@johnrobb We have abandoned competence,
in the futile search for universal expertise.

"What?" I hear you say.
Clearly definitions and explanations are in order.

1/
@johnrobb Expertise, certainly as regards this discussion,
but perhaps also universally, should be regarded
as the knowledge of a very great deal - about very
very little.

2/
@johnrobb To become an expert in a field requires
years - nay, decades - of diligent study of that
solitary field. In diving deeper, the pool in turn
becomes ever smaller: a diving pool rather than a
swimming pool. Nothing is free.

3/
@johnrobb The effort expended
in learning one discipline, ever better, is time spent
NOT learning about the World in general.

But expertise - knowledge for its own sake - is rarely
the answer to any problem; and certainly not in Real
Life.

4/
@johnrobb All decisions are inevitably trade-offs. Losses
here must be weighed, as honestly and openly as possible,
against gains in the other. Hard choices must be made.
The making of such choices requires judgement; and the
possession of judgment is competence; not expertise.

5/
@johnrobb To be competent is to comprehend the arguments of
competing experts, in varied fields; to assess and
weight the testimony of those experts; to place those
arguments on the balance of public good;

6/
@johnrobb and finally,
to make a decision as well informed and argued as
possible with never enough data.

and finally,
to make a decision as well informed and argued as
possible with never enough data.

7/
@johnrobb Competent individuals are 1 above. More than
that, they accept responsibility for their decisions.
They don't hide behind the blinkered recommendations
of experts in any one field - the balancing, and the
decision, was made by them and they accept the
accompanying responsibility.
@johnrobb So the next time a politician, or manager, proudly
exclaims:
"The experts said such-and-such." - know
this:
that claim is no more than an idler's boast of incompetence;
and of possessing the power to make YOU pay for it.

end/

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More from @pgeerkens

15 Jan
@GWOMaths One might say that physicists study the symmetry of nature, while mathematicians study the nature of symmetry.

1/
@GWOMaths Observing symmetry in nature, such as noting the similarity between the symmetries of a snowflake and a hexagon, is readily comprehensible. What does it mean then to study "the nature of symmetry"?

2/
@GWOMaths Mathematicians define a "group", G, as a set of elements {a,b,c, ...} with a binary operation ⊡ and a distinguished element e (the identity of G) satisfying these specific properties:

3/
Read 14 tweets
2 Dec 20
@pnjaban None of the above:
Field-trained former military paramedic.

I don't want anyone not trained specifically in emergency medicine anywhere near; and none of those civilian trained E.R. either, cause they're trained in CYA first, and I want someone who's serious about saving my life
@pnjaban When my Dad suffered acute hemechromatosis at ~34,
for which the ONLY treatment is *bleeding*,
and the only options "a whole lot" and "a whole lot more",
the attending physician was too embarrassed to prescribe the correct treatment.
@pnjaban The nurse (Irish of course, because they understand hemechromatosis) told me Mom:

Mrs. Geerkens:
Your husband will die tonight
unless we remove him from this hospital immediately.
I'll help.

The nurse lost her job;
but my Dad lived another 45 years.
Read 4 tweets
2 Dec 20
From Albert H. Beiler's
Recreations in the Theory of Numbers:

Calculate in your head:
47² = ?
96² = ?
113² = ?
179² = ?

goodreads.com/book/show/5855…
47² = (47 + 3) ⋅ (47 - 3) + 3² = 50 ⋅ 44 + 9 = 2209

96² = (96+4) ⋅ (96-4) + 4² = 100 ⋅ 92 + 16 = 9216

113² = (113+3) ⋅ (113-3) + 3² = 116⋅110 + 9
= 12760 + 9 = 12,769

179² = (179+21) ⋅ (179-21) + 21²
= 200 ⋅ 158 + (20² + 20 + 21)
= 31600 + 441 = 32041
The trick is from noting that from difference of squares
a² - b² = (a + b) ⋅ (a - b)
one can obtain by rearrangement
a² = (a + b) ⋅ (a - b) + b².
Read 4 tweets
22 Nov 20
@GWOMaths Hint follows
@GWOMaths Rochambeau is just a fancy name for Rock-Paper-Scissors.
@GWOMaths If you're having difficulty visualizing this,
consider the situation after Game 1 as the baseline.
Read 12 tweets
6 Nov 20
@LarrySchweikart My take:
SCOTUS must not be seen to play favourites - yet has an obligation to ensure that corruption is voided.

So wherever widespread and continuous failure to observe due process (as per State law) is seen, void all ballots from that county / counting centre.

1/
@LarrySchweikart If the number of voided counties exceeds more than 1 or 2, then void the entire election for the State.

In the case of House and Senate representatives, require special elections.

2/
@LarrySchweikart For Presidential Electors, legislation now in effect gives the State legislature responsibility and authority to select the State's slate of Electors - as per the original Constitutional design.

3/
Read 9 tweets
20 Mar 20
@GWOMaths Define
y ≡ x - 16
to allow factoring the term 2¹⁶ completely.

Then 2¹⁶ + 2¹⁹ + 2ˣ
= 2¹⁶ + 2¹⁹ + 2ʸ⁺¹⁶
= 2¹⁶ . (1 + 2³ + 2ʸ)
= 2¹⁶ . (9 + 2ʸ)

Now a solution, viz y=4, is readily obvious as yielding
= 2¹⁶ . (9+16)
= 2¹⁶ . 25
= (2⁸ . 5)²

∴ x = y + 16 = 20.
@GWOMaths However - is our solution unique?

Suppose
∃ a ∈ Z
such that
9 + 2ʸ ≡ a²

Then
2ʸ = a² - 9 = (a-3) . (a+3)
and both (a-3) and (a+3) must be powers of 2.

This only occurs for
a = 5 => 2ʸ = 16 => y = 4 => x = 20.

Our solution is unique.
@GWOMaths Finally - as a fun calculating observation,for those who have memorized powers of two at least to 2¹⁶:

(2⁸ . 5)²
= (2⁷ . 2 . 5)²
= (2⁷ . 10)²
= (128 . 10)²
= 1280²

= 2¹⁶ . 25
= 2¹⁴ . 4 . 25
= 2¹⁴ . 100
= 16,384 . 100
= 1,638,400.
Read 5 tweets

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