Trump, Watergate, Nixon, Rockefeller: the real lesson

Trump, Watergate, Nixon, Rockefeller: the real lesson —Two very different men, two very different presidents, Trump and Nixon; but the real reasons for attacking them are the same— by J…

Source: Trump, Watergate, Nixon, Rockefeller: the real lesson

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What have those godless anti-American libtards done for me anyway?

(Copied from elsewhere; author unknown but reprinted with thanks to whoever it was. Also thanks to my friend Kathryn Wadsworth who put this out on FB!) A DAY IN THE LIFE OF JOE REPUBLICAN AMERICAN …

Source: What have those godless anti-American libtards done for me anyway?

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“Digital”, the new buzword

Now for more exiting and less mathematical stuff.

I don’t know if this is “the way forward” or “just bullshit”, but McKinsey knows (something).

So on with “Digital” in education:

This is the introduction –

Companies today are rushing headlong to become more digital. But what does digital really mean?

For some executives, it’s about technology. For others, digital is a new way of engaging with customers. And for others still, it represents an entirely new way of doing business. None of these definitions is necessarily incorrect. But such diverse perspectives often trip up leadership teams because they reflect a lack of alignment and common vision about where the business needs to go. This often results in piecemeal initiatives or misguided efforts that lead to missed opportunities, sluggish performance, or false starts.

And the rest of it is here

http://www.mckinsey.com/industries/high-tech/our-insights/what-digital-really-means

Have fun. The words are easy.

 

 

 

;

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Matrix inversion, row ops, program added

The row operation matrix inversion method is so neat and ingenious, and it has the same operations for all dimensions of matrix.

Here is a step by step approach, where firstly the dimension is chosen, then the first of the buttons is selected (Start). After which the buttons are selected in order. The states of the left and right matrices are displayed at each stage, and finally the identity matrix appears on the left, and the inverse of the original matrix appears on the right.

http://mathcomesalive.com/mathsite/matrix%20prog%203.html

matrix-inverse-screen-dump-0

The first display shows the original matrix on the left. Nothing has been done yet.

 

matrix-inverse-screen-dump

The second one is the 2 x 2 matrix inverted.

matrix-inverse-screen-dump-2

The third is the 4 x 4 matrix inverted.

The matrices can be altered with the file name for the application, “matrix prog 3.html”. using right click and “view page source”. You are then on your own, with javascript !!!!!!!!

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Matrix inversion made relatively easy

This is the standard way of inverting a matrix. I came across this first in 1960. Oh so long ago! Goodbye Cramer’s Rule.
matrix-inverse-theory

matrix-inverse-theory-p2

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Matrix multiplication without tears!

My dad figured this out years ago.

mult-1-1

The string method work for all matrices, and it is at least ten times quicker to “do” than to “write about”.

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aggravatED: The education consultant-management education consulting firm

Optional, yet optimal…..

A Total Ed Case

Dear Assistant Superintendent MacGuffin:

Thank you for your interest in partnering with aggravatED, the education consultant-management education consulting firm, and for so thoughtfully completing our preliminary readiness screening tool, the Partner, Initiative, & Stakeholder Survey (PISS™).

Our consultant-management consultants looked with great interest at your PISS™, and they concluded definitively that your district would benefit from our innovative, strategic, and accountability-focused guidance.

As you may remember from our informational materials, our initial PISS™ analyses categorize participating schools/districts into four categories describing overall focus and consistency: Laser, Inconsistent, Diffuse, and Without Tangible Focus (WTF).

According to this scale, our initial analysis — which included a study of historic district performance and engagement data — identified your district’s PISS™ as just at the division between ‘Diffuse’ and ‘WTF’. Below are a few noteworthy — and seemingly competing — initiatives/partners that helped us reach these conclusions:

  • Partnership with disruptED, ed-tech firm facilitating district’s…

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Negative numbers, the minus sign, abstract algebra.

I was pondering the reality of negative numbers and after figuring out that a sequence of dots on a line can be extended in each of the two directions, and then arbitrarily selecting one dot as “the zero”. The line can be further labelled as 1, 2, 3, … to one side and -1, -2, -3, … on the other side.
(better to label the 1, 2, 3, … as +1, +2, +3, … and consider the lot as “signed numbers”)

Soon proceeding towards arithmetic I concluded that 7-3 is 4, and also 8-4 is 4, and therefore 13-9 is 4, and then 3-7 is -4, and -2-2 is -4. It was then observed that if a-b=c then a-y-(b-y) is also equal to c, regardless of the signs of the specific numbers involved.
This of course is stunningly obvious when looking at the signed difference of the first and the second number as an extended number line diagram.

The outcome of all this was an arithmetic for 0, 1, 2 modulo 3, and  the signed difference x-y is a binary operation diff(x,y) with table:

…x  … 0     1     2
y
0         0     1     2
1         2      0    1
2         1      2    0

Example: 1-2 is -1, which is 2 modulo 3

So a non abelian, non associative algebra with a not quite identity satisfies the conditions, where A=1, B=2 and C=0
—————————————————–
There are three objects and an operation called “doesn’t have a name”.
Two are similar, and the third is a bit different
They are paired to yield a single object as follows:

AA = BB = CC = C
AB = BC = CA = B
AC = CB = BA = A

Notice that BC and CB are different, so non-abelian.
Worse is that (AC)A = C and A(CA) = B are different, so non-associative.
And consequently A and B and C are different.
—————————————————-

Interestingly, and maybe separately, the minus sign behaves very differently from the plus sign:

a-(-b) is a+b, but there is no way of writing a-b using only addition.

This means that all expressions can be written with “minus” alone.

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Minimal Abstract Algebra

This is a challenge !!!!!

There are three objects, A, B, and C, and an operation called “doesn’t have a name”.
Two are similar, and the third is a bit different
They are paired to yield a single object as follows:

AA = BB = CC = C
AB = BC = CA = B
AC = CB = BA = A

Notice that BC and CB are different, so non-abelian.
Worse is that (AC)A = C and A(CA) = B are different, so non-associative.
And consequently A and B and C are different.

Your job is to identify (model, in current jargon) the objects and the operation.”

The next post will be “the solution”.

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Ed Reform 2.0: If You Can Train a Pigeon to Detonate Bombs…

The video is scary:

Save Maine Schools

Back in 1977, Superintendent James Guines of Washington D.C. explained his district’s competency-based education pilot program like this:

“The basic idea is to break down complicated learning into a sequence of clear simple skills that virtually everyone can master, although at different rates of speed.If you can train a pigeon to fly up there and press a button and set off a bomb, why can’t you teach human beings to behave in an effective and rational way?”

“We know we can modify human behavior. We’re not scared of that,” he added. “This is the biggest thing that’s happening in education today.”

laughing-gif1.gif

HA! Those crazy 70’s! Boy did they have some crazy ideas back then.

But wait…

Now check out this recent video from Angela Duckworth and Katherine Milkman:

Here’s what Milkman has to say:

“If you repeatedly reward good behavior, and pair it with memorable cues, positive routines become…

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