21 APR 2014 by ideonexus
Five Strands of Mathematical Literacy
Recognizing that no term captures completely all aspects of expertise, competence,
knowledge, and facility in mathematics, we have chosen mathematical proficiency to capture what we think it means for anyone to learn mathematicssuccessfully. Mathematical proficiency, as we see it, has five strands:
• conceptual understanding—comprehension of mathematical concepts, operations, and relations
• procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and a...Folksonomies: education mathematics
Folksonomies: education mathematics
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notes
notesCognitive tools.
30 JUN 2013 by ideonexus
Our Collective Memory
Taken globally, the set of traces that we leave in the world does without doubt add up to something. It is through operations on sets of traces that I understand an event that I take part in. Tolstoy wrote about the foot soldier in the Napoleonic wars. The soldier he describes cannot have the experience of the war he is waging nor the battle he is fighting because the only “global” traces of the war are inscriptions—notably, maps and statistics. There is no scalable observation that mov... 1 notes
notesNo one soldier experiences a War. They experience details from their microcosm encounter with the war. The war itself is a collective memory experienced only in history books.
11 JUN 2012 by ideonexus
The Brain's the Thing
I consider the differences between man and animals in propensities, feelings, and intellectual faculties, to be the result of the same cause as that which we assign for the variations in other functions, viz. difference of organization; and that the superiority of man in rational endowments is not greater than the more exquisite, complicated, and perfectly developed structure of his brain, and particularly of his ample cerebral hemispheres, to which the rest of the animal kingdom offers no pa... 1 notes
notesThat contains all our operations and distinguishes us from the other animals.
08 JUN 2012 by ideonexus
The Problem with Paradigms
The success of the paradigm... is at the start largely a promise of success ... Normal science consists in the actualization of that promise... Mopping up operations are what engage most scientists throughout their careers. They constitute what I am here calling normal science... That enterprise seems an attempt to force nature into the preformed and relatively inflexible box that the paradigm supplies. No part of the aim of normal science is to call forth new sorts of phenomena; indeed those... 1 notes
notesIs that scientists tend to try and keep nature in the box, ignoring phenomena that fall outside the paradigm.
29 MAY 2012 by ideonexus
Nature Uses the Same Materials and Forms in Life
We know that nature invariably uses the same materials in its operations. Its ingeniousness is displayed only in the variation of form. Indeed, as if nature had voluntarily confined itself to using only a few basic units, we observe that it generally causes the same elements to reappear, in the same number, in the same circumstances, and in the same relationships to one another. If an organ happens to grow in an unusual manner, it exerts a considerable influence on adjacent parts, which as a ... 1 notes
notesA brilliant early observation, crucial to understanding evolution.
30 AUG 2011 by ideonexus
Reduce Phenomena to the Proximate Causes and Primitive Fo...
I think that considerable progress can be made in the analysis of the operations of nature by the scholar who reduces rather complicated phenomena to their proximate causes and primitive forces, even though the causes of those causes have not yet been detected. 1 notes
notesSounds a little like Occam's Razor, with an additional acceptance of some uncertainty.
03 JAN 2011 by ideonexus
The Chance of Error in Atomic Sized Computers
The first thing that you would worry about when things get very small is Brownian motion--everything is shaking about and nothing stays in place. How can you control the circuits then? Furthermore, if a circuit does work, doesn't it now have a chance of accidentally jumping back? If we use two volts for the energy of this electric system, which is what we ordinarily use, that is eighty times the thermal energy at room temperature (kT=1/40 volt) and the chance that something jumps backward aga... 1 notes
notesAs things get very small we have to worry about brownian motion and quantum effects on the system.
01 JAN 2010 by ideonexus
How the Analytical Engine Goes Beyond Mathematics
Again, it [the Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine . . . Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adapt... 1 notes
notesDistinguished from the Difference Engine, Ada Lovelace describes how the Analytical Engine could produce logical outputs, not just the results of mathematical equations.
