

expression as a binary decimal is obtained by prefacing this sequence by a decimal
point is called the

number computed by the machine.

At any stage of the motion of the machine, the number of the scanned square, the
complete sequence of all symbols on the tape, and the

m-configuration will be said

to describe the

complete configuration at that stage. The changes of the machine

and tape between successive complete configurations will be called the

moves of

the machine.
{233}
Circular and circle-free machines.
If a computing machine never writes down more than a finite number of symbols of
the first kind it will be called

circular. Otherwise it is said to be circle-free.

A machine will be circular if it reaches a configuration from which there is no
possible move, or if it goes on moving, and possibly printing symbols of the second
kind, but cannot print any more symbols of the first kind. The significance of the
term “circular” will be explained in

§8.

Computable sequences and numbers.
A sequence is said to be computable if it can be computed by a circle-free machine.
A number is computable if it differs by an integer from the number computed by a
circle-free machine.
We shall avoid confusion by speaking more often of computable sequences than of

computable numbers.

The difficult bit starts on the next page. http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf.

lemonjelly

tomterm8 wrote: »

His theory of information and computing is probably the reason we are typing on this forum today. He was, in my view, a genious the equivalent of einstein.

Turing was/is a genius. The Turing test is still a phenomenon which AI researchers still coninue to be befuddled by. Indeed, in recent times people have been given machine status because their responses were well structured & punctuated correctly the judges obviously felt this was a non-human trait!:eek: Or that humans have lost the ability to use correct punctuation & grammar!:eek:)

PasturesNew wrote: »

I could do that. Sitting and thinking. Easy!

Actually, philosophy is the opposite of that. I'd argue that it is an exercise you have to engage in. Sitting & thinking ain't philosophy. Engaging in debate, critical analysis, looking at assumptions, presuppositions, judgements, logic & logical flaws & the like. It is an activity in which you partake.

You don't grow a beard & then sit in a library stroking it...;)

lostinrates

chick watch.

And another one

The five eggs the two chickens were sharing should have hatched by sunday. Nothing was doing and as there have been some late hatchings (and some of the incubator eggs were early) I decided not to remove on Sunday, but to give them a couple more days. Two had definitely tried and died. This morning ther is one (no obvious sex ink in his markings, but..I'm taking a punt at ''boy'') little chick.

Incubator 12/12, mother nature, 1/5. Showing nothing at all in truth, but a nice little example of how easily man can skew the figures.

PasturesNew

tomterm8 wrote: »

Here's the introductiory definitions segment of Alan Turings seminal paper ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE
ENTSCHEIDUNGSPROBLEM to get you started.





The difficult bit starts on the next page. http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf.



[/LEFT]

I left it all in to annoy people.... and the system truncated it.

I can't read that (cr4p/small font ... on a tiny monitor) ... but, it's about numbers.

I LOVE NUMBERS!!!!

PasturesNew

lemonjelly wrote: »

Engaging in debate, critical analysis, looking at assumptions, presuppositions, judgements, logic & logical flaws & the like. It is an activity in which you partake.

You don't grow a beard & then sit in a library stroking it...;)

Well, I can't do either of those things.

As for debating, present me with the opener and within three days I can come back with a comeback. You can then fire your answer back at me ... just give me another three days to think up my next bit. I am not good with verbal/aural skills, nor remembering and tying up pieces (debate).

I am what I am ... speshul

If I could grow a beard, I could join the circus ... I think there's more chance of that than me debating.

vivatifosi

lemonjelly wrote: »

You don't grow a beard & then sit in a library stroking it...;)

We have all sorts of oddballs in our library, but I can't say I've ever seen anyone sitting and stroking their beard for a long period - with or without a philosophy text:rotfl:.

SingleSue

Eldest is doing philosophy at A level starting September...he actually joked about growing his beard long and stroking it.

As he was clean shaven at the time, he just stroked his chin instead much to the merriment of the philosophy teacher.

misskool

Davesnave wrote: »

I have summer & winter squashes forming and a cucumber, but no courgettes. The early ones died from too much 'young' manure, then I put another lot of seed in a glass of water to get it going, and promptly washed it up by accident.....:o So, the third lot will be started today.

Mange tout peas are flowering, so they shouldn't be long.:)

Lovely drop of rain yesterday. Much needed, but it's b*ggered up the hay-making for now.

I keep fondling the peas to see if they'll be ready. Someone forgot to tell me that feltham first grow up to 5feet :eek:

I have 5 summer squashes and no place to plant them out :rotfl:

You make your own hay? :cool:

lemonjelly

PasturesNew wrote: »

Well, I can't do either of those things.

As for debating, present me with the opener and within three days I can come back with a comeback. You can then fire your answer back at me ... just give me another three days to think up my next bit. I am not good with verbal/aural skills, nor remembering and tying up pieces (debate).

I am what I am ... speshul

If I could grow a beard, I could join the circus ... I think there's more chance of that than me debating.

Ah, but this is philosophy PN. It isn't about instant answers, but moving towards the truth...

If it takes a day, a minute, a second, 3 days, whatever. It doesn't matter. What is important is the learning, understanding etc that occurs.:)

lemonjelly

vivatifosi wrote: »

We have all sorts of oddballs in our library, but I can't say I've ever seen anyone sitting and stroking their beard for a long period - with or without a philosophy text:rotfl:.

Oh they're there somewhere. You just need to look harder.
Perhaps in your area they're more into transcendentalism...:D