Monday, May 23, 2016

Fluidic computers - Logic gates

In an innocent way, and mainly based on my ignorance, in 2001 I developed an online toy about building tiny computing objects with logic blocks:
Is my OBBLOG

Ignoring the equivalences of the Karnaugh table, OBBLOG contains all the possible logic gates with two inputs and one output.

This is the partial living OBBLOG Truth Table:



For to build a operating toy, I added forks, crossings at different levels and  bit visualizers. (Similar to a light bulb)

However, the toy did not have flip-flops, so you could not make a numbers counter, although small binary calculators 1 to 16 bits.

The toy allows to build little and simple animated toys:


Or more complex constructions:
Binary Tree:



But from the initial basic logic gates, I discovered that it was possible to build a flip-flop:
(And consequently a counter of binary numbers):
 (The obblog allows a closed loop that continues 
to circulate indefinitely if not obstructed)


Thanks to this, the obblog could become able to build calculators calculating in binary system and be able to show results in decimal system. But being only in 2 dimensions can never bequeath to do what you can get to perform with Minecraft. (Koala steamed) (see: official Minecraft logic gates)



(without flip-flops)






I posted all this, because yesterday I found similar artifacts along the history of computing:
The article published in Scientific American the December of 1964:

Fluid logic devices, all based in the Coanda effect: 









And the conference at MIT:  
Referred by:  Fluidic computing at Bowles Fluidics: 
http://strangebits.blogspot.com.es/2007/05/i-had-pleasure-of-participating-in.html

Coding and computation in microfluidics.
http://cba.mit.edu/events/07.05.fluid/

And the conference from Manu Prakash, 
http://cba.mit.edu/events/07.05.fluid/Prakash.pdf

The manu Prakash Thesis: (About "microfluidic bubble logic"), and inside this beautiful Truth table about logic gates and its equivalents in transistors, valves, electrical devices, and fluidics:



Some examples of projected fluidic devices:
(from Prakash thesis)
 Integrated fluidic logic gates with a schematic integrated control circuit 



  
The main patents about fluidics, come from the sixties:
https://www.google.com/patents/US4854176
(from wikipedia)

And schema about Coanda effect from Popular Science (Jun 1967 Pag 118) : 

And the:  Fluidics: Basic components and applications 
By: James W. Joyce  (1977; Unclassified: 1983)





And from the conference:
APPLIED HYDRAULICS AND PNEUMATICS U5MEA23 Prepared by Mr. Jayavelu.S & Mr. Shri Harish Assistant Professor, Mechanical. http://slideplayer.com/slide/5675986/







I would like to see these companions of my program, running.

Anyway, everybody can see them inside the Bowles products:
 

And inside of the Theranos patented devices: (Lab-on-a-chip)






More serious and basic information: Introduction to fluid Mechanics:  

Follow: Reflections about all this at: https://plus.google.com/communities/102467630739607363236


Wednesday, May 11, 2016

Dancing numbers: (Math Circus)

Dancing numbers: Numbers Circus: Modulo choreography.
( And:  Circus for to tame numbers, too )

After the post dedicated to dancing sort algorithms,  I think it's time to show a program made and published in 2004, which it could be useful in teaching elementary mathematics.


Is the "Dancing numbers

Originally made for MathCats.com , it never has been published. Finally I posted it on my page so do not be missed for the moment.

The program allows you to manipulate a lot of integers (up to 2000) with some simple rules: decide the number of columns that are to line up neatly from lowest to highest.
(Also possible to arrange smaller amounts of numbers)

The program allows for reflection on the divisibility of numbers and remainders:

It is also advisable to use the mode 9 columns, that shows the rule of divisibility for 9.
(The sum of all members of any number equals the heading number of the column)

And all the rules explained in https://en.wikipedia.org/wiki/Modular_arithmetic
(related to addition, subtraction, multiplication and division (sometimes), and congruence).

Here is a sample of how the program works:




You can use the application here: http://www.nummolt.com/obbl/dancingnumbers/modular_xtd_01.html

I hope its use will be useful to teach elementary mathematics.

Sunday, May 8, 2016

Noting mathematics education in the world, from the statistics page of my Android apps

This is just a small observation, based on my own stats:
As the numbers that I show are not too high, observation may not have enough value.

Typically, the math apps downloads have a proportion of users fairly well distributed among all countries. However, there is always a predominance of the US downloads:

Example graph of a usual app of active users statistics:


(humble numbers related to a calculator)

In my  Google Play page, there is one of the oldest applications that I've done, devoted to linear algebra and the  Gauss-Jordan elimination as a method of solving two equations with two unknowns.

For the application to be a little more attractive, I called it "Adding apples and oranges", referring to an equation are getting really different variables to give a result.


The proportion of current statistics of this application are quite different from other applications. There is a predominance of US downloads:

(humble numbers related to a Apples and oranges app)


While this difference so marked, it makes me think:
It could be that the education authorities of the US had greater knowledge of applied mathematics than education authorities of other countries?

Knowledge of the intellectual basis of the information revolution which we live has influenced the educational guidance of the US?
Or is the result of many parents with deep and old computer knowledge?

What is it that justifies this big difference?

I've searched Common Core related items with the elimination of Gauss-Jordan:
Here are some examples about the related items:

CCSS.MATH.CONTENT.8.EE.C.8 - A, B, C.
CCSS.MATH.CONTENT.HSA.REI.C.6
CCSS.MATH.CONTENT.HSA.REI.D.12


I can not draw a conclusion. Just leave the data in case anyone is able to solve these questions.