Education must hold on to learning-as-adventure or it goes stale.
Here’s a real example:
A man goes to his American Heritage Dictionary, to look up the word “vinaigrette” which he seems to remember as a salad dressing but finds there are as so often happens, other meanings.
You also wonder about the nature of alkaloids and whether there are some evolutionary reasons why some plants produce food, some poisons (poison ivy, say), and others “good poisons” (i.e., alkaloids that can be made therapeutic through pharmacology).
Percy Lavon Julian (April 11, 1899 – April 19, 1975) was a research chemist and a pioneer in the chemical synthesis of medicinal drugs from plants. He later started his own company to synthesize steroid intermediates from the wild Mexican yam. Julian received more than 130 chemical patents.
You can be dismissive and dismiss this “spontaneous questing” as a kind of woolgathering or “lolling about” mentally but the truth is often the opposite: it is only such “productive daydreams” that allow you to penetrate fields and topics and questions and problems by finding a “surprise window” or “backdoor” into them. Serendipity is very related to education, which has both formal or “do your homework” components to it and also a “wander about” one when you’re quite relaxed and mentally receptive.
The holy grail for reducing this digital demand is to develop microelectronics that operate at much lower voltages, which would require less energy and is a primary goal of efforts to move beyond today’s state-of-the-art CMOS (complementary metal–oxidesemiconductor) devices.
Non-silicon materials with enticing properties for memory and logic devices exist; but their common bulk form still requires large voltages to manipulate, making them incompatible with modern electronics. Designing thin-film alternatives that not only perform well at low operating voltages but can also be packed into microelectronic devices remains a challenge.
Now, a team of researchers at Lawrence Berkeley National Laboratory (Berkeley Lab) and UC Berkeley have identified one energy-efficient route—by synthesizing a thin-layer version of a well-known material whose properties are exactly what’s needed for next-generation devices.
Crystals of the material respond quickly to a small electric field, flip-flopping the orientation of the charged atoms that make up the material in a reversible but permanent manner even if the applied field is removed. This provides a way to switch between the proverbial “0” and “1” states in logic and memory storage devices—but still requires voltages larger than 1,000 millivolts (mV) for doing so.
Seeking to harness these properties for use in microchips, the Berkeley Lab-led team developed a pathway for creating films of BaTiO3 just 25 nanometers thin—less than a thousandth of a human hair’s width—whose orientation of charged atoms, or polarization, switches as quickly and efficiently as in the bulk version.
“We’ve known about BaTiO3 for the better part of a century and we’ve known how to make thin films of this material for over 40 years. But until now, nobody could make a film that could get close to the structure or performance that could be achieved in bulk,” said Lane Martin, a faculty scientist in the Materials Sciences Division (MSD) at Berkeley Lab and professor of materials science and engineering at UC Berkeley who led the work.
Historically, synthesis attempts have resulted in films that contain higher concentrations of “defects”—points where the structure differs from an idealized version of the material—as compared to bulk versions. Such a high concentration of defects negatively impacts the performance of thin films. Martin and colleagues developed an approach to growing the films that limits those defects. The findings were published in the journal Nature Materials.
To understand what it takes to produce the best, low-defect BaTiO3 thin films, the researchers turned to a process called pulsed-laser deposition. Firing a powerful beam of an ultravioletlaser light onto a ceramic target of BaTiO3 causes the material to transform into a plasma, which then transmits atoms from the target onto a surface to grow the film. “It’s a versatile tool where we can tweak a lot of knobs in the film’s growth and see which are most important for controlling the properties,” said Martin.
Martin and his colleagues showed that their method could achieve precise control over the deposited film’s structure, chemistry, thickness, and interfaces with metal electrodes. By chopping each deposited sample in half and looking at its structure atom by atom using tools at the National Center for Electron Microscopy at Berkeley Lab’s Molecular Foundry, the researchers revealed a version that precisely mimicked an extremely thin slice of the bulk.
“It’s fun to think that we can take these classic materials that we thought we knew everything about, and flip them on their head with new approaches to making and characterizing them,” said Martin.
Finally, by placing a film of BaTiO3 in between two metal layers, Martin and his team created tiny capacitors—the electronic components that rapidly store and release energy in a circuit. Applying voltages of 100 mV or less and measuring the current that emerges showed that the film’s polarization switched within two billionths of a second and could potentially be faster—competitive with what it takes for today’s computers to access memory or perform calculations.
The work follows the bigger goal of creating materials with small switching voltages, and examining how interfaces with the metal components necessary for devices impact such materials. “This is a good early victory in our pursuit of low-power electronics that go beyond what is possible with silicon-based electronics today,” said Martin.
“Unlike our new devices, the capacitors used in chips today don’t hold their data unless you keep applying a voltage,” said Martin. And current technologies generally work at 500 to 600 mV, while a thin film version could work at 50 to 100 mV or less. Together, these measurements demonstrate a successful optimization of voltage and polarization robustness—which tend to be a trade-off, especially in thin materials.
Next, the team plans to shrink the material down even thinner to make it compatible with real devices in computers and study how it behaves at those tiny dimensions. At the same time, they will work with collaborators at companies such as Intel Corp. to test the feasibility in first-generation electronic devices. “If you could make each logic operation in a computer a million times more efficient, think how much energy you save. That’s why we’re doing this,” said Martin.
You’re then told that’s a no-no and that’s because zeros and infinities lead to all kinds of arithmetic “bad behavior” or singularities.
You’re then supposed to see that x2 – 1 can be re-written as (x – 1)(x + 1) and since “like cancels like,” you cancel the x – 1 is the numerator and denominator and “get rid” of it.
This leaves simply x + 1. So, as x goes to 1, x + 1 goes to 2 and you have a “legitimate” answer and have bypassed the impasse of 0 acting badly (i.e., zero divided by zero).
If you re-understand all this more slowly you’ll see that there are endless potential confusions:
For example: you cannot say that (x2 – 1)/(x – 1) = x + 1 since looking at the two sides of the equal sign shows different expressions which are not equal.
Math and science for that matter, are based on taking a formula or expression (like the one we saw above) and “de-cluttering” it or “shaking loose” a variant form which is not identical and not the same but functionally equivalent in a restricted way.
A lot of students who fail to follow high school or collegescience sense these and other “language and number” problems of hidden vagueness. School courses punish students who “muse” to themselves about hidden vagueness. This behavior is pre-defined as “bad woolgathering” but we turn this upside down and claim it is potentially “good woolgathering” and might lead to enchantment which then underlies progress in getting past one’s fear of something like math or science or anything else.
Think of daily life: you say to someone: “you can count one me.” You mean trust, rely on, depend on, where count on is a “set phrase.” (The origin of the phrase and how it became a set phrase is probably unknowable and lost in the mists of time.)
“You can count on me” does not mean you can stand on me and then count something…one, two, three.
In other words in all kinds of language (English, say, or math as a language) one is constantly “skating over” such logic-and-nuance-and-meaning issues.
The genius Kurt Gödel (Einstein’s walk around buddy at Princeton) saw this in a deep way and said that it’s deeply surprising that languages work at all (spoken, written or mathematical) since the bilateral sharing of these ambiguities would seem deadly to any clarity at all and communication itself would seem a rather unlikely outcome.
We started this book with a quote from Wittgenstein “Light dawns gradually over the whole” and argued that the meaning of the “whole” is and will be elusive forever.
That is as it should be:
Think of the final pages of John Dewey’s classic book, The Quest for Certainty. You’ll sense how Dewey oscillates between the “pin-down-ability” of the “whole” and its eternal slipperiness:
“Diversification of discoveries and the opening up of new points of view and new methods are inherent in the progress of knowledge. This fact defeats the idea of any complete synthesis of knowledge upon an intellectual basis. The sheer increase of specialized knowledge will never work the miracle of producing an intellectual whole. The astronomer, biologist, chemist, may attain systematic wholes, at least for a time, within his whole field.
“Man has never had such a varied body of knowledge in his possession before, and probably never before has he been so uncertain and so perplexed as to what his knowledge means, what it points to in action and in consequences.”
Wholeness, Dewey senses, like the white whale in Moby-Dick, “won’t sit for a portrait.” That is why the student should take an eternally “non-rigid” answer to these questions which are “arguments without end” and that’s fine.
We sometimes use the phrase “epochal waters” to refer to the deepest layers of the past which we “swimmers” at the surface of the ocean don’t see or know. “Epochal waters” are latent, currents are closer to the surface.
“In essence, Les mots et les choses (Foucault’s The Order of Things) maintains that every period is characterized by an underground configuration that delineates its culture, a grid of knowledge making possible every scientific discourse, every production of statements. Foucault designates this historical a priori as an episteme, deeply basic to defining and limiting what any period can—or cannot—think.
Each science develops within the framework of an episteme, and therefore is linked in part with other sciences contemporary with it.
(Didier Eribon, Michel Foucault, Harvard University Press, 1991, page 158)
Take a simple example. A discussion comes up about what man is or does or thinks or knows. In today’s episteme or pre-definition, one thinks immediately not of man in terms of language or the invention of gods, but in terms of computational genomics, big data, bipedalism (walking upright on two legs). Its assumed in advance via an invisible episteme, that science and technology. physics, genetics, big data, chemistry and biology hold the answer and the rest is sort of outdated. This feeling is automatic and reflexive like breathing and might be called “mental breathing.”
One’s thoughts are immediately sent in certain directions or grooves, a process that is automatic and more like a “mental reflex” than a freely chosen “analytical frame.” The thinker has been “trained” in advance and the episteme pre-decides what is thinkable and what is not.
There are deep episteme that underlie all analyses: for example, in the Anglo-American tradition of looking at things, the phrase “human nature” inevitably comes in as a deus ex machina (i.e., sudden way of clinching an argument, the “magic factor” that has been there all along). If you ask why are you suddenly “importing” the concept of “human nature,” the person who uses the phrase has no idea. It’s in the “epochal water” or Foucault’s episteme, and it suddenly swims up from below at the sea floor.
Another quick example: In the Anglo-American mind, there’s a belief from “way down and far away” that failure in life is mostly about individual behavior (laziness, alcoholism, etc.) and personal “stances” while “circum-stances” are an excuse. This way of sequencing acceptable explanations is deeply pre-established in a way that is itself hard to explain. It serves to “frame the picture” in advance. These are all “epochal water“ or episteme phenomena.
