Saturday, July 26, 2008

Is there a plausible basis for faster-than-light travel? (III)

In this last part, I consider possible shortcuts in a "multiverse". One of the more controversial scenarios for superluminal travel entails a different sort of universe than the one we tend to think of. Most commonly it has been popularized by David Deutsch as the ‘multiverse’ in his book, The Fabric of Reality . However, there are a number of variants of this. One hyper-dimensional form is based on a hyper-toroid such as depicted in the top figure.

Each longitude circle is a quotient space q1 and each latitude circle is a quotient space q2. More exactly, q2 denotes the fifth dimensional connector that links multiple parallel universes. Each of these can be represented by one single longitudinal loop marking off a coordinate on q1 (e.g. Θ). Since time can be broken down in fundamental units of tau (τ) then each q1 is separated by its neighbor universe by one tau. This neighbor is impossible to access from within the fixed coordinate quotient space (q1) but can be accessed if one can find a way to get to q2 and traverse it. Thus, in simplest terms, each “slice” q1 can be regarded as an alternate or parallel universe.

More explicitly, one may adopt absolute toroidal (Θ,φ) coordinates to locate events in the multiverse system. There are a number of fascinating aspects of this model. First, the toroidal hypersphere implies an endlessly repeating universe that is the same in each new cycle - instead of being different (i.e. with different physical constant as the reprocessed model demands). The key to this aspect is the fact that the radius R remains constant.

A second intriguing aspect is that the exact same point of space-time occurs for each "beginning" (Big Bang) and "end" ("Big Crunch"). This point is easily identified in the diagram as the most constricted part of the interior "hour-glass" shape defining the inner wall of the torus-hypersphere.

Third, the overall configuration is exactly the same as that defined for the high-energy "twistors" used in the 1980's by Roger Penrose and his colleagues at Oxford. The twistors are discrete points of space, each defined by 4 real numbers and 4 imaginary numbers. Without getting bogged down in the mathematics, I find it more than coincidental that the shape of the hypersphere model cosmos and the high-energy twistor are the same. Could it be that this relationship is holographic? That is, each twistor of space-time is the miniaturized "image" of the whole hypersphere?

If so, then a torsion acting in a localized space-time of the hypersphere could serve to twist it, permitting a shortcut. Under what conditions might such a torsion arise? One would require fiber bundles, which then have capacity for expansion to a sub-space large enough to provide a folded-space corridor. (A 'Klein bottle' is an example of a fiber bundle see, e.g.

The important geometric concept here, discerned from the situation shown, is that two distinct parallel universes (recall these are given by different longitudinal coordinates, Θ) are linked by the bundle’s vortex. Thus, such a linkage between parallel universes (within the defined multi-verse) is equivalent to an enormous short cut for the craft that seeks to exploit it.

What would the conditions have to be for linkage? Let the two parallel universes be distinguished by a 1-τ difference in fundamental time parameter, viz. [1 + 2τ] and [1 + 3τ], then we would require for connection, a mapping such that:

f:X -> X = f(Θ,φ) = (Θ, 2φ)
f:X -> X = f(Θ,φ) = (Θ, 3φ)

which means the absolute coordinate φ is mapped onto itself 2 times for [Universe A] and mapped onto itself 3 times for [Universe B]. Clearly, there’ll be coincidences for which: f(Θ,2φ) = f(Θ,3φ) wherein the two universes will 'interweave' a number of times. For example, such interweaving will occur when φ = π/2 in [A] and φ = π/3 in [B]. The total set or system of multiple points obtained in this way is called a Synchronicity Matrix. The distinguishing feature of this matrix is that once a single point is encountered, it is probable that others will as well. If one hyperspace transformation can occur linking parallel universes, A and B, then conceivably more such transformations can occur, linking A and C, D and E, or (exhausting the Latin alphabet), X1 and X oo(_1)

What if both absolute toroidal coordinates (Θ,φ) map into themselves the same number of times? Say, something like:

f:X -> = f(Θ, φ) = (2Θ, 2φ): Universe A
f:X -> = f(Θ, φ) = (3Θ, 3φ): Universe B

For example, given the previous conditions for coordinate φ, now let 2Θ = 3Θ for discrete values of Θ (e.g. 2π). For all multiples of 2π, the same toroidal cosmos will be experienced - if the absolute time coordinates are equal (e.g. π/2 = φ in A, and π/3 = φ in B) then we will have: Universe A = Universe B. The exact same physical state-space prevails in both A and B. For all intents and purposes there is no difference between them. In this case, we say that there exists an interpenetration of different parallel universes. Note that though the physical state spaces (e.g. with constants h, G, e/m, etc.)may be alike, they can still differ in dimensionality. And we cannot disregard fractal dimensionality.

If this is so, then it may account for a frequently cited phenomenon connected to many UFO observations, that of seemingly ‘instant’ appearance and disappearance. To fix ideas, assume you are a denizen of a two-dimensional world, confined to the plane of that world. How would you be aware of contact with a hyper-dimensional entity? Imagine a 3-D ellipsoidal disk (like a UFO) as an example, which is 'hyperdimensional' compared to a 2-D plane (like a sheet of paper). To enable detection, the disk must progressively intersect the plane. The observer sees a mystifying object suddenly grow to vast size, then contract and finally disappear! (See the diagram below - where the horizontal line is a 1D infinite object, intersected by an elliptical 2D object, which might be the 'cross-section' of the UFO).

( U F O )

--------( U F O )--------B

( U F O)

In the changing situation or transition from A to B to C, the interpenetration is such that the dimensions of the intruder appear to contract or shrink. But this is only a consequence of its departure from our own (linear, in this case) dimensionality. Say, in transit to a parallel universe with (slightly) different dimensionality. This is precisely analogous to the case of UFOs regularly observed to 'shrink' or contract.

A similar manifestation is called ‘skipping’. The UFO appears to be at one location, say over a building, and in the next instant far displaced, without having traversed the intervening distance! It appears to have simply jumped or 'skipped' the space from A to B! This sort of quantized travel is another example of hyperdimensional passage, since no normal macroscopic object exhibits quantum jumps in transport. In our (‘Universe A’) frame of reference, all discrete objects must transit from point X say to point Y. However, if our ‘Universe A’ is really interpenetrated by an adjoint ‘Universe B’ of slightly different dimension, then non-local jumps are possible. In fact, it’s not really a ‘jump’ per se, merely the craft or object exploiting the inherent geometric features of two parallel universes that are intermeshed. This can also account for the apparent FTL displacements observed.

Brane space folding:

What if space is not itself structured for shortcuts, or folding? Might it be feasible for a device to be designed that can change the structure of space and facilitate FTL transport? This is, incidentally, of a totally distinct nature from Alcubierre’s warp drive (Section 1). While the warp drive mechanism produced local effects in the form of a wake in space-time, D-brane craft would generate non-local effects to enable it to instantly connect to a distant region of space.

Branes are surface representations of strings, and include p-, and D-branes. The latter are most useful for our purposes since they comprise a five dimensional hyper-surface in which propagates in time t, thus sweeping out a six dimensional space-time.

How to apply to a transport device? I suggest here that an internal brane is manipulated so that its physical parameters comport to those of a distant region of space. (Given the fact that branes are manifestations of charges, fields, etc.).

The principle at work is so profoundly radical that it requires further explication. We are not talking so much of a “propulsion” system as a resonance mechanism capable of instantaneously connecting distant regions. Thus, the ‘craft’ depicted uses no “fuel” as such but rather a form of local engineering on a distinct and malleable mem-brane that alters its (electrical, magnetic, etc.) properties to adjust to some brane-space, X(B). When a suitable adjustment is made between two branes (one for UFO, the other for a distant target) an instantaneous linkage is forged as a brane-hole expands and detaches in the distant space – emerging as the UFO. Let’s look at it in stages, from the diagram of Fig. 2 (above).

At the far left we see the craft’s internal brane, labeled ‘B’ in the previous diagram. This D-brane must be manipulated so that it’s ambient physical properties (charge q, B-, E-field strengths, polarizations, etc.) are altered to mimic those of the distant ‘target’ space. As the manipulation proceeds, the D-brane fluctuates and its manifolds separate as depicted in the center frame. The arc deforming from the brane’s top edge represents tachyon’s localizing. These are hypothetical faster-than-light particles, not yet observed but with a mathematical basis. The closed oval (actually called a “hole”) near the top of the fluctuating D-Brane manifolds is the crude ‘mirror’ image of the craft. It may be thought of roughly as its “echo” in imaginary time. In the last phase of the sequence (far right) the “hole” detaches entirely from the embedding brane-space and the craft re-materializes. Now, many light years from where it originally had been located.

Underpinning the above portrayal are several key principles:

i)D-branes, by definition, are dynamical objects that can fluctuate. This means they are perfectly adapted for manipulation – given the necessary energy requirements- of UFOs.

ii)The dynamical aspect is a result of the ability of D-branes to couple to closed strings. Recall here that the latter embody a description of gravity. (See also Fig. 3c and the manner in which a closed string can append to a D-brane manifold. Thereby weakening it, leading to fluctuation).

iii)D-branes act as fundamental sources of the various physical fields (e.g. E-, B-, G-)

iv)D-branes as sources of fields carry the smallest charge(-s) possible. For example, q E for E.

The quantitative description of brane phenomena is enormously complex and far beyond the scope of this Appendix, or book. However, some simple insight and appreciation for the complexity can be gained by looking at the simplest brane of all, the D-0 brane consistent with the point particle. Without going into the details of obtaining the (fiber) bundle map, we require for completeness the tachyon field described by:

T(x) = SIGMA_n=1..9 GAMMA_n X^n

where the summation is taken from n = 1 to n = 9, with x^n the coordinates for the rotation space (group) R(9), and GAMMA_n , the matrices needed. Then the tachyon field consistent with the above would be:

T =

( x^9 GAMMA*x)
( GAMMA^T*x -x^9)

Here, the Gamma matrices (GAMMA) and their transposes (GAMMA^ T ) are predicated on the basis for SO(9) spinors, viz. S = [S+ , S - ], such that the mappings: GAMMA : S - -> S +, and GAMMA^ T : S + -> S - apply, respectively. For a system of D-0 branes parameterized by such matrices and defined by the given tachyon field (T(x)), we have a system of 9 x 9 matrices, defined by [x_t9]. This will feature a diagonal specified by: x_N (τ), τ = 1…..9, and zeros everywhere else.

Note that in the special case of D-branes widely separate, say analogous to the UFO example described at the beginning of the section, the matrix can be rendered as the much simpler diagonal case above.

All of the preceding is intended to show how the very basis for even the simplest (D-0) brane rests on a dynamical (fluctuating) vacuum, strings and in particular the faster-than –light tachyon. It remains to be ascertained, however, how a UFO- brane can be manipulated in terms of the energy required. At the very least, we’d like to set some kind of threshold on the magnitude of energy.

Since the fields, and dynamics (as well as the tachyon field) are occurring at the level of the vacuum, that is the first place to start. Thus, to manipulate the brane B, in Fig. 3a, it seems clear that energy consonant with a vacuum energy – or more exactly, a vacuum energy density- is needed.

The conclusion from all this is that, assuming we take the brane-driven UFO seriously as an FTL device, it must somehow make use of dark energy (repulsive gravity) to manipulate distant branes to achieve nonlocal (FTL) transitions. This is also the only venue in which the enormous energy density makes any sense.

Thursday, July 24, 2008

Is there a plausible basis for faster-than-light travel? (II)

FIG. 1 Basis of Variable tau.
Variable Speed of Light and Variable Time:

More fundamental than the warp drive concept is that of a variable speed of light, proposed by Joao Magueijo of Imperial College, London. Magueijo’s theory is that the speed of light is not always constant, so can sometimes (under special conditions in vacuo) exceed 186,000 miles per second. If so, then it might be used for practical applications. (Though one is left to ponder whether what might happen if, while in transit, the speed of light ratchets back to below 186,000 msp!)

Up to now, Magueijo’s theory has received little by way of attention, other than in a recent book he published, entitled ‘Faster Than The Speed of Light’. This is because he has found no referees willing to validate his assorted papers for publication. His book itself, alas, sheds little actual light on the physics issues, and is more in the way of a long personal account (including harangues) against his presumed oppressors and censors.

That being the case, it is still worthwhile to inquire how a variable speed of light theory might work. My own solution to this entails not variability in the speed proper, but rather a variability in time, which leads to variability in speed. (since v = d/t so as t -> 0, v -> oo for some finite distance d).

The concept of a variable time vector is not new. A. Achong first proposed a possible elastic temporal vector that could have uses in physics. He invoked an ansatz in which particles possess an internal (intrinsic) time vector arising from the internal structure of their individual constituents, including quarks. The individual time vectors for each particle are allowed to assume either (+) or (-) signs, depending on whether the constituent is associated with normal matter or anti-matter- and the direction of global time is determined by the dominant sign. [1]

A somewhat different take can be developed by using quantum set theory in relation to time, as originally developed by Finkelstein.[2] In line with this, we adopt time vectors such that there exist intrinisic variable magnitudes. I use the term tau (t) for these, based on the same unit from quantum set theory. According to this definition, 'one tau' is:[2]

10^-43 < τ < 10^-23

This is an extremely small time unit to be sure, but up to twenty orders of magnitude larger than the Planck time (10^-44s).

The tau, or variable tau, can be thought of as a ‘building block’ or element of proper time. In another guise, as the smallest conceivable increment of temporal difference. An aggregate or set of elemental taus yields the normal, standardized units such as ‘second’, ‘minute’, ‘hour’ and so on. The cautionary note here being that all these can vary in duration (from an extrinsic objective observer’s view) depending on what its tau component is at the time of measurement.
Tau changes, as well as the derivative unit times dependent on it, by virtue of tau expansion (Fig. 1)

This may most probably occur by distortions or discontinuities in fiber bundle sheafs at different levels. Tau expansion assumes that conservation of quantum probability currents[3] is valid throughout. This means that the area shown for the probability space must be equal throughout. Hence, if I stretch the tau, elongating it as shown in the upper view (Fig. 1), the Planck Length (L_P) will be contracted in order to compensate and keep the same phase space area.
Tau expansion is possible based on the well-known second postulate of quantum mechanics:
II. The independent variables x, p of classical mechanics are replaced by Hermitian operators x _op, p_ op. Operators corresponding to dependent variables (i.e. H ) are also assigned Hermitian operators. Thus we have:

x _op <-> x and p_ op(x) <-> -ih/2pi (d/ dx)

In the context of temporal uncertainty:

t _op <-> t and E _op(x) <-> -ih/2pi ( d/ dt)


delta E (delta) t > h/ 2pi
Which is the energy-time format for the Heisenberg Uncertainty Principle. That is, the simultaneous product of uncertainty in energy, by uncertainty in time, yields the Planck constant divided by 2 pi. Another way of putting this, is:

delta(t) > h-bar / delta (E)
Where the numerator, called ‘h-bar’ is equivalent to h/ 2pi. This inequality is telling us that we can expect, based on the Heisenberg Principle, uncertainties in the properties of time – as well as of space. (I.e. measuring position of an electron during a momentum measurement). This uncertainty is such that the temporal variation (dt ) increases as the energy variation associated with the particular region of space (dE) decreases. This leads directly to the inference of variable c, supposing there are two separate regions (1,2) for which:

delta (t2) > delta(t1)

so that, c (1) = D/ [delta(t1)] > c(2) = D/ [delta(t 2)]

In other words, the speed of light in region (1) exceeds that in region (2), all other things (e.g. distance D) being equal IF the times are not. (The longer time interval delta (t2) gives rise to slower light speed, for the same distance D covered). For concreteness, let:

delta (t2) = 0.11 sec, delta (t 1) = 0.10 sec

Then: V(1) = 1.1 c and V(2) = c, taking D = 186,000 miles

This is well and good, but we need to go deeper into the tau connection (tau expansion). First, as to physically how variable time is possible, we note that the creation of particles and energy can be spontaneous. Thus, the quantum of energy:

delta (E) > h -bar/ delta (t)

say appearing in pair production, can be wholly spontaneous. By extension, as James Gott and other physicists have noted, the same energy-time principle can be used to account for the spontaneous appearance of the cosmos. Based on some initial energy uncertainty, delta (E). It follows from this, that spontaneous time variation is also possible.

Finkelstein actually created an operator explicitly to vary time via ‘bracing’. The operator is called ‘the brace operator’, Br. To see how it works on an elementary level, select a quantum unit set (say of cardinality 1) over some sub-module S (1) of the Clifford algebra S, with basis B(1). Then it follows from application of Br, and its conjugate Br*:

Br* Br = 1

Br Br* = [unit]

Br* Br - Br Br* = [non-unit]

A more graphic way to see this in term of tau change is as follows:

After delta (t) = 1 τ, Br = { }

After delta (t) = 2 τ, Br = { { } }

After delta (t) = 3 τ, Br = { { { } } }

Notice that the brace creation increases arithmetically as the unit tau increases. The operation Br, equivalent to C(b) in Grassman space, generates an elemental tau (τ). It is easy to see from this that the inclusion of Br* is equivalent to generating a state projector [unit] τ_ 1 >. Conversely, brace annihilation reduces tau, viz.

Br* Br - Br Br* [ { { { } } } ] -> { { } } or 3 τ -> 2 τ. It can be shown that, just as say for quantum mechanics, Ψ > = Ψ 1 > + Ψ 2 > + Ψ 3 > + Ψ 4 >+ …….Ψ N >, so also in ‘tau mechanics’: τ > = τ1 > + τ2 > + τ3 > + τ4 >+ …….τN >, where the τ are resultants in an N-dimensional complex vector space (or Hilbert space). This leads naturally to a conception of an infinite ‘tau’ Hilbert space embedded in a Euclidean 4-space manifold (Think of each elemental τ lined up head to tail along an infinitely long 'box'). In effect, unit temporal vectors (taus) shown, extend all the way to unit temporal vectors (taus) shown, all the way to τ (oo).

What if a ship were to travel over a region in which variable tau applied, say in τ-Hilbert space from τ1 to τN? in particular, such that the tau gradient ( dτ / d x) decreased say by 10^-23 second each meter? Even traveling at constant velocity (by ship controls) we’d expect it to undergo acceleration on account of the changing tau.

Elementary calculation shows that it would take ~11 million light years displacement to attain a time differential of one second. 5.5 million light years for a half second. Whether such increments could translate into super-light velocity depends upon the initial velocity of the craft. Say the hypothetical craft was traveling at 200,000 km/s (or 2 c/3) initially. Then after 5.5. million light years it would be at: v = 200,000 km/s/ 0.5s = 400,000 km/s or 4c/ 3. This would increase to 800,000 km/s (8c/ 3) after another 2.75 million LY. Obviously, super-light speeds could be attained over much shorter distance spans if the tau gradient is higher. (For instance, the distance threshold for v > c would be 100 times less, if d τ / dx increased the same magnitude tau each centimeter.)

In the case depicted above, a temporal Br (brace) operator projects the unitary temporal state τ > into a multiple of the chosen state, Uτ_s > and U τ >.

Br = exp (iE) = cis E Br* = exp(-iE) = cis (-E)

It is this quantification basis, applied to a certain region of space, that allows for variable tau as I’ve described it. Of course, the discussion can easily be extended to two (or more) dimensions with appropriate modifications of the mathematics. This can be the subject for a future article.

Next: A Multiverse and Cosmic Shortcuts?

[1] Achong, A., 1984, Internal Time and Global Time, Proceedings of the 2nd Caribbean Physics Conference, Leo L. Mosely (Ed.)

[2] Finkelstein, D.: 1982, Quantum Sets and Clifford Algebras, in International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, p. 489. (Reference to tau on p. 494).

[3] Think of the quantum wave function ι changing over time. Then the wave probability, P = Ψ Ψ* will also change. This can be thought of as a 'current' in time.

Wednesday, July 23, 2008

Is there a plausible basis for faster-than-light travel? (Part I)

An inherent premise of the extraterrestrial hypothesis for UFOs, is that the vehicles or craft must possess FTL (‘faster than light’) speed capabilities. This stands to reason. If interstellar craft are constrained by the Einsteinian limit of 186,000 miles per second, then long interstellar voyages and colonization become highly problematical. Particularly, since the probability for star systems with planets that support intelligent life increases with distance.

Hence, if UFOs are truly the craft of extraterrestrial ‘visitors’- and not some hitherto unknown meteorological, optical or electrodynamic phenomenon- then they must have traveled to Earth at higher-than-c velocities. But how is this possible if special relativity forbids anything traveling faster than light?

In this article, I examine a number of hypothetical explanations that also have some basis in either mathematics or physics. Each of these incorporates or allows FTL in some kind of limit. While not proving that such mechanisms actually underlie UFO operation, I argue that they certainly lend credibility to the concept of FTL interstellar travel via artificial craft.

Before proceeding to informed speculations, let’s consider actual experimental verification. In a paper appearing in the journal Nature, in July 2000, physicists at the NEC Research Institute in Princeton, New Jersey. claimed to have broken the limit set by the speed of light. They achieved this by firing a laser pulse into a glass chamber filled with a cesium (Cs) atom vapor.

NEC’s Lijun Wang, in fact, insisted he’d created an experiment in which light speed was not merely exceeded by an added increment, but by a factor of three hundred! This meant that an almost identical light pulse exited the chamber and traveled about sixty feet before the main part of the laser pulse finished entering the chamber, Wang said.

Needless to say, this flouts well-known accepted precepts of causality. (Wherein causes are assumed to precede effects). Relativity purists may also be gratified to know that a number of physicists question the interpretation of the results.

Validity will therefore have to await a confirmation of the experimental results. In the meantime, let’s move on to consider other more speculative scenarios:

1. The Alcubierre Warp Drive

The concept of the FTL warp drive was probably first coherently developed by Miguel Alcubierre of The Department of Physics and Astronomy, University of Wales, in 2000. For this to work, he postulates a ‘local expansion of space-time’ behind a spacecraft, while at the same time there’s an opposite contraction of space-time in front of it. The resulting distortion is analogous to many ‘warp drives’ invoked in science fiction.

However, there is this important difference: in the Alcubierre warp drive travelers are never really moving faster than the speed of light, since technically they always remain “in their own light cones”. So, rather than an FTL displacement of their inertial reference frame (attached to the ship) itself, it is the expansion of space-time that creates the enormous speed of separation.

To obtain this, the appropriate metric must be found, e.g. to “push” the craft along a trajectory described by an arbitrary function of time x S (t). . For a 4D, Cartesian system, with displacement along the x-axis, Alcubierre provides:

alpha = 1

beta^ X = - v S (t) f (r_s (t))

beta ^y = b eta^z = 0

gamma_ ij = delta_ ij

In the preceding formalism, gamma_ ij denotes the 3-metric of hyper-surfaces with constant coordinate time t, a is the ‘lapse function’ (generally a = 1) giving the proper time interval between hyper-surfaces as determined by Eulerian observers[2], the beta_i (i= x, y, z) denotes the ‘shift vector’ relating spatial coordinate systems on different hyper-surfaces. The full metric (for a line element or interval) in this space-time is given by (cf. Alcubierre, 2000):

ds^2 = -dt^2 = g_alpha beta dx_alpha dx_beta = - (a^2 - beta_i beta_i) dt^2 + 2 beta_i dx_i dt + gamma_ ij dx_i dx_j

The primary proviso for the above, is that the 3-metric be ‘positive-definite’ for all values of t, so the space time is then globally ‘hyperbolic’. The key point is that for the conditions set out, there’ll be no causal curves, generating the sort of paradox described in the experiment on the laser pulse at NEC Research Institute. It’s important to bear in mind that proper time always applies to the coordinates of the starting and destination points, as well as to the craft. (Though the latter will be subject to time dilation during the initial and final stages of the trip – when moving through flat space-time). This means that only the time on the craft is affected, but that the home world of the travelers – say if at immense distance – would long since have changed by their return. A depiction of an Alcubierre –style ‘warp deformation’ is given at the link below

As described already, the cylindrical deformation represents the expansion of space-time behind the hypothetical craft (in hyperbolic space) while the reverse deformation or contraction lies in front of the craft. The tandem is what generates an acceleration leading to v > c in the ship’s reference frame.

NEXT: Variable Speed of Light and Variable Time

1-A ‘hyperbolic’ space-time is one in which the curvature has the value k = -1.

[2] That is, with 4-velocities normal to the given hyper-surface.

Monday, July 21, 2008

The Mugging of Stanton Friedman

For those who may not know, Stanton Friedman is a nuclear physicist and one of the most articulate voices for the reality of UFOs as extraterrestrial craft. Two nights ago, he appeared on the 'Larry King' show which also featured skeptic Bill Nye ('the Science Guy' and member of the Skeptic Society) and an astronomer involved with SETI work.

While Stanton attempted to make his case, especially in regard to the evidence for missile interference that occurred in 1967 in Montana, Nye kept interrupting and casting cutesy aspersions. Stanton attempted to defend his position and was promptly smacked down by King who barked, 'Don't interrupt, Stanton!'.

As far as I could see, that was it. Following that "mugging" by King (who never should have had the likes of Nye on) one scarcely heard another cogent peep from Mr. Friedman. Which was most unfortunate.

As a person who has taught critical thinking myself, I was absolutely ashamed of the act the two skeptics put on. It distracted from what could have been a serious discussion, and ended as more of a row than anything meaningful.

The difficulty in formulating UFO hypotheses, and interpreting UFO reports, is a first-hand experience for me. Not only have I investigated other people's reports and published the results[1] but I've observed a "UFO"myself. The incident occurred in March of 1962 while at the opening of a shopping center in Carol City, Florida. While awaiting the start of festivities I happened to look up at the night sky, being the amateur astronomer that I was. Amazingly, I witnessed a brilliant orange disc, at least the same diameter as a full Moon, moving rapidly from north to south.

It hovered for two to three seconds above the crowd at the shopping center and I detected the odd "Oooh" or "Aaah" from random spectators. Thus, I knew I was not having a simple hallucination (at least not by myself!) The most ironic and notable thing to me was the complete absence of sound. No whirring, like one would expect from a helicopter's propeller blades, or engine noise. The object - if "object" it was - appeared to be a light source rather than just reflecting light from elsewhere. After about three seconds it took off due south at what I estimated to be an incredible speed. As a seasoned sky observer, even at the age of 16, I was able to quickly eliminate all known man-made or natural objects from consideration. The exceptional luminous and dynamical behavior allowed this. Nevertheless, to this day I am not prepared to pinpoint a specific hypothesis in any dogmatic sense. Nor am I prepared to assert it as a "craft" from another planet.

To me, it was and remains a "UFO".

What IS a "UFO"? The late Prof. Allen J. Hynek (former Professor of Astronomy at Northwestern) offered the first truly scientific definition of the UFO:

A UFO is the reported perception of an object or light seen in the sky, the appearance, trajectory and general dynamic behavior of which do not suggest a logical, conventional explanation and which is not only mystifying to the original percipients but remains unidentified, after close scrutiny of all available evidence by persons who are technically capable of making a common sense identification, if one were possible.”

A common misperception is that UFOs are “flying saucers” or space ships. However, this is actually only one possible hypothesis among several. The main thrust of Hynek's definition is one must not automatically jump to any conclusion that conflates the UFO with an extraterrestrial craft.

But let us get back to Stanton Friedman and what he had to endure with Nye and the astronomer. To be sure, this is not the first time such an altercation has occurred, but with different subjects. It's interesting that not even the late Carl Sagan could refute Jacques Vallee's extensive reports (cf. Forbidden Science, North Atlantic Books, 1992) , nor did he even attempt to go after the sole UFO report in Edward U. Condon's Air Force commissioned Scientific Study of Unidentified Flying Objects(1969, NY Times Books): Case 46, p. 396 from McMinnville Ore. (11 May, 1950) that concludes - and I quote, from p. 407:

"This is one of the few UFO reports in which all factors investigated: geometric, psychological and physical appear to be consistent with the assertion that an extraordinary flying object- silvery, metallic and disc shaped flew within sight of two witnesses. "

Vallee himself has also taken Sagan to task in this case, for proposing a scientific process:getting extraordinary evidence first, before forming a hypothesis on the basis of existing investigations and doing an extraordinary investigation. Nowhere else in science, or its possible objects of inquiry, are we expected to start with extraordinary evidence (which usually isn't available yet) then go to the process.

A perfect case is plasma double layers, which possibly occur in coronal arches and help to trigger solar flares. Despite the fact no one has proven these artifacts exist, they are regularly used to support the observations of certain solar flares.

So, here is where Sagan fell down, by allowing his skepticism to undermine his objectivity. Sagan himself has also been taken to task by the likes of astrophysicist Frank Tipler for instigating millions of dollars for planetary, or SETI research when "he hasn't demonstrated adequate criteria or justification for doing so". In particular, many of Sagan's papers to support or rev up funding for planetary explorations (like with the Viking probes) were entirely based on speculations to do with mathematical probabilities of life existing - say on Mars- rather than any inherent hard data for such. Such critiques could also be leveled at the astronomer skeptic who appeared alongside Nye.

Nye himself, sad to say, demonstrated the same promotion of skepticism for skepticism's sake in his appearance on King, which merely reinforces the sterility of his position. To be far more cogent, the REAL skeptic must take one step further. If his adversary makes a claim, he needs to make a counter claim or offer an alternative hypothesis, to neutralize it.

Thus, if Nye didn't accept Friedman's claim of an actual craft, the onus was on him to offer an alternative hypothesis as to what the interfering Montana UFO was.

It was, of course, acceptable for Bill Nye to simply withhold acceptance of Friedman et al's claim passively, but this usually makes the hard-edged skeptic position much more difficult to hold. If you adopt the passive stance, in other words, you really cannot be too aggressive in your take on the event, or use clever putdowns. You merely open yourself up as a target.

Something Mr Friedman would no doubt have alluded to had he not been "mugged" (shushed) by Larry King earlier!

[1] See Stahl,P.A.: Transient Optical Phenomena of the Atmosphere - A Case Study, in The Journal of the Royal Astronomical Society of Canada, Vol. 74, No. 3, June 1980.

Saturday, July 19, 2008

Making Short of the Short Sellers

Within mere days of the Security and Exchange Commission's announcement of a tough new rule designed to limit "short selling" (now believed responsible for driving share prices of financial stocks into the tank) you can see and hear the howls of protest erupting from every quarter (e.g. 'SEC Short-Sale Rule Gets Negative Reviews', The Wall Street Journal, July 19, p. B1).

What is short selling, also called "shorting"? This occurs when financial (especially) share sellers aim to profit from share declines by selling borrowed shares then buying them back in the market at a lower price. In a more egregious variation, called a "naked short sell", the shares are sold without any arrangement to have borrowed them first. The end result? These shorting operators make a killing with little or no risk, and certainly none of the upfront exposure that normal purchasers of shares have. (So, in many respects they are like the oil commodity speculators who only have to produce 5% of the total purchase to speculate a much higher price). Prior to the SEC rule, by one report, it was estimate short sellers had creamed $11 billion of profits from their short sales.

What is amazing to me, especially in view of the much reported market timing ploys of a few years ago, is how many average Joes and Janes still entrust their hard earned money to Maul Street. This, despite all the recent markers that disclose it is a bad bet.

The cold, brutal and hard fact of the matter is that most Americans (unless they have at least $2-3 million in disposable wealth) had best stay out of the Maul Street casino. It is purely a game for the 'whales' (as huge bettors are called in Vegas). Even mutuals offer little or no assurance of getting anything more than chump change - unless you are remarkably lucky in your redemptions.

A Stanford University study- based on the median return of 62 mutual funds- showed that $1 invested in 1962 would have grown to $21.89 by 1992, on a pre-tax basis. The study disclosed that the $1 would have grown to only $9.87 on an after-tax basis. And the investor would have had to come up with $12.02 to pay the taxes. By contrast the study showed that a “conservative” investor who put assets into a U.S. Savings Bond in 1962, had every $1 become $10.93 by 1992.

It is easy to work out from these numbers which investor actually fared better over the thirty-year interval according to the study. Hint- hint: it wasn't the sucker in stocks. Unless mutuals investors do the math and watch the numbers they cannot be aware of how little they're actually taking home. (A point also made emphatically in The Wall Street Journal, Nov. 27, 2003, page D1, 'A Harsh Truth: Most of Your Investments Won't Make Money- Even in the Long Term', after assessing stocks, bonds and mutuals).

Recent articles appearing in MONEY magazine, and The Wall Street Journal bear this out, noting that in the past ten years the S&P 500 has barely eked out 1.6% a year, not even matching the gains of CDs or Treasuries. Plus, one has to contend with onerous expenses, fees )e.g. 12b-1) clobbering from every angle.

It is also well for small investors to understand that, to a large degree, they are in a game with a 'stacked deck'. Not only that, but under current laws their investments are almost entirely blind. Like buying a pig in a poke. This point was emphasized in a London Financial Times article (‘A Metaphorical Proposal’, Mar. 13, 2003, p. 11A) by Michael Skapinker. He cited remarks by Joseph Berardino – chief exec of Arthur Andersen- who noted how the current reporting system “fails to communicate essential information about the real risks facing companies” to the small investor.

The basic Wall Street pyramid game is elementary to grasp. Pundits, wags and paid flacks on cable business channels hype the various stocks, funds or instigate a "buzz" about them - to get suckers to buy in. The increasing buy-in inflates the price-to -earnings ratio (P-E ratio) and produces a bubble of high profits. The "Big boys" (mostly large, institutional investors, but also big money single investors) get tipped 1-2 days in advance and cash out, leaving the little guys to sink. If they're lucky they may earn a few bucks. Not much.

For example in the Financial Section of the Balt. Sun of 1/27/97, p.1C there was this little headline: INVESTORS COMPLAIN OF UNEVEN EXPOSURE :

General Motors Corp. gave a welcome warning last month to a few close friends. One by one, the automaker called analysts at top brokerage firms on Dec. 18 to say that fourth quarter costs would be higher than expected. Word was quickly passed to those (brokerage) firms' big clients, whose sales of GM stock sent the shares tumbling $1.375 on a day when the Dow Jones Industrial Average rose 38 points. Other investors had to wait until the next day - when nine analysts cut fourth quarter earnings estimates - to find out what GM said in private.

The thievery works eventually because most manjacks are conditioned to "buy and hold" rather than fold when the share price dives below a certain threshold. (Which ought to be the tip off). Thus, there are always ample marks left at the end game to be properly fleeced. Amazingly, they're always ready to play the game again, and pile their newly saved up money in.

I wised up in 1997 after the DOW was "juiced" and reading a lot of books and article on how the game was played, especially the psychological enticements to become "an investor". (I.e. you were "missing out" if you didn't plunk that cash into the Street). I cashed out of all the high risk equity and other funds before the 2000 bubble burst. I've stayed strictly with money market accounts, funds, and laddered CDs since. I did lose more than I'd like to have in a few bond funds, but also pulled out of all those in early 2000. (That was after I learned of the collateralized mortgage obligations or "toxic waste" piled into many of them)

Slow and steady is the way to go, albeit not "sexy" - and anyone who tells you any differently is trying to pick you off. I may not have millions at the end of the day, but won't have to go back to work prematurely because an IRA tanked by 40% or 50% - as many too trusting people are learning now.

The only real diversification in the end, is not to keep all the eggs in Maul Street's casino coffers. As Joe Dominguez and Vicki Robin note in Your Money or Your Life, about 20% on the Street is perhaps the maximum, the rest in cash (money market) accounts, laddered CDs and Treasuries. That way - when the market tanks by 40-50% as it surely will when the next bubble bursts, you don't have to commence from square (X- 100) again. Particularly as all losses are compounded in a downmarket environment - since as I noted- Maul street will still exact its Shylock cut (in expenses, fees, commissions etc) even as you're reaping market losses! Add a 15% loss to a 5% load, and more than 3.5% in fees-expenses and the results are not very pretty.

However, the hype and media fomenting of the PR of the market mythology keeps most prospective retirees thinking that they must be in the market or they won't be able to retire. Even now, the media drumbeat has begun for people – with portfolios and 401ks still in tatters- to get back into the market game. “Buying opportunity” is the mantra issued to rope in millions more suckers. Meaanwhile, oldsters who've taken a beating in the current Bear market may be looking at another ten to twelve years of work to make up their losses - assuming they can find work!

The stock market's sole purpose, As E. Brockway observes in his The End of Economic Man, 1990, is to steal capital from the poor or middle class (that can least afford losses) and give it to the rich. The means to achieve this are not obvious, but all one needs to do really is pay attention to the financial news and especially how market manipulation rears its ugly head again and again.

One day, perhaps, people will learn how to protect their assets themselves, without being drumbeaten into being hostage to stock sharks, con artists, shorters, speculators and other denizens!

Thursday, July 17, 2008

Fractional Gamma Functions

Earlier we explored how the Gamma function works. One of the more useful formulas for generalizing integral forms was found to be:

G(x + 1) = x G(x)

This will also be found very useful in working with fractional Gamnma functions, as I will show in this article. Most solutions of fractional G(x) entail already knowing at least one basic form, usually obtained from a special integral.

For example, working with most fractional halves we make use of the basic integral that generates:


This is defined:

G(1/2) = INT (0 to oo) t^-1/2 exp(-t) dt

where 'INT' denotes an integral, taken in this case from 0 to infinity. The resulting integral yields:

G(1/2) = pi

Now let's see how it works, say to obtain G(-1/2):

From the basic Gamma function formula (letting x = -1/2) :

G(-1/2) = G(-1/2 + 1) = -1/2 G (-1/2)


G(-1/2) = -2 G(1/2) = -2 pi

That was easy enough. Now what about G(3/2)?

Use same sort of procedure:

G(3/2) = G(1 + 1/2) = 1/2 G(1/2) = pi/2

(Readers are invited here to find G(5/2) on their own!)

Another application, decimals - which are merely another form of fraction:

Say you wish to obtain G(-0.30)

(In this case, one already is assumed to know the basic Gamma function G(1.70) = 0.90864)

In this case, from the Gamma formula given earlier:

G(-0.30) = G (1 - 0.30) = -0.30 G (-0.30)

G(0.70)/ (-0.30) = G(-0.30)

But: G(0.70) = G(1.70)/ 0.70 = (0.90864)/ 0.70 = 1.29805

So: G(-0.30) = G(0.70)/ -0.30 = 1.29805/ -0.30 = -4.32683

Fractional sequences can also come into play, e.g.

Find: G(n + ½):

G(n + ½) = (n- ½) G(n – ½)

Since: we use x = (n – ½) in: G(x + 1) = xG(x)


G([n – ½] + 1) = (n – ½) G(n – ½)

-> G(n + ½) = (n – ½) G(n – ½)

And we can go further, focusing on treating the right hand side:

(n – ½) G(n – ½) = (n – ½) (n – 3/2) G(n –3/2)

= (n - 1/2)(n - 3/2) . .. . .3/2* 1/2 * G(1/2)

But, G(1/2) = pi, so:

G(n + 1/2) = (2n -1)/2 * (2n -3)/2 . . .. 3/2* 1/2* (pi)^1/2

Further factoring and additional algebra will yield:

G(n + 1/2) = (2n)! (pi)^1/2 / 2^n n!

This is left as an exercise for the ambitious reader!

Wednesday, July 16, 2008


The question of curing the religiously crazed or psychotic is one that has emerged on many forums I’ve frequented. Some, of course, are horrified at the very notion that one would wish to “cure” the religious, since they don’t identify it as a disease or mental aberration. Thus, there is an impetus to “leave religion alone”.

However, if you treat religion as taboo and "out of bounds" for commentary or prescriptive cure, you essentially give mental dysfunction (which often operates under religious cover) a free pass. You also leave religious memes unexamined. Including those that emerge as when attention is drawn to the heaven-hell myth, viz. via the "Hell House" horrors now being used by evangelicals to prepare children for what they will face if they become "unbelievers". In these odious performances, kids are forced to watch plays depicting infidels being tortured and burned by Demons. Many come away in partial or full psychoses.

These scenes - "real" (based on biblical bunkum) or imaginary ("Hell House")- also raise an eschatological problem: Could devout fundamentalists really enjoy paradise as their friends, relatives and neighbors were heaved into hell?

These sanctimonious, insufferable Christianoids (especially) insist that they have earned their 'just rewards" and they mean to enjoy them. Even at the expense of cousin Tommie, Uncle Fred, Aunt Millie or Grandpa Ed - seen now perpetually frying and getting impaled with Lucifer's pitchforks with the other unbelievers, sinners and spiritual riff raff!

Here's the real question to ask an unctuous believer who insists he or she is 'above it all' and merely looking out for the "advancement" of humanity (by which they really mean being "personally saved"):Do you have a "hard on" for afterlife exclusion, segregation? Dividing humanity's dead into the permanently "saved" and "unsaved"? The former sitting at the "right hand" and watching on as we ("unsaved") unbelievers, along with Buddhists, Hindus, Jews get cremated for eternity? Is this important for your own spiritual satisfaction? Or, can it be dispensed with?

If your God is truly one of Love, why on Earth does he need a “Hell”? (And please don’t hand me the malarkey that God “doesn’t send people to Hell but people choose to send themselves:”. This swill is definitely the last refuge of scoundrels and imbeciles)

My point is that no matter how devout a person insists he or she is, if s/he believes in "Heaven" and "Hell" the words are already hollow and show that - whatever the particular "hard-on" requires- it means more than five billion frying in a nuclear holocaust initiated in the Valley of Megiddo.

It means > 100 billion crisping in fires for eternity as some snotty little "elect" enjoys sitting at the "right hand" of their little lord and master watching the infidels writhe. And then these fart will have the nerve to say: "Oh, but we hate the sin and love the sinner" Yeah, right.

Whether many want to admit it, or realize it or not, many evangelical Christians' entire life is bound into and promotes, defines their ultimate “salvation”. I have no problem with that, until they also posit my exclusion, e.g. damnation, based on my unbelief. (Never mind the exclusion may be from an unreal existence from my Atheist POV, the point is not the existence per se but the person's absolute mental exclusion in the first place!)

In other words, fine if you want to believe you're saved, but don't pillory or condemn me as "unsaved". Don't grab your "heaven" ticket, by handing me my "hell" ticket. (E.g. you're attaining the heavenly clouds, means I must descend to the hellish pits). I also totally question the premise that anyone can "behave with decency" in this world, if they also believe in their heart of hearts that a good portion of humanity will be condemned at the end of time - for either never having heard of Jesus, or not believing in him.

That makes a mockery of any decent acts they might do, and makes them hollow at core, since their governing belief is whatever people they help (or cooperate with in helping others) will ultimately be destroyed in some eternal holocaust. How does that reconcile? It doesn't - unless one is a madman. Speaking of madness, there is enough evidence now to show that the vast bulk of religiosity and its expressions are centered in the temporal lobes as epiphenomena.

Experiments by J.M. Persinger at Laurentian University have exposed these, by stimulating the temporal lobes of numerous subjects with specially designed helmets. In each case, religious visions or "insights" emerged, as well as beliefs. Eventually, Persinger had to call it quits after receiving death threats (according to a 1989 OMNI piece, 'Transcending Science') One would think people wouldn't get so lathered up at this.

Beholding the sheer wonder of the brain as a 3 lb. mass of gray matter. Packed with over ten billion cells - able to deliver everything from the most advanced tensor equations, to building space well, providing the most exquisite visions and beliefs on demand. (Read some of Telhard's writings, like The Divine Milieu, to see how his own temporal lobes excited his neocortex and conjured up his marvelous visions of the Alpha and Omega).

But people (believers) almost uniformly 'lose it', perhaps because - as Daniel Dennett once noted - they want to build their world and universe on "skyhooks" not cranes. Cranes, after all, have to hoist from the ground up. They're prosaic, dirty material flotsam and jetsam like cells, electric signals and chemicals. But oh those skyhooks! To toss them upwards and hook on to the ethereal, immaterial realm in the hyper yonder beyond the clouds and matter!

"BWAAAAAA....We don't want that! We wanna be GRANDIOSE beings! Made of sky and spirit not filthy matter! Or derived from it like those dirty atheists!"

They fail to comprehend that for humanity to be in harmony - no single subset can elevate itself as "more special" or “more worthy" or more "grandiose" than any other, irrespective of who or what they believe in. And while it might be nice or appealing to believe ALL humanity is skyhook-engendered, in practice it never works! Because once the skyhook meme is admitted, one segment seeks to claim its grandiosity and specialness for itself, and excludes the others!Much better to look at basic evolution by natural selection, and how we all came to have the same basic DNA in our cells. Sharing the same basic chemical arrangement. Indeed, this sharing can be extended to all living things on the planet- removing the specialness of humans as a species.

What is the prescription therefore to cure exaggerated religiosity? It is simply an adaptation of Persinger’s own methods: in this case using quantum dot electrodes inserted into the temporal lobes to control the “temporal lobe transients” that give rise to religious visions, beliefs, rituals, and the arrogant, exclusionary condemnations of others.

If every religiously-driven extremist could be identified, tagged and implanted the world would be a much better place, since the extremist manifestations of religion would be held in check. Then, people could still practice interior meditation and worship – but their yen to interject it into the outside world (and onto unwilling others) would be suppressed.

For an Atheist this is as close as it gets to “heaven”.