Day: June 26, 2016

Fuzzy logic is good

Fuzzy logic as defined at the site above

  •  

Fuzzy logic is an approach to computing based on “degrees of truth” rather than the usual “true or false” (1 or 0) Boolean logic on which the modern computer is based.

The idea of fuzzy logic was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960s. Dr. Zadeh was working on the problem of computer understanding of natural language. Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1. (Whether everything is ultimately describable in binary terms is a philosophical question worth pursuing, but in practice much data we might want to feed a computer is in some state in between and so, frequently, are the results of computing.)

Fuzzy logic includes 0 and 1 as extreme cases of truth (or “the state of matters” or “fact”) but also includes the various states of truth in between so that, for example, the result of a comparison between two things could be not “tall” or “short” but “.38 of tallness.”

Fuzzy logic seems closer to the way our brains work. We aggregate data and form a number of partial truths which we aggregate further into higher truths which in turn, when certain thresholds are exceeded, cause certain further results such as motor reaction. A similar kind of process is used in artificial computer neural network and expert systems.

It may help to see fuzzy logic as the way reasoning really works and binary or Boolean logic is simply a special case of it.

An error

DSCF0228 2

A garden

I once read that writers throw away  90% of what they  produce.I can understand that now as some days I have to write a lot of not very good stuff until by the evening I suddenly find my voice.Unfortunately I left all the earlier attempts here!

A state which cuts off love and grace.

A hermit fell in love with my face
Can a problem  like this be embraced?
He looked at  my eyes
Till he was advised
Staring too much causes rage.

The real problem is hermits need space
They prefer distance to an embrace.
So they live in a dream
A  fantasised   scene.
A state which cuts off  love and grace.

Like an animal  once subject to abuse
They wander on the edge as they muse
We must look at them slantwise
Not argue when they fantasise
Run away when they blow their own fuse.

 

Finally, negative numbers and imaginary numbers

http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/

Quote from the  above link:Negatives were considered absurd, something that “darkened the very whole doctrines of the equations” (Francis Maseres, 1759). Yet today, it’d be absurd to think negatives aren’t logical or useful. Try asking your teacher whether negatives corrupt the very foundations of math.

What happened? We invented a theoretical number that had useful properties. Negatives aren’t something we can touch or hold, but they describe certain relationships well (like debt). It was a useful fiction.

Rather than saying “I owe you 30” and reading words to see if I’m up or down, I can write “-30” and know it means I’m in the hole. If I earn money and pay my debts (-30 + 100 = 70), I can record the transaction easily. I have +70 afterwards, which means I’m in the clear.

The positive and negative signs automatically keep track of the direction — you don’t need a sentence to describe the impact of each transaction. Math became easier, more elegant. It didn’t matter if negatives were “tangible” — they had useful properties, and we used them until they became everyday items. Today you’d call someone obscene names if they didn’t “get” negatives.

 

 

Transcendental: the meaning

transcendental
ˌtransɛnˈdɛnt(ə)l,ˌtrɑːn-/
adjective
adjective: transcendental
  1. 1.
    relating to a spiritual realm.
    “the transcendental importance of each person’s soul”
    • relating to or denoting Transcendentalism.
  2. 2.
    (in Kantian philosophy) presupposed in and necessary to experience; a priori.
  3. 3.
    MATHEMATICS
    (of a number, e.g. e or π) real but not a root of an algebraic equation with rational coefficients.
    • (of a function) not capable of being produced by the algebraical operations of addition, multiplication, and involution, or the inverse operations.
Origin
early 17th century: from medieval Latin transcendentalis (see transcendent).

Another look at the transcendental number e

1yqum52oyl9ai_l.jpg

https://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/

Here is an extract from the above site which I recommend if you’d like to learn a bit more about why people enjoy mathematics which can be boring if it is just long v= calculations

“Describing e as “a constant approximately 2.71828…” is like calling pi “an irrational number, approximately equal to 3.1415…”. Sure, it’s true, but you completely missed the point.:

Pi is the ratio between circumference and diameter shared by all circles. It is a fundamental ratio inherent in all circles and therefore impacts any calculation of circumference, area, volume, and surface area for circles, spheres, cylinders, and so on. Pi is important and shows all circles are related, not to mention the trigonometric functions derived from circles (sin, cos, tan).

e is the base rate of growth shared by all continually growing processes. e lets you take a simple growth rate (where all change happens at the end of the year) and find the impact of compound, continuous growth, where every nanosecond (or faster) you are growing just a little bit.

e shows up whenever systems grow exponentially and continuously: population, radioactive decay, interest calculations, and more. Even jagged systems that don’t grow smoothly can be approximated by e.

Just like every number can be considered a scaled version of 1 (the base unit), every circle can be considered a scaled version of the unit circle (radius 1), and every rate of growth can be considered a scaled version of e (unit growth, perfectly compounded).”