Math tales: a short story about everything

At the edge of the Universe, located in its center, there is an amazing Machine: with an unimaginable speed it repeats again and again some very simple operations. At  first it extracts Something from All Things That Already Exist, then from the same source — from the All Things That Already Exist — it takes Some Set. Having these two, it proceeds to the third operation — the Union — and gets as a result a New Set. The fourth operation is combining items of the New Set in all possible ways. It worth to mention here that the Machine is able to extract items without corruption of their source.

So, after the fourth step the Machine has a Set Of Subsets of the New Set.

At the fifth operation it creates One More Set, but… its content is undefined. Yes, it is undefined because at this stage the Machine doesn’t know it. At the sixth step it resorts to the Union again — now it applies it to the One More Set and the New Set mentioned above. On the seventh step our mechanism behaves quite tricky: it jumps to two-step-earlier past — thankfully it’s easy enough for the Machine as each operation lasts exactly 0 seconds — and at the fifth step (two-step-earlier than the current seventh step) and talks to itself from the past that what is the content of the One More Set is — thus revealing that it is the United set produced  at the sixth step.

And the final chord — Operation №8 (of course after completing the 7th the Machine returns to the present time): putting all the entities produced by 1..7 operations into the All Things That Already Exist — obviously excluding anything that is already there — and in such way Everything is born in the Universe.

Comments

Post a Comment

Popular posts from this blog

💻 Programming: recipe: response validation against OpenAPI schema in Python

Image
Summary: code snippets and explanation of how to validate HTTP-response using  openapi-core package If you deal with some service based on OpenAPI Specification you might want to perform validation of HTTP responses returned by it. One of the ways to do this an internet search provides for Python is to use openapi-core package. If you look at their documentation ( here or here ) you will find it very stingy: couple of short code snippets and couple of sentences just stating what is done. In particular for response validation we have exactly the following:   You can also validate against responses   from openapi_core . validation . response . validators import ResponseValidator   validator = ResponseValidator (spec) result = validator . validate (request, response)   # raise errors if response invalid result .raise_for_errors()   # get list of errors errors = result .errors ...   Here we see some confusing things: why do we need a request object to be able to validate the respo
Read more

Ï• Logic vs. ‘common sense’

Logic is a doctrine of correct judgment and it’s “our everything” (in the sense that it is necessary for any theory and learning). But to discover or ‘invent’ (formulate for the very first time) the laws of logic it is already necessary to think (judge) correctly — so there is a question: Isn’t there a kind of paradox? Or at least a vicious circle? Indeed, if you think correctly you can formulate correct logic laws and using them prove something (and maybe the way of how you judged about correctness of the laws formulated) — but if you don’t then the laws are invalid and you are unable even to find that. Seems the ability of reasoning is intrinsic for people (at least for those who is educated enough) and the ‘discovery’ of the ‘laws’ is just a result of observations (of own and other people thinking and judgments and their correspondence to a real state) and further refinements of them. But usually that ability is unconscious (intuitive) and informal (nobody judges like “A is true bec
Read more

💻 Programming: recipe: pytest: assertion after all tests run

Example of how to check some conditions when ALL test suites finished (or enforce some test running at the end of session). This may be useful to ensure that you have tested all functions of some module whose interface can change in future. The code: from   pytest   import   fixture     Data  =  dict ( cnt  =  0 )   @fixture ( scope = 'session' ) def   data_0 ():        yield   Data        # (this will be done AFTER all tests below)      assert   Data [ 'cnt' ] ==  3 ,  f 'data-cnt:  { Data [ "cnt" ] } '   @fixture def   data ( data_0 ):        Data [ 'cnt' ] +=  1        return   Data [ 'cnt' ]   def   test_11 ( data ):        print ()      print ( 'test-11:' ,  data )   def   test_12 ( data ):        print ()      print ( 'test-12:' ,  data ) Output: ERROR test_1.py::test_12 - AssertionError: data-cnt: 2 _________ Other articles ~ programming
Read more