[svlug] This mess is surely a conspiracy, my brain hurts and I don't like complexity or live long and prosper

Karen Shaeffer shaeffer at neuralscape.com
Mon Jan 19 08:04:05 PST 2015


On Sun, Jan 18, 2015 at 04:50:53PM +0000, Karen Shaeffer wrote:
> On Sun, Jan 18, 2015 at 08:21:39AM -0800, Michael Eager wrote:
> > On 01/17/15 21:52, Karen Shaeffer wrote:
> > >On Sat, Jan 17, 2015 at 09:33:43PM -0800, Michael Eager wrote:
> > >>On 01/17/15 20:53, Karen Shaeffer wrote:
> > >>>On Sat, Jan 17, 2015 at 04:27:48PM -0800, Michael Eager wrote:
> > >>>>On 01/01/15 17:31, Karen Shaeffer wrote:
> > >>>>>Indeed, but Albert Einstein said keep it simple. Paraphrasing, Einstein
> > >>>>>said: Never construct a theory that is more complex than it needs to be.
> > >>>>>If you have two theories, and one is more complex than the other, while
> > >>>>>both fully account for all observed data, then always pick the simplest
> > >>>>>of the two.
> > >>>>
> > >>>>William of Ockham?
> > >>>
> > >>>Hi Michael,
> > >>>Certainly an interesting guy. But I am personally a big fan of AE. He had a
> > >>>lot of character flaws -- so he was human... If only AE had lived during our
> > >>>time, he would have had a lot of fun with his very own linux cluster. AE is
> > >>>an amazing human being in my opinion. He didn't have any computers. All he
> > >>>had was paper, pencil, and his imagination.
> > >>
> > >>Einstein was interesting and 1905 was an excellent year.  But he didn't
> > >>say what you attribute to him.
> > >>
> > >>Occam's Razor predates Einstein by some 500 years.
> > >>
> > >
> > >Hi Michael,
> > >Fair enough. I'm not suggesting AE was the first to make the observation.
> > >It's actually an intuitive notion that generalizes to all of life. And
> > >so, I doubt William of Ockham was the first to contemplate the notion
> > >either. But he does get credit for it in Wikipedia. (chuckles ;)
> > >
> > >Albert Einstein made the comment exactly as I stated it, in the context
> > >of developing theories and hypotheses. I don't think he cited Ockham
> > >either... I am certain he didn't consider his statement to be novel. He
> > >simply was stating the obvious.
> > 
> > Where did he make this statement, which was exactly as you stated?
> > Do you have a citation for this?
> > 
> > 
> > I'm pretty sure that Eistein was acquainted with Occam's Razor, even
> > if you aren't.  It appears that education was more comprehensive a
> > century ago.
> >
> 
> Hi Michael,
> I don't need a citation. Albert Einstein was famously known for advocating
> the concept of "Keep it Simple". If you aren't aware of this, then I suggest
> you go study physics.
> 
> I've been aware of Occam's razor since high school. Since you seem to want to
> make a big deal about it, lets put William Ockham and his razor in its proper
> perspective.
> 
> The notion of Occam's razor is obvious common knowledge to anyone who has
> a rudimentary understanding of rational numbers, or real numbers, or complex
> numbers, because it is an explicit property of those sets over the binary
> operation of addition. And so, no one need cite Occam's razor in relation
> to the notion -- it is common knowledge embedded within the vernacular of
> basic algebra.
> 
> Here's a citation from the book, "Fundamental Concepts of Abstract Algebra",
> “Based on Hindu and Greek sources, Mohammed ibn Mûsâ al-Khowârizmî of Baghdad,
> in 825 A.D., wrote a textbook called Al-jebr, which, following its translation
> during the twelfth century, was to have considerable influence on the subsequent
> development of algebra in Europe.”
> 
> Here's another citation from http://science.jrank.org/pages/5743/Rational-Number.html
> "More than 4,000 years ago the Babylonians coped with the need for numbers that would
> measure fractional or continuously variable quantities. They did this by extending
> their system for representing natural numbers, which was already in place."
> 
> And so it should be obvious that the concept of Occam's razor was well known and
> firmly established in the number systems used during the time of William Ockham's
> life. Occam's razor was of no mathematical or scientific significance at the time
> William Ockham published it. What he did was generalize the well known mathematical
> property into layman's terms, enabling common folks to appreciate it. And this
> was rightfully perceived as a direct threat to the dogmatic structure of the religious
> views of the day. And so it became controversial in that context. Nothing more and
> nothing less.

At the time of William Ockham's life, one of the perplexing issues in mathematics
was dealing with infinity and more generally limits. These issues were finally
resolved mathematically by Newton and Leibniz in the 17th century.[1,2] In the
centuries preceding Newton and Leibniz, the notion of infinity was an unresolved
problem in mathematics that was generally defined as being associated with evil
or God by different cultures at different times.[3]

In Europe, infinity was being associated with God by the time of William Ockham's
life.[3] And this mathematical problem, in conjunction with it's entertwined
dependencies with cultural perceptions relating to God, inspired William Ockham
to form and opine his own conclusions. The problem is simple to fully appreciate
with rational numbers. Define a recursive sequence:

                   A(n) = A(n - 1) + A(n - 1) * (1/10), with A(0) = 9/10

Thus the infinite sequence is 0.9, 0.99, 0.999, ... I'm using the limit of 1
in this example, but it is trivial to define a sequence where the limit is
infinity. This example is more easily appreciated. Everyone knows what 1 is.
The question is at what point does the sequence equal 1? In practice, it
never quite gets to 1. But, using the concepts of limits, as n approaches
infinity, A(n) approaches 1. In Ockham's day, infinity was associated with God.
And a more direct example would be to define a recursive sequence:

                  A(n) = A(n - 1) * 10, where A(0) = 1

Thus the infinite sequence is 1, 10, 100, 1000, 10000, 100000, ... And the limit
is infinity -- a property associated with God in Ockham's day.[3] But how many
times do you need to multiply the value by 10 to reach infinity?

>From what I can glean from the web, Ockham stated, "Entities should not be
multiplied unnecessarily." And he applied this mathematical notion to conclude,
"God's existence cannot be deduced by reason alone."[4] Here the reason was that
multiplying digits in an infinite sequence is pointless and cannot rationally
be defined in a deterministic process. And he analogously concluded "God's
existence cannot be deduced by reason alone."[4]

Occam's razor came much later. The "Principle of Plurality" and the "Principle of
Parsimony" were attributed to the notion of Occam's razor.[5] And this was all
attributed to William Ockham, even though the Greek philosopher Aristotle first
formalized these ideas.[5,6]

And it was the work of Albert Einstein, where he famously advocated the concept
of "Keep it Simple" throughout his life that catapulted Occam's razor to its
current form and notoriety.[4] But Albert Einstein never attributed his
advocacy of "Keep it Simple" to Occam's razor nor William Ockham.[4,7] I
believe the reason he didn't is because it is intuitively obvious. And, when
you look at how Occam's razor evolved, it is a derivative of many contributions
from many different folks over the ages, where contemporary interpretations
wrongfully attribute it all to William Ockman and Occam's razor. In
contemporary writing, they use Einstein's Theory of Relativity as a concrete
example of the application of Occam's razor.[4,5] But be aware, this conclusion
is the contemporary interpretation of the author of the web page.[4,5] It was
not in any way concretely associated with the work by Albert Einstein himself.
I beleive Albert Einstein never once attributed his thinking on "Keep it Simple"
to Occam's razor. I do not believe anyone can produce any statement by Albert
Einstein, where he attributes his thoughts on the concept of "Keep it Simple"
to William Ockham. And the same can be said of many other great scientists
such as Ernst Mach[5], Leibniz[4], Newton[4], and Heisenburg[4] as examples.
I do not believe any of them recognized nor cited Occam's razor in their
work. It's not necessary.

That's my point of view on this matter.

[1] http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html
[2] http://www.uiowa.edu/~c22m025c/history.html
[3] http://www.math.tamu.edu/~dallen/history/infinity.pdf
[4] http://math.ucr.edu/home/baez/physics/General/occam.html
[5] http://science.howstuffworks.com/innovation/scientific-experiments/occams-razor.htm
[6] http://en.wikipedia.org/wiki/Occam's_razor
[7] My own knowledge of Albert Einstein's work

enjoy,
Karen
-- 
Karen Shaeffer                 Be aware: If you see an obstacle in your path,
Neuralscape Services           that obstacle is your path.        Zen proverb



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