Self-referential systems, recusion and other stuff.

[TheGreenAnger]

Interesting recursive patterns... .e.g. the Fibonacci Sequence....

Fn = Fn-1 + Fn-2, where n > 1

[TheGreenAnger]

Recusion... I recuse myself!

Recursion - Grrrr!

Then there is the Mandlebrot set.

f(x) = x² + c

[TheGreenAnger]

Talking of the Fibonacci series and recursion, the lambda calculus predicated programming language Lisp/LISP uses recursion as opposed to the loop and is a very good programming language for efficiently, some might say elegantly, generating such series.

The BBC micro had a good Lisp interpreter all those years back. I wonder if any fellow nerds here remember that?

[talmacapt]

Now that brought back memories of doing a pure mathematics degree in the sixties.

Calculators were not generally available and computers consisted of large rooms and punch cards.

Very often the only way to solve a function, what today would be done on a calculator, would be to recursively approach a solution.

A very time consuming process for even fairly simple expressions.

Just realised there is a post in the aftn section where this really belongs.

Can you move it for me?

[TheGreenAnger]

Now that brought back memories of doing a pure mathematics degree in the sixties.

Calculators were not generally available and computers consisted of large rooms and punch cards.

Very often the only way to solve a function, what today would be done on a calculator, would be to recursively approach a solution.

A very time consuming process for even fairly simple expressions.

Just realised there is a post in the aftn section where this really belongs.

Can you move it for me?

I remember Algol 60 had a very good recursive ability, whereas the Fortran compiler, used by me at UCT on the Sperry Univac in the early 80's, didn't support the same at the time. Programmable scientific calculators were available by then, but weren't cheap, and there was a lot of HP, Casio and Texas instruments rivalry going on. One still had to book mainframe time and type all the cards up oneself. The halls of residence, conveniently, had a punch card machine in a room in the foyer, if one was too slack to walk up the hill to the computer centre. Later I used the BBC micro which had a LIsp interpreter which supported recursion, and I purchased the BBC Micro Forth interpreter/ 6502 compiler which did the same, the language having originally been designed to control the Jodrell Bank telescope which I only got to see many years later as a tourist. Here is a copy of the manual. Brings back memories.

http://stardot.org.uk/mirrors/www.bbcdo ... mputer.pdf

[Ex-Ascot]

Looks like a nice day there today. As a kid I used to cycle there from home.

https://www.jb.man.ac.uk/webcam/

[Undried Plum]

The Hewlett Packard 9845 manual had a glossary at the back. The entry for Recursion said simply "See Recursion".

[TheGreenAnger]

The Hewlett Packard 9845 manual had a glossary at the back. The entry for Recursion said simply "See Recursion".

A bit like this... Self-referential systems, recursion and other stuff.

Long live the Casio fx-100C.

[Boac]

What do you put on a Christmas card to a Conservative voter?

"Please turn over"

On both sides?

[TheGreenAnger]

What do you put on a Christmas card to a Conservative voter?

"Please turn over"

On both sides?

Yes.

Or confuse the already confused Conservative with:

Front: The sentence on the other side of this card is True.
Back: The sentence on the other side of this card is False.

All of those deluded C's should be forced to listen to the high priest of non-contradiction (although he seems to avoid quantum systems which may be true and false simultaneously until a measurement is made and the system decoheres into a true or false outcome, a superposition of spin up, spin down, with a 50% probability of either.) Sorry I digress!




for those that find this stuff interesting.... (I have deviated from recursion but will return) ...

Semantics in natural language should be avoided and replaced with the clarity of mathematics in these cases. Philosophers seeking to count the number of angels that can dance on a pinhead methinks!

[Fox3WheresMyBanana]

Is the political system not recursive?
Each generation possesses all the prejudices and sins of the previous, only with less intelligence and fewer principles.

Recursion was necessary with jet engine design (probably still is). At University, one would start with a guess at initial parameters, and after several manual calculations, if one was close enough, the output the first time could be fed back in, and after about 3 iterations one would end up with a stable answer. If the guess was wrong, the solutions would diverge, and one had to start again with another guess. I was most fortunate in my final exam, in that being on an RAF Scholarship I recognised the design profile given as that of the Nimrod - not much else bimbles about at sea level on two engines. Banged out the right answer in half the usual time.

[TheGreenAnger]

Is the political system not recursive?
Each generation possesses all the prejudices and sins of the previous, only with less intelligence and fewer principles.

Recursion was necessary with jet engine design (probably still is). At University, one would start with a guess at initial parameters, and after several manual calculations, if one was close enough, the output the first time could be fed back in, and after about 3 iterations one would end up with a stable answer. If the guess was wrong, the solutions would diverge, and one had to start again with another guess. I was most fortunate in my final exam, in that being on an RAF Scholarship I recognised the design profile given as that of the Nimrod - not much else bimbles about at sea level on two engines. Banged out the right answer in half the usual time.

Finite Systems Analysis 101 I guess.

Run the function(s) popping everything onto the stack, run again and again ad infinitum, or to the point of stack overflow or the point where the numbers reach optimal boundary conditions and roll up again, popping the variables off the stack as you go and generate your model.

How to grossly simplify everything in one crude sentence.

[llondel]

Finite Systems Analysis 101 I guess.

Run the function(s) popping everything onto the stack, run again and again ad infinitum, or to the point of stack overflow or the point where the numbers reach optimal boundary conditions and roll up again, popping the variables off the stack as you go and generate your model.

How to grossly simplify everything in one crude sentence.

Technically you push it onto the stack and pop it off again...

[TheGreenAnger]

Finite Systems Analysis 101 I guess.

Run the function(s) popping everything onto the stack, run again and again ad infinitum, or to the point of stack overflow or the point where the numbers reach optimal boundary conditions and roll up again, popping the variables off the stack as you go and generate your model.

How to grossly simplify everything in one crude sentence.

Technically you push it onto the stack and pop it off again...

You are right Sir, but outside the 8086 and 68000 Motorola family, as one wandered into Seymour Cray land into the new quantum world, a push and a pop are statiscally equivalent. All just depends on which way you run the equation.

[TheGreenAnger]

I guess this fits into the other stuff category, but it is an interesting diversion into the world of large but still finite numbers.

Tree 3





Once one gets into the world of infinite numbers one teeters into a mind-boggling world that was reputed (probably apocryphally) to have precipitated mathematician George Cantor's breakdown.

[TheGreenAnger]