A fragment of an essay on wonder.

With our fangs of taxonomy muzzled with wonder, as the alluring fragrance of mystery provides no substance for their bite to seize, we are drawn toward its promising source. During that earliest stage of our encounter, we dare to look closer, and quietly step forward, slowly becoming aware of a latent form emerging out of the formless, secret garden, as a cloud would gather out of a homogeneous haze, slowly transforming into a barely perceptible,  faintly budding, chimerical sprout – as we step closer, the quivering penumbra of this autogenetic presence remains unstartled, as the zephyr of wonder conceals our scent. Every such step is what we call metaphysics.

Captivated by this animated apparition, as it blossoms into a seductively incandescent form, we pause mid stride, reach out, and grasp it. As the phantasmagorical fog of indeterminacy recedes, we remain transfixed by the now tangible, floral epiphenomenon, quivering weakly on our palm, its vivid fragrance stirring a familiar, sweet melody – of the lullaby we loved so much as children. As the abandoned blossom quietly withers before our eyes, its poignant odor reverberates into the somber motif of a Requiem for metaphysics.

We’ve clumsily drawn on the eternal sands of mystery’s boundless shore the laughable content, and modus operandi of our mind – the sad part lies in the inevitability of that outcome – we carry the stigma of our finitude with us all the time, and before long, its viral character infects any realm of being, totally.

The link between Heisenberg's Uncertainity Principle and the 2-nd Law of Thernodynamics.

I met the New Scientist article which I read this morning with mixed feelings. This is the bitter-sweet taste of being right. I guess this is what intellectualists generally feel when they eventually see their (good) ideas finally vindicated, yet initially thought of by the community of experts (and purported, self-proclaimed experts) to be at best proposterous if not nonsensical.

Below is my idea, with justifications of a physics freshman (at the time I had first year thermodynamics and quantum physics under my belt), and the audacity of a philosopher, which I posted years ago in the Philosophy Forums. Needless to say, as it is clear, my idea was met with scorn to say the least.

My Philosophy Forums entry, from 4th March 2010 (emphasis added):

* * *

Subject: Uncertainity and Entropy 04/03/10

This rumination does not purport to be scientific so I guess it may be free of the objection of pseudoscience. This disclaimer I think is useful in order to appreciate the creative aspect/potential of the idea behind the post and will hopefully make it more digestable to all the physycists cringing at the eclectic application of physical concepts in what follows.

The main idea has the following conceptual chain: uncertainity*knowledge*information*entropy. Hence a connection between Heisenberg's principle (quantum mechanics) and the second law of thermodynamics (classical mechanics).

Some useful quotes from Knight: as for photons - "The fact that waves are spread out makes it meaningless to specify an exact frequency and an exact arrival time simultaneously. This is an inherent feature of weaviness that applies to all waves", for matter particles - "Our knowledge about a particle is inherently uncertain. Why? Because of the wave-like nature of matter. The "particle" is spread out in space, so there simply is not a precise value of its position x. Similarly, the de Broglie relationship between momentum and wavelength implies that we cannot know the momentum of a wave packet any more exactly than we can know its wavelength or frequency".

Now, insofar as knowlwdge is knowledge of something, i.e. information (see Shannon), hence there is, I suggest, a positive correlation between knowledge and entropy.

I conclude that the uncertainity principle is (also) a classical statement about the entropy of a system in which the agent's knowledge (neural firing pattern(?)) is taken to be part of the experimental system. The random nature (conforming to some wavefunction, where position and momentum are random variables) of the "potential observable" within the broader system "potential observable + brain of scientist" would proceed to a lower entropy state if the experimenter yielded more precise information then the uncertainity principle allowes, and thereby violate the second law of thermodynamics.

* * * 

And here is the link to the patronising, stubborn and contemptous replies I received from the pseudo-experts on the forum (I think one of them is even a moderator in the matters of physics).

And below is the New Scientist article which both did and didn't make my day this morning ;)

From the New Scientist 23rd June 2012 (emphasis added):

Stephanie Wehner and Esther Hänggi at the National University of Singapore's Centre for Quantum Technology have taken a new tack, recasting the uncertainty principle in the language of information theory.

First, they suggest that the two properties of a single object that cannot be known simultaneously can be thought of as two streams of information encoded in the same particle. In the same way that you can't know a particle's momentum and location to an arbitrarily high level of accuracy, you also can't completely decode both of these messages. If you figure out how to read message 1 more accurately, then your ability to decrypt message 2 becomes more limited.

Next the pair calculate what happens if they loosen the limits of the uncertainty principle in this scenario, allowing the messages to be better decoded and letting you access information that you wouldn't have had when the uncertainty principle was in force.

Wehner and Hänggi conclude that this is the same as getting more useful energy, or work, out of a system than is put in, which is forbidden by the second law of thermodynamics. That is because both energy and information are needed to extract work from a system.

To understand why, imagine trying to drive a piston using a container full of heated gas. If you don't know in which direction the gas particles are moving, you may angle the piston wrongly and get no useful work out of the system. But if you do know which way they are moving, you will be able to angle the piston so that the moving particles drive it. You will have converted the heat into useful work in the second scenario, even though the same amount of energy is available as in the first scenario.

Being able to decode both of the messages in Wehner and Hänggi's imaginary particle suddenly gives you more information. As demonstrated by the piston, this means you have the potential to do more work. But this extra work comes for free so is the same as creating a perpetual motion machine, which is forbidden by thermodynamics (arxiv.org/abs/1205.6894v1).

"The second law of thermodynamics is something which we see everywhere and basically no one is questioning," says Mario Berta, a theoretical physicist from the Swiss Federal Institute of Technology in Zurich, who was not involved in the work. "Now we know that without an uncertainty principle we could break the second law."

Jessica Giggs "To be quantum is to be uncertain", New Scientist v214 n2870 (online here)

Ironically, being a philosophy major, I identify more with being part of a community which includes peolple like Stephanie and Esther, rather than one that gives authoritarian roles (as moderators on Philosophy Forums) to such pseudo-intellectuals as the ones that have been shown (above) to be resistant to new ideas.

Mad Hatter Paradox.

DEFINITION: Mad as a Hatter  – someone is said to be mad as a hatter iff there exists a mental illness (madness) from which they suffer, and they’re ignorant of its existence.

Now, consider someone asserting “I know that I’m mad as a hatter”. Call it the Mad Hatter sentence, and denote it with MH.

Is MH true or false?

Suppose MH is true. So it’s true that the person uttering it knows that they’re mad as a hatter. But by knowing that they are mad as a hatter they’re aware of the illness they purport to be suffering from, i.e. being mad as a hatter and so by definition fail to satisfy the conditions for being mad as a hatter. Hence MH is false, it seems.

But if they are not mad as a hatter, and assert a knowledge of being such, the person asserting MH is oblivious of that ignorance (them in fact not being mad as a hatter), a delusion of sorts, and hence qualifies them for being mad as a hatter, thus rendering MH true - but we know where that leads.

My independent discovery of the sequence A007526

I came across a rather surprising property of the above recurrence relation which I defined when counting the number of models of conditional logics with Lewis-Stanlaker type semantics, i.e. similarity spheres. Because the structure of nested sphere assignments happens to correspond in its form to permutations of non-empty subsets of some set, the formula, known to combinatorialists since Bernoulli, had emerged.

Below is an example taken from The Encyclopedia of Integer Sequences: sequence A007526 entry.

I say those properties were surprising given the context, for in and of themselves they’re not surprising at all. I simply didn’t expect such interesting properties to be inherent in the structure of the systems I was studying.

The sequence s is related to the number of models, given certain parameters (more precisely, the parameter is the size of the filter which is the set of all subformulae of a formula whose satisfiability is being tested - hence the requirement to generate all and only those models which are sufficient and necessary for that task), and given by the following recursive definition:

And this is the "curious" result, which links the above recursively defined function with Euler's Constant e:

It's easy to show that the explicit solution to the above recursive definition of s is given by the formula:

And considering the well known Taylor series, it's easy to show that the result stated above follows.

It turns out that this is a known sequence A007526., whose earliest references are Izquierdo (1659), Caramuel de Lobkowitz (1670), Prestet (1675) and Bernoulli (1713). So it appears that I've discovered/defined this sequence independently of those great mathematicians.

Combinations, permutation matrices, and a solution to n-valued valuations (truth value assignments for many-valued logics).

This result can be interpreted as a solution to n-valued valuations (truth value assignments for many-valued logics). A detailed proof is given in a later post.

First we define and construct the extensional valuation function , (intuitively, it can be thought of as the generating function for the classical truth table). The valuation function θ will have dimensions (k = 2ⁱ rows by i columns), and the value of each binary entry is given by the following formula, as can easily be checked.

Example θ(7,2), represented on a truth table exhausting all valuations (truth value assignments) for 3 propositional variables (atomic formulae). CORRECTION --- the formula works for the table generated such that zeros come before ones, i.e. with the ones and zeros inverted, so the table below is generated incorrectly for this formula, as we should start with zeros first. (Consequently all the m-valued generalizations should be generated analogously --- starting with the smallest value.)

This map, i.e. θ can be generalized to m-ary truth values. The explicit formula is given below:

I've skipped examples here, naturally since the truth matrices get very large, very quick.

Those explicit solutions to the recursive definitions (truth tables) make computation significantly more efficient. They also turn out to be handy (they're both elegant and compact) when writing algorithms for k combinations on n sets, or k partitions on n sets. They should prove useful to anyone working in writing algorithms for systems based on multiple value assignments.

Proof (sketch) --- a detailed proof is given in a later post.
First we express the truth tables as recurrence relations of congruences modulo the number of truth values in that given logic, then solve them by iteration, i.e. see the pattern. Finally give the solutions an elegant form (ceiling notation) using some useful number theoretic identities. QED

Zen Koan Therapy

A careless monk experienced a fall,
Thus dislocating his fragile soul.

Reflecting on the apparent pain,
He puzzled over the insight that came.

For there was nothing beneath at all,
upon which one may even fall.

Reason then led him to finally state:
"There is no soul to dislocate."




This poem has been published in the New Lotus magazine.

Olympian Spring Song

There is a place one ought to know,

Since reason’s envoy had told me so.

One may rest also firmly assured,

That no virtue’s boundaries here will be blurred.

For I would never dare to reveal,

That which is lacking heart’s precious seal.

The rays of Spring in sunrise borne,

Whilst mending clouds that have been torn,

Decided finally to bring the song,

One which Olympians have known for long.

The world Olympus which bears their name,

Witnesses wonders our minds can't tame,

Among their many abilities,

Olympians utter infinities!

This springtime favorite, Olympian rhyme,
Has been composed to last all time,
Hush little human! and lend an ear,
Is that spring's anthem that you can hear?



Music is currently being written for this piece,