Computers, Memory Pyramid & Code Size Optimization.

What is a Computer?

In Computer Sciences, Computer - by definition - is processor with memory and input/output devices. Any electronic device that has these is considered Computer. This includes Smartphones and many other tools.


Memory, Persistent or Transient.

There are two types of memory / pl: 'Są dwa rodzaje pamięci' /:
- Persistent / pl: 'Trwała' /,
- Transient / pl: 'Ulotna' /.

Persistent objects are those which continue to exist even after the program that created them has stopped running.

Transient objects cease to exist when program that created them stops.


Pyramid of Needs.

There are many types of memory, differing in price and speed of access.

Starting from the most expensive but fastest, there are:
- processor's registers,
- layers of the processor's cache (L1-L3, for example),
- RAM (Random Access Memory),
- persistent SSD/HDD storage.


Code Size optimization.

Smaller programs can be very quick in their execution.

When the whole program fits - for example - in L2 Processor's Cache, there's no need to reach RAM via BUS, so the code runs very quickly - as it's closer to the processor than RAM.


What if a Program doesn't fit in Transient Memory?

When a program needs to be executed, it needs to be loaded into the transient memory first.

However, Modern Operating Systems can send currently unused Program's parts & other Resources / for example: graphics image files, sound files and/or text files / from Transient Memory to Persistent SDD/HDD Memory and retrieve other Resources/Part(s) from Persistent Memory to Transient Memory / Usually from disk to RAM /.

/ pl: 'Współczesne Systemy Operacyjne mogą wysłać aktualnie niewykorzystywane części Oprogramowania i innych zasobów na dysk... i sprowadzić inne zasoby/części z pamięci trwałej do ulotnej, najczęściej do pamięci RAM' /.

Let's note, however, that loading/storing data in persistent memory is much slower than loading/storing from/to Transient RAM.

This is an automated operation in Modern Operating Systems, so programmers do not need to worry so much about that. Computers just slow down sometimes - and SSD/HDD becomes quite busy, when doing that.


This sometimes causes 'Flickering' / pl: 'Migotanie', 'Szamotanie' /, however. Code & Data is loaded/unloaded from/to persistent memory too slowly and can cause a Computer System to slow down or crash, as the Computing Resources run out. / Mostly CPU usage & Memory usage /.

So - in theory at least - a Computer can try to run larger programs than Computer has RAM.

Often it fails, but in theory this can work well.

Logic & Axioms.

'My Logic is based on different Axioms than Yours'.


There are many Logics, based on different Axioms.

/ EN: 'Axiom' = PL: 'Aksjomat' /.

Axioms are statements that are not proven, but assumed as true, taken on faith.

/ EN: 'assumption' = PL: 'założenie' /.

Depending on the Axioms used, Theorems can be proven or disproven, and the whole Mathematical & Logical Apparatus can be developed.


Basing on Boolean Algebra, double negation evaluates to confirmation, but in some languages - polish for example - double negation does not mean confirmation, it does mean emphasis on negation, giving negation more power.

There are rules for negating Quantifiers as well.

/ EN: 'negation' = PL: 'zaprzeczenie' /,
/ EN: 'confirmation' = PL: 'potwierdzenie' /,
/ EN: 'emphasis' = PL: 'nacisk' /,
/ EN: 'quantifier' = PL: 'kwantyfikator' /.


/ PL: 'nigdy nie zgodzę się na te warunki'. /

/ według Algebry Boole'a i Teorii Kwantyfikatorów wylicza się do:
'istnieje taki moment w czasie kiedy zgodzę się na te warunki'. /

/ a w mowie potocznej znaczy: 'nie istnieje taki moment w czasie kiedy zgodzę się na te warunki'. /

Therefore, Speech of the Art, Literature, can have the Logic based on different Axioms than Boolean Algebra.

We can say that: 'Life is more than Boolean Algebra and Quantifiers' when we want to use casual, non-logical talks.

When Boolean Algebra and Quantifiers are useful then? It's useful in computer programming, or when we want to talk logically and precisely, or when we want to express our wishes logically and precisely. But when we opt for logical and precise speech, let's make sure first that other people we talk with understand our logic.


We can also define the addition operation / it's an Axiom too / differently as well.

We can have an exception:

for example:

1+1 = 2, 1+2 = 3, 2+1 = 3, 1+3 = 4, 3+1 = 4, 2+2 = 5, 1+4 = 5, 4+1 = 5, 2+3 = 5, 3+2 = 5, 1+5 = 6, 5+1 = 6, 2+4 = 6, ...

We can also redefine the addition operation differently on the more general, more universal scale:

for example:

n+2 in our redefined addition operation is n+2+1 in classical addition operation.

By doing so, by changing Axioms, we just have revolutionized the Mathematics. ;)

Many different theorems apply now, but at least we know that we can make expression 2+2 = 5 to be evaluated as true in a certain Context - even if this brings more or less desired effects in process ;).


We are free to assume any Axioms we want, examples can be multiplied infinitely.


Which Logic is 'better' than other, then?

... it depends on the assumed Criteria, which might be Axioms as well.

The Enigma Cipher of WW2 & the Turing Machine.

Polish and British mathematicians were among the best of people who cracked the Adolph Hitler's cipher named Enigma, it happened during the World War 2nd.

Enigma breaking was hard, and the mathematicians were hunted by Germany's spies.

Enigma evolved, so parts of the cipher were to be cracked again and again. It was not about making an automaton once, and letting it work for the rest of WW2 ... but statistically it worked so the effort was continued.

Doing maths when time flew and lives were at stake.... so stressful. The Germany's spies added to the dangers & to the stress too.

Polish mathematicians had one of few of first computers ... it was nicknamed: 'Bomb', for it was so big invention. It increased efficiency of the enigma cipher cracking.

And there was Alan Turing's effort of course. He was a British scientist who laid foundation-theory of computer's construction.

His thinking is still present in computer sciences of modern days.

(We were taught about Languages & Automatons in Warsaw University when i was studying computer sciences. Turing's Machine was a part of this lecture).

> [ https://en.wikipedia.org/wiki/Turing_machine ].

The Turing Machine is programmed in a similar way to programming the Register Machine.

> [ https://en.wikipedia.org/wiki/Register_machine ].


--
Sources:

1. 'Cubits & Shrodinger's Cat. From Turing Machine to Quantum Computers' by John Gribbin.
(Polish Edition).

2. The internet (wikipedia & the ważniak mostly) and my own thinking.

3. My (unfinished because of health problems) education at Warsaw's University (Mathematics, Informatics & Mechanics Faculty).