REPORT ON A DREAM & RELATED
MATTERS & THE GOD PARTICLE

In June 1995, the writer noticed that the inverse 256th root of 1E33 is approximately the product of the fine structure constant and the edge of the 'absolute dead center cube', 10368^.5.¹ He also noted that if 1E33 is first multiplied by the square root of 1.1 (the ratio of the body-diagonal to the face-diagonal of the triple-cube²) before taking this root, the result is then 0.007297 353 93, which is the physics value of the fine structure constant, 0.007297 352 533, exact to the 8th place.

About a week after this observation the writer had a dream. In his dream he was in a large hotel looking for a room. The room number on his key was 2808. He was having a great deal of difficulty finding this room. He asked some vaguely defined hotel person for help. He was told he was on the wrong floor and that he needed to go down 2 floors. But when he went down the 2 floors he still couldn't find room 2808. He discovered that he was now on the 27th floor. He failed initially because he had been on the 29th floor. Because of the peculiar elevator arrangements in the hotel in the dream he had to go down to the lobby and start all over in his attempt to get to the 28th floor. At this point he woke up.

Since the writer had never considered the number 2808 in his waking state, he puzzled over its significance after his dream. What he eventually discovered is this: first of all, the ratio of the 2 of the 3 floors in his dream on which he actually found himself to have been, the ratio of these two to each other, 29/27, raised to the power 2/3, and multiplied by 1E33, when raised to the inverse 256th root and divided by the length of the edge of the 'absolute dead center cube', is the fine structure constant exact to the 8th place:

[(29/27)^2/3 × 1E33]^−1/256/10368^.5 = 0.007297 354 38. . ..

It turns out that 2808 is approximately the square root of the division in extreme and mean ratio, φ, raised to the 33rd power,

2808 (φ³³)^.5,

or, 2808 is approximately 36/100 the inverse square of the fine structure constant divided by the inverse alternating L series sum,³

2808 .36(.007297 352 533/.6444762592780)^-2.

What was known before the dream.
 

It was known that if the Fibonacci sequence was anchored in the trinary logic, thereby renumbering the traditional sequence so that *F₁ is 1 and *F₂ is 2, etc., then, when the first hundred numbers in the newly numbered sequence are arranged in a 10 × 10 grid,⁴ the final 3 × 3 subsquare in the grid (lower right corner) has the following properties: it corresponds, in its arrangement qua logical, to the pattern of digits in the 'cornerstone' arrangement of the logic (bottom row, 0 1, middle row, 1 0, top row, 1 0 ) and the numerical products of the end values of each diagonal row and middle vertical and horizontal row (the products of *F₇₈ × *F_100, *F₇₉ × *F_99, *F₈₀ × *F_98, and *F₉₀ × *F₈₈₎ in this subsquare are each approximately 8.2944E36. It was also known that the products of the place numbers themselves of the opposite ends of these rows were, respectively, 7800, 7821, 7840, and 7920, with an average of 7845.25, and 7800 having logical priority as the product of the diagonal each of whose three places is inhabited by a logical 1. It was also known before the dream that

7800 (0.007297 352 533/.6444762592780)^-2

and that

.6444762592780/[(*F_{{78, 79, 80, or 90}} × *F_{{100, 99, 98, or 88}})/1E36]^.5 0.007297 352 533.

What the dream added.
 

Prior to the dream it was also noticed that (1.1^.5 × 1E33)^−1/256/10368^.5 0.007297 352 533. Both the 1.1 and the 10368 are functions of the triple 'absolute dead center cube', the latter a specific function of just that cubic arrangement. But there was no explanation for the fact that the multiple of 1.1^.5 is 1E33. The dream, in effect, substituted (29/27)^2/3 for 1.1^.5. It did so by focusing on the search for room number 2808 ( [φ³³]^.5 [φ¹¹]^1.5 [φ^5.5]³). It is this focus of the dream which leads to an appreciation of the significance of 1E33. The room number on the key in the dream, 2808, is exactly 36 × 7800/100 or 36/100 × 7800. .36 times the product of the opposed place numbers on the left-handed diagonal in the final subsquare of the unum-founded Fibonacci sequence. The dream calls attention to the deep relationship between the logically renumbered place numbers and the numerical relationships existing between the contents of the places so renumbered, and to the relation of the 10 × 10 grid to the fundamental parameters of physics in a beautifully general way. The dream says there is no need to strip the final square constant 8.2944E36 of 1E36, as is done above, in order to demonstrate that the fine structure constant is one of its functions. The equivalent of (1.1^.5 × 1E33)^−1/256/10368^.5 0.007297 352 533 or [(29/27)^2/3 × 1E33]^−1/256/10368^.5 0.007297 352 533, it turns out, is, where 2808/.36 = 7800,

(7800/8.2944E36)^1/256/10368^.5 0.007297 352 533.

The results are, first, that the 1E33 is accounted for. (1.1^.5 × 1E33)^−1/256 = 9.534625894E-34^1/256 and [(29/27)^2/3 × 1E33]^−1/256 = 9.53477636E-34^1/256 are of the specified order of magnitude because the relevant operation of the fundamental logically grounded mathematics is. That is, (7800/8.2944E36)^1/256 = 9.403935189E-34^1/256. Second, the fine structure constant is defined entirely in terms of the logical and numerical parameters of the trinary logic, and it is they which account for what otherwise would be unaccounted for, the role of 1E33. Third, it is clear that the logical structure, independently of any element outside of its domain, defines the order of magnitude of the Planck constant of action, 6.62606876E-34, where 7800/8.2944E36 = 9.403935189E-34, and

9.403935189E-34 - 6.62606876E-34 3.6E33⁻¹.

Now, consider that the first 100 numbers in the unum-founded Fibonacci sequence arranged in the 10 × 10 grid may be replaced by the first 100 numbers of the traditionally numbered sequence. The additional 1 of the traditional sequence will move each subsequent number one place forward in the grid, with the obvious result that the final 3 × 3 subsquare will now consist of different numbers and have a different common product of the end values of each diagonal row and middle vertical and horizontal row, in the event, approximately 3.168E36. Since this subsquare already exists in the unum-founded arrangement, with the last two of its columns coinciding with the first two columns of the final subsquare of the unum-founded set, and with 3.168E36 the approximate common product of *F₇₇ × *F₉₉, *F₇₈ × *F₉₈, *F₇₉ × *F₉₇, and *F₈₉ × *F₈₇, let this subsquare be compared, as it stands in the unum-founded arrangement, to the final subsquare previously analyzed. The products of the place numbers themselves of the opposite ends of the specified rows in this square are, respectively, 7623, 7644, 7663, and 7743, with an average of 7668.25, with 7623 having logical priority as the product of the diagonal each of whose three places contains the identical logical digit (in this case an ).⁵

This comparison yields a further equivalent to (1.1^.5 × 1E33)^−1/256/10368^.5 0.007297 352 533, and to [(29/27)^2/3 × 1E33]^−1/256/10368^.5 0.007297 352 533, and to (7800/8.2944E36)^1/256/10368^.5 0.007297 352 533.⁶ The square of the ratio of the products of opposite place numbers on the left-handed diagonal in the alternative final squares is the equivalent of the hotel-floor factor previously discovered in the production of the fine structure constant. Where 7800/7623 is the ratio, approximating 1.1^.25,

[(7800/7623)² × 1E33]^−1/256/10368^.5 0.007297 352 533.

Also, the sum of the independently derived inverse alternating L series, .6444762592780, is approximately the square root of the division, by the key order of magnitude, 1E33, of the ratio of the numerical and place-number constants in the alternative final subsquare:

[(3.168E36/7623)/1E33]^.5 .6444762592780.

Recalling that the length of the edge of a cube whose surface area is the sum of the only three numbers in the infinite series of natural numbers whose integral products are the very numbers, 1 + 784 + 82944 = 83729, (101.8233765/α)^1/2, the square root of the edge of the 'absolute dead center' cube divided by the electromagnetic coupling constant, and that the ratio of the surface of the 'absolute dead center cube', 62208, to the surface of this 83729-cube 101.8233765 × α, and that (where 1.1^.5 is the body-diagonal to face-diagonal ratio of the triple-cube) (1.1^.5 × 1E33)^−1/256/101.8233765 α, what is now to be noticed is that (where h is the Planck constant) the area of the face of the 83729-cube (1.1^.5 × h)^-.125.⁷

As of April 2002, with approximately 14 billion calculations performed, the writer's computer program calculating the alternating inverse L series sum (where the logic dictates a value of .5 for both 0 and , the L series = the arithmetic transcription of the sequential summing of the infinite repetition of 1, 0, , 1, 0, , 1, 0, , . . ., 1, 1.5, 2, 3, 3.5, 4, 5, 5.5, . . .) projects the sum of the series to be .6444762592780 . . .. The ninth place after the decimal of the raw number was settled upon after approximately 2.7 billion calculations.  The program is now calculating the tenth place of the raw number.  The 0 in the thirteenth place of the projected number has not varied since April 2000 (when the program had completed approximately 6.5 billion calculations).

Let this 0 in the sum of the series represent a break in the string of digits, so that the set of the first 12 digits might be considered in itself. To make matters easy, move the decimal to replace the zero in the string of numbers. Then investigate the properties of the number 644476259278. Its linear product, 6×4×4×4×7×6×2×5×9×2×7×8 = 162570240, is exactly the quotient of 82944 divided by 1/1960.

But what is 1/1960? The .125 root or power may be understood to be especially fundamental because it is the base power of the denominators of the infinitely alternating sequence of the infinite series of natural numbers and the infinite series of odd numbers which produces the infinite lattice composed of the natural numbers, the differences of their squares, the differences of the squares of those differences, the differences of the squares of those differences, etc., etc., etc. (The exponents of .125 in the odd-numbered rows of the lattice are 0, 1, 1 + x, 1 + x + x², 1 + x + x² + x³, . . ., and, in the even-numbered rows, their respective doubles, where x = 4.)⁸ Notice above that the face area of the 83729-cube (1.1^.5 × h)^-.125.

In 1985 the writer had taken the first four sets of numbers in the first two tiers of this infinite lattice created by the aforesaid squaring of the differences, reduced each set to a single number by a common operation, and, as is fundamentally consistent with the thinking now occurring, took the resulting four numbers to be elements in a proportion. He then calculated the rational product of this proportion, the product of the ratios which compose it. The result was 1/1.96.⁹ Thus, the factors of the linear product of 644476259278 are two most fundamental numbers.

The rational product and the integral product of 644476259278, are, respectively, 6/4×4/4×7/6×2/5×9/2×7/8 = 2.75625, and, (6×4×7×2×9×7)² = 448084224. The rational product, 2.75625, (1/1.96e7 × φ³⁷). That is interesting, of course because of the role of the extreme and mean ratio, but especially because 37 is the total number of prenumeral blue, green, and yellow diagonals in the logically outfitted triple-cube. In fact φ³⁷/1E8 α^.125 (the .125 power of the fine structure constant) or the ratio of the 20 green and yellow diagonals to the total of 37.¹⁰

The integral product of 644476259278 is the approximate product of 8.2944 and φ³⁷, plus 33000. What could this 33000 be? It turns out that 33000 the fourth root of the cube of (φ³⁷ × 1.96E-2), so that the integral product of the first 12 digits before the zero in the alternating inverse L series, 448084224,

(8.2944 × φ³⁷) + (φ³⁷ × 1.96E-2)^3/4,

precisely, 448084227.051706.

Now,

448084227.051706/448084224 = 1 + (1/146830715.261863),

where

146830715.261863^.125 10 × 1.1^.5,

the .125 power of 146830715.261863, ten times the triple-cube body-diagonal to face-diagonal ratio. If the decimal is not moved in .644476259278, then the integral product is 4.48084224E-64, which is interesting because, in the form of the equations above, 146830715.261863^−1/64 divided by the edge of the 'absolute dead center cube' the fine structure constant:

146830715.261863^−1/64/101.8233765 α.

2808, 82944, and the 'God Particle'.

114 GeV/c² 2808^-2 × 10 eV m⁻¹ s [(82944 - [δ/π]⁸) × 10^-5]⁸³ kg.¹¹
 

As of November 3, 2000, CERN produced the following tentative results: with a current bound on the Higgs boson mass of m_H > 113.5 GeV/c² and an expected m_H = 115.3 GeV/c²,

m_H = 115.0 (+1.3, -0.9) GeV/c².

With respect to the current value, note that

m_H = 115 GeV/c² (2808 - 4π)^-2 × 10 eV m⁻¹ s [(82944 - 10[δ/π]²) × 10^-5]⁸³ kg.

With respect to the expected value, note that

m_H = 115.3 GeV/c² (2808/.36 - φπ)⁻¹ × 10^-2 eV m⁻¹ s [(82944 - [δ² + (28.08/.36)²/82944]) × 10^-5]⁸³ kg.¹²

Using the reported results, the possible range of the Higgs boson mass in electron volts is approximately between m_H (2808 - 2^1/2)^-2 × 10 eV m⁻¹ s and m_H (2808 - 2808/10²)^-2 × 10 eV m⁻¹ s, and in kilograms approximately between m_H [(82944 - [(δ/π)⁸-(δ/π)⁸/10²]) × 10^-5]⁸³ kg and m_H [(82944 - 10[.82944]^-4) × 10^-5]⁸³ kg.¹³

Finally, where the masses of the weak force carrier bosons, Z and W, are, respectively, m_Z = 91.1882 GeV/c² and m_W = 80.419 GeV/c², note that the possible mass of the Higgs boson is

m_H ~ π(m_Z+m_W)/δ,¹⁴

and, at the high end of the range of the possible Higgs boson mass,

m_H + m_Z + m_W  ~ 82944^1/2 GeV/c² ~ .82944³ × 10^-41 kg.¹⁵

Addenda

On September 4, 2000, Mr. J. Iuliano communicated to the writer his observation that 82944/2808 = 29.53846154, which approximates the number of days in the mean lunar synodic month, 29.5306.

On September 20, 2000, Mr. Iuliano forwarded a formula employing "the π dimensional constant 23" (where π⁵/(π + 23) α^-.5) and linking the fine structure constant with 2808 in the production of 82944, as follows: (2808 + α^-.5/100)^1/π × 23 82944^.5.  The writer's transcription of this formula, in terms of the analysis above, including note 6, below, (where is the rational product of Yahweh's triple designation in Exodus 3:6), is as follows: (2808 + α^-.5/100)^1/π × ([δ/π]⁸ - φ/2) 82944^.5 + ^-2/100.  This equation squared is approximately: [(2808 + α^-.5/100)^1/π × ([δ/π]⁸ - φ/2)]² 82944 + .82944⁸.
 

4 July 2012 Higgs Boson

See, on this web, The Higgs Boson & the Absolute Dead Center Cube: Predictions Within the Probable Range

Notes

¹ For the 'absolute dead center cube', see, on this web, Logically Outfitted Cube(s), and D.G. Leahy, Foundation: Matter the Body Itself (Albany, 1996), Section III.5, et passim. For the significance of 256 (=16²), see, on this web, Real Trinary Logic Geometric Series Infinite Iterative Sequential Summing. 1E33 is the inverse order of magnitude of the Planck length (l_P = 1.6160 × 10^-33 cm).  For the most recent recommended values of the fundamental physical constants, cf. P. J. Mohr and B. N. Taylor, "The 1998 CODATA Recommended Values of the Fundamental Physical Constants, Web Version 3.0," available at http://physics.nist.gov/constants (National Institute of Standards and Technology, Gaithersburg, MD 20899, 23 July 1999).
² For the triple-cube, see, on this web, Logically Outfitted Cube(s); see also Leahy, Foundation, Section IV.2, p. 524, n. 98.
³ For the L series, see Leahy, Foundation, Section IV.2, pp. 519ff.  See also, on this web, The Magnitude of Being and The Diagonal Logic of the Triple Absolute Dead Center Cube & Certain Fundamental Mathematical & Physical Constants.
⁴ For the 10 × 10 grid, see Leahy, Foundation III.2.
⁵ 7623 = 33² × 7. Analogously, 3.168E36 1E33 × 7 × 144π. 144π is the unique value of the 'absolute dead center cube'.  It is at once the length of the circumference of the circle circumscribing the face of that cube and the area of the circle in which each of the 36 equal subsquares of that face may be inscribed (cf. Leahy, Foundation, Section IV.2, p. 524, n. 98, and p. 525, n. 99).  See also, on this web, The Deep Epidermal Surface: The Cornerstone Construction Order, Minimum Order Tetrahedron Hypercube, & Absolute Dead Center Hypercube and Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube, where it is shown that for all cubes (x/6)⁴/x³ × 8x³/x⁴ = 162⁻¹, and uniquely for the absolute dead center cube that [(x/6)⁴/x³]² = (8x³/x⁴)² = 162⁻¹.  See, also, on this web, The Magnitude of Being.  Note that, where is the ratio at infinity of the total arithmetic value of the edge-sharing triangles to the total arithmetic value of the whole infinitely expanding triangle of digits produced by the iterative sequential summing of the real trinary logic geometric series (see, on this web, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers), 162⁻¹ × = 10/2808.
⁶ The integral product of the designation of Yahweh in Exodus 3:6 as אלהי אבדהם אלהי יצחק ואלהי יעקב ('the God of Abraham, the God of Isaac, and the God of Jacob') is 8.2944E26, while its rational product is , values such that [(8.2944E26^1/)^1/256 × 1E33]^−1/256/(82944/8)^.5 0.007297 353 58.  8.2944/ 8^.5/3^.5, the ratio of the diagonal of the base to the height of the smallest square-based pyramid the area of whose face is a whole number not 1 and one half the area of the base of the pyramid, and the sum of whose ascending edge and one half the base of its face is to the height of its face as φ : 1 (cf., on this web, Thinking Creation Ex Nihilo; cf., also, Leahy, Foundation, Section IV.2), at once the ratio of the relative length of the shortest diagonals in the logically outfitted triple cube to that of the diagonals in the crystal triple-Rubidium-3-cube (cf., on this web, Rubidium (37), Lanthanum (57) & the Logically Outfitted Cube[s]).  Further for , see, above, Addenda, para. 2. The 4th root of 8.2944 is a factor in the equation, (1E33 × 8.2944^.25/φ)^−1/256/10368^.5 0.007297 353 12, which is the physics value exact to the 8th place. For the uniqueness of the number 82944 and the presentation of the essentially mathematical reading of Hebrew and Greek texts, see Leahy, Foundation, Sections III.5-7 and IV.2. For 'integral' and 'rational' product, ibid., p. 357, n. 13, or, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product and Related Terms. Cf. also, on this web, 82944 & the Four Fundamental Forces & the God Particle, and The Difference.
⁷ Cf. Leahy, Foundation, Section IV.2, pp. 524ff.
⁸ Cf., on this web, Real Trinary Logic Geometric Series Infinite Iterative Sequential Summing.
⁹ Cf. Leahy, Foundation, Section IV.2, pp. 486ff.
¹⁰ See, on this web, Sorted Diagonals.
¹¹ In this equation δ is the Feigenbaum bifurcation constant, 4.669201609102990.  For δ/π, see, on this web, Rubidium (37), Lanthanum (57) & the Logically Outfitted Cube(s).  Note that not only is the possible mass in electron volts of the Higgs boson a function of 2808, but that in kilograms the possible mass of this particle responsible for the sudden inflation of the universe in the first billionth of a second of its existence is a function of 82944, the common coefficient of the four fundamental forces, as demonstrated elsewhere on this web at 82944 & the Four Fundamental Forces & the God Particle.   In the recent test of QED in the highest possible electric fields at the Experimental Storage Ring in the GSI lab in Darmstadt, Germany, the measured value of the ground-state Lamb shift in uranium ions, U91+, is 468 eV = 2808/6 eV, (see Physics News Update, October 10, 2000. Online. Available: http://www.aip.org/physnews/update/506-2.html. October 14, 2000).
¹² For the ratio, 2808/.36, see, in the text above, "What the dream added."
¹³ For the results from CERN, see P. Igo-Kemenes, "Status of Higgs Boson Searches." Online. LEP Seminar, November 3, 2000, CERN. Available: http://lephiggs.web.cern.ch/LEPHIGGS/talks/pik_lepc_nov3_2000.pdf.   November 4, 2000.
¹⁴ For the values of Z and W, cf. D.E. Groom et al. (Particle Data Group), "Index for Gauge and Higgs Bosons Summary Table." Online. Eur. Phys. Jour. C15, 1 (2000). Available: http://pdg.lbl.gov/2000/gxxx_index.pdf. November 8, 2000.  For the ratio p/d, cf. the text above, including n. 11.  Where m_H is the possible Higgs boson mass, note also that m_Z+m_W ~ (1+δ/π×10^-3)(10φ²/2)² GeV/c² ~ m_Hδ/π.  See, on this web, W Boson Mass & the Mathematics of the Absolute Dead Center Cube (dated March 2012).
¹⁵ .82944³ × 10^-41 kg ~ (2808/.36)^−1/16 × 10^-41 kg ~ d²/10 × .82944⁸³ kg.  82944^1/2 GeV = (8.2944 × 10²²)^1/2 eV.  8.2944 ×10²² = the integral product of נקדת האפס של תנופה ('point zero of energy'/'dead center').  (8.2944 × 10²²)^1.5  = the linear product of Genesis 1:1, בראשית ברא אלהים את השמים ואת הארץ ('In the beginning God created the heaven and the earth').  Where 21 and 34 are Fibonacci numbers, and 21 ~ 82944^1/2/2φ⁴ and 34 ~ 82944^1/2/2φ³ and the decimal point ~ the point of division in extreme and mean ratio, 10^-21[10^-34([8.2944 ×10²²]^1.5)] = (.82944³ × 10^-41)^1/2.  For 8.2944 ×10²² and (8.2944 ×10²²)^1.5, cf. Leahy, Foundation, pp. 505f., where it says, "Now the mind stands in the center of the absolute circle of absolute thought."  Further, with respect to the possible Higgs boson, the center of the absolute circle of absolute thought additionally manifests itself - paralleling the procedure equating the linear product of Genesis 1:1 and the coefficient of mass in the sum of the three bosons - as follows, now starting with the physical coefficients: where 82944^1/2 GeV/c² and .82944³ × 10^-41 kg are equivalently the mass sum of m_H + m_Z + m_W, the coefficients of mass in the equivalent sums, designated, respectively, x and y, are related in such a way that - where 42 and 68 are the doubles, respectively, of the Fibonacci numbers 21 and 34, and where 42 ~ x/φ⁴ and 68 ~ x/φ³ and the decimal point ~ the point of division in extreme and mean ratio - 10^-42[10^-68(10⁹x)⁶] ~ y, and in such a way that the integration with x of the powers of the rescaling negative exponentials in this last equation yields x- [x²-(-42 ×-68)^1/2]^1/2 ~ 116^−1/2 ~ the inverse square root of the coefficient of mass of m_H in the original equation.  Further for 82944, see, above, notes 6 and 11.  Note also that .82944⁸³ ~ φ² × 10^-42.  With respect to φ-proportionality - beautifully manifest here in understanding the possible Higgs boson - in understanding in general the fundamentals of the physical universe, cf., on this web, The Golden Bowl Structure: The Platonic Line, Fibonacci, and Feigenbaum and The Physical Constants: Functions of the ‘Golden Bowl’ Arrangements on the Φ-Level of Existence Itself.

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