Lowering the Wacky Factor in Extending the Three Dimensions
- A Linguistic Approach -
Volume I in the Millennium Orienteering Trilogy
121 pages, available online from ©2002-15 Timesizing.com, Harvard Sq PO Box 117, Cambridge MA 02238 USA 617-623-8080 - HOMEPAGE
Today, just as it was 300 years ago, the secret to knowing where you are is knowing what time it is.
(final sentence in Lost at Sea: The Search for Longitude, the video script for Dava Sobel's "Longitude.")
And to really know what time it is, you have to know what time is.
I know what time is, said Augustine, but if someone asks me, I cannot tell him.
The following overly long paragraph does some Sherlockian reverse-engineering from three paradigms that evolved in parallel: mainly the months observing their evolution driven by the precession of the early too-short moon-counts and the two Avrodites (April & Febru), the numbers, the days of the week, and the names of the planet-gods; mostly in English cuz it's such a great language for linguistic fossil hunting, but with input from Latin and Greek, French and German. ... Why are we humans so confused about time? Let us count the reasons. Time is based on comparing what little you and yours are doing with what something big and everywhere and repetitive and sortof regular is doing. So we had three things to watch = three time units alias watches (get it?): one watch (or maybe two) at the Moon ("By Ea, it's getting bigger...and smaller!") and two watches at the Sun: horizon-crossing and zodiac-crossing. The big thing we noticed first was probably the Moon because we humans have a tendency to notice contrasting, obvious things first (light-dark in this case) and close, blindingly obvious things later (Sun). The thing we probably noticed first was the zodiac-crossing Moon so we could hunt&gather, then herd&gather, then farm&breed-&plant&harvest more easily (=fewer mistakes =less repetition). So we gave the Moon activity names like Hunting Moon, Planting Moon, Harvest Moon... And these may have become our first count words alias numbers. At first we thought there were the same number of them in a year alias zodiac-crossing Sun as our fingers, ten: ten Moons in a year, (I don't have the original names handy but they'd be Ares (Mars), April, May, June, not.original.Julius, not.orig.Augustus, Septem (7), Octo (8), Novem (9), Decem (10). But as we migrated out of Africa and north into Asia and Europe, these Moons alias months were always slipping backward because they were only 29&abit horizon-Suns (alias days) long and the seasoning (alias zodiac-Sun alias year) seemed to be taking longer. So first we noticed there was one-leftover Moon, one-left, een leofen, e-leven, so we named an additional Moon for Aphrodite (April) because love was so much fun and the key to continuity, children, which were the key to an easier seniority (old age or sickness) and an easy end (the holy mawle); we may have named it VenerVenerus as Aveneris-Apeneris-Amneris-Avneris-Apneris-Aperis-Apris-Apros-Aphros-Aphro+dite's name gradually morphed in our mouths, varying be which peninsula we were on, the Greek or the Latin, and it finally got shortened to Phenphrus-Fenvrus-Fenbrus-Februs (I don't necessarily have these modifications in the right order, and there were likely several competing orders...). So we had Mars, April(dite - note BeLgrade>BeOgrad), May, June, (Julius), (Augustus), Septem, Octo, Novem, Decem, Februs = a double honoring of the love goddess covering two peninsulas, Greek and Latin. But the Moons slid further and we finally faced the fact that were actually two Moons left, twe leofen, twe-lve. So we added another one at the end, one with two faces to look backward and forward, Janus. So we had Mars, April(dite - note BeLgrade>BeOgrad), May, June, (Julius), (Augustus), Septem, Octo, Novem, Decem, Janus, Februs. We inserted Janus before Venus II (Februs) to surround angry redgod Mars/Aries with gentle love - "a soft answer turneth away wrath," and hoped that Janus was tall enough to look forward to the new year over Februs' head. But we got nervous about that and thought of a compromise: we'd move the beginning of the year back to Janus, since spring had slipped back there anyway, but just to make sure the wargod Aries/Mars wasn't angry about this displacement from first in the year, we would sortof keep him first by adding him to our first two moons; so, Janu-Aries and Febru- Aries, then safe to Mars=Aries, with, oops, a bit of confusion to swallow as 7-8-9-10 had to add two (7/8/9/10 +bi/2). And regularize everything on 30days/moon, not just actual 29. So 30x12=360. Oops, still slippage so what to do? Well, MEANWHILE, the days of the littleweak4sunmoon (4sunX7=28) 9-4-(FIVExFIVE) (29-9-(4x5)) had gone from Moon (1), Tiu (2), Thor (3), Frigga (4) like the fingers, or Luna Dzeu Dzeupater Venerus to fimfi/pumppump/FIVEbase when discovered a fifth wanderer (planet) to avoid neglecting, so we added Saturn (5) and got Moon, Tiu/Mercury, Thor, Frigga, Saturn: One Two Three Four Five in the count/dance words. So what to do about that slippage? How about we add a Saturnalia of 5 days to the end of the twelve 30-day "Moons" or months?! Pretty good. Only glitch left was the quarter day slippage that eventually necessitated Leap Year (when actually it was the other three years that LEAPed over the extra day in February!). At some point in here (gotta try for a better sequence) we realized we'd dissed the Sun, so we messed up the numbering one-two-three-four-five = Moon-Tiu-Thor-Friyya-Saturn by sticking the Sun on the front = Sun Moon Tiu/Dzeu/Mercury Thor/Dzeupater Friyya Saturn, which gave us a 6Sun Weakmoon = 6day week, so to avoid confusion we added the word "day" to the messed-up week count: Sunday Moonday Tiu'sDay Thor'sDay Friyya'sDay SaturnDay. There was still a slower slippage, so we made some radical modifications. We departed from 29 days per Moon to 30 (cuz a real Moon was little longer than 29 days anyway); good, that made 5 six-day weeks per "moon", six 60sun bimonths in a year, 60 sixday weeks in a 360-day year, all nice and even except for we needed a 5sun-alia (saturn-alia) to get to the less sliding 365-day year. But then why did we go on from a nice neat six-day week to a mind-boggling seven-day week? Musta been some war disaster that made us stop omitting the wargod from our week. The Babylonians already had the seven-planet, seven-day week didn't they? or did they just have the seven planets without applying them to a partmoon group of suns? Why do we have so goddam little documentation/notice/attention to the story of time? Why are there so few basic texts? Why is it not gathered somewhere? Why hasn't Ken Burns does a video history, at least of the American workweek?! Why is time below the radar? such an invisible part of the woodwork of life? Aaaaaaaaarrrrrrgggh! If I can turn that primal croak into a curmudgeonlyl growl, grrrmpf, maybe I can DO something about this. What a joke that kids including moi-même occasionally think there's nothing left to write a PhD dissertation about cuz it's all been taken, all done! ... So the Italic branch of Indoeuropean (and Hellenic?) added Mars right second after Moon/Luna and the Germanic branch had already added it (and kept it) in the middle of the 4-day week: Sun-Mon Woden Thor-Friyya and therefore had difficulty fronting a Germanic god to follow Friyya and wound up just accepting Saturn from Italic via the Romans. Back to why time confusing... After all these counting and tryingtofit (daytomonth &monthtoyear &daytoyear) and adding and naming sortof-improvements on the three main units, there was a developing need to have shorter units, like the six?perday&night "watch" for ships sailing&/or-rowing, and for prayers or orae, twelve per daylight, four per Watch. Sundials could help in cloudless daylight. Mechanical things were possible, starting with the one-handed clock that modeled the Sun's apparent movement from horizon to horizon (and assumed connection below the horizons. Why were humans confused about time? Stopping to dig into it, it's a wonder that time didn't turn us into blithering idiots. (And some of us it did!) So bottom line = conclusion/summary: What we're making-do / getting-along / workaround-ing with, with our insanely irregular time units, are the messy survivors of long and duplicated/parallel attempts by several different-language populations over thousands of years and sky observations to get some nice agreeable easy fitting-together units to compare our activities+inactivity to.
The author simply draws out the obvious definition based on highschool physics (density = mass/volume), based on Newton (to correct Einstein's assumption of convenience, that time may be regarded as the fourth dimension, nevermind his enshrining of an absolute (speed of humans' fastest perceptual sense, sight) at the core of his theory of "relativity"), and based on a preliminary tightening up of the first three commonly accepted dimensions using linguistic standards. Then, for good measure (pun), Einstein is invoked to identify the sixth dimension.
Volume I identifies all six of these "dimensions" or senses of measurement, on the basis of linguistic factors, as-yet unconnected highschool physics, the first two definitions in Newton's Principia, and Einstein's famous e = mc2. The full, tightened, six-set paradigm (there are more than six but we'll pause here and take time to get everyone "on board"), in the form of a series of stepped formulas, is, first simple, then annotated:
nothing x perceptibility = speck (prerequisite for measurement)
speck x length = lineness (1st measurement, or "dimension")
line x width = area (2nd dimension)
area x height = volume (3rd dimension, of which space is a special case)
These are the familiar "three dimensions." But notice now that we have "neatened them up." there's a new feature: they now have not only cardinality, but ordinality. Order is now important - and fixed. It is not optional or arbitrary or capricious. No longer can we say, lwh, or hwl, or whl, or hlw, etc. Each builds on the previous and is lethally flawed without it. Or if we were running the series in reverse, each subtracts from the previous and is meaningless without it (for example, volume x *flatth= area, area x *narrowth = line, line x *shortth = speck, speck x invisibility = nothing). So we can build further without "creeping ourselves out" with woo-ooooo, "higher dimensions"! -
volume x density (or velocity"', of which gravity is a special case) = mass (4th dimension, of which matter is a special case)
mass x velocity' = momentum (5th dimension, of which time is a special case)
momentum x velocity" = energy (6th dimension, of which light energy is a special case)
Note that skipping momentum gives us: mass x velocity' x velocity" = energy, and substituting c (light) for v: mcc=e or e=mc2.
Annotated Presentation (Format: dimensional step, then basic formula or equation, then notes)
to 0: nothing x perception = speck,
where we could also say, nothing x notice = something (as in "I think there's something there")
or we could say, the invisible x perceptibility = the just barely made out (but not enough to measure)
0 to 1: speck x length = line,
where "speck" (or "point") has zero dimensionality (that is, perceptibility without measurability) and in this basic formula functions as a unit or a one (1), while on a graph it functions as the origin, that is, zero (0),
and where the term "line" is introduced on the analogy of the next two steps, to differentiate the "climbing terms" (such as length, width, and height) from the "plateau terms" (such as line, area, and volume)
1 to 2: line x width (or breadth) = area (or field or plane)
2 to 3: area x height (or depth) = volume (or space or room or bulk)
3 to 4: volume x density = mass (or quantity of matter, or 'body at rest'), from d=m/v in every highschool physics book and from Definition I at the beginning of Newton's Principia :
The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.
[See bottom of this page for reconstruction of Newton's first three dimensions from this definition.]
Note that Newton's reference to bulk as space in his explanatory paragraph clarifies its meaning of "volume."
Let's translate Definition I step by step:
The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.
The quantity of mass is the measure of the same, arising from its density and volume conjunctly.
The quantity of mass is the product arising from its density and volume multiplied together.
Compact: Mass is density multiplied by volume.
Mathematize: Mass equals density times volume.
In symbols: m = d x v
Transpose right-side terms: m = v x d
Transpose sides: v x d = m
Desymbolize terms: volume x density = mass: QED
4 to 5: mass x velocity (uniform or balanced) = momentum (or 'body in uniform motion'), from M=mv in every highschool physics book and from Definition II at the beginning of Newton's Principia :
The quantity of [balanced] motion is the measure of the same, arising from the [balanced] velocity and quantity of matter conjunctly.
[See bottom of this page for reconstruction of Newton's sixth dimension from this definition.]
Let's translate this step by step:
The quantity of momentum is the measure of the same, arising from the velocity and quantity of mass conjunctly.
The quantity of momentum is the product arising from its balanced velocity and mass multiplied together.
Compact: momentum is velocity multiplied by mass.
Mathematize: momentum equals velocity times mass.
In symbols: M = V x m
Transpose right-side terms: M = V x d
Transpose sides: V x d = M
Desymbolize terms: mass x velocity = momentum : QED
The qualification that the velocity here must be balanced or uniform is taken up in Newton's Definition III:
The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forward in a right line.
Naturally, there is no way to ascribe rest or uniform motion to a body except in relation to a minimum of five bodies. For example, given only Earth (E) and Moon (M), there is no way to ascribe rest or uniform motion to either, except that if M is at rest, E must be in uniform motion around it, and vice versa. So we can say EM (Earth is circled by Moon) or ME (Moon is circled by Earth) where the "-form" in "uniform" is a smooth circle (more precisely, a smooth ellipse).
However, introduce the Sun (S) and Venus (V), for example, and we have the same ambiguity relative to each and every pair, making for some 12 two-sets;
that is: uniform motion characterizes EM (Earth is circled by Moon) or ME (Moon is circled by Earth); or ES, SE; EV, VE; MS, SM; MV, VM; SV, VS.
This constitutes a "grammar" that accounts for the observed data with one "rule" of 12 parts.
If we ascribe rest to Earth and motion to the other bodies, and introduce non-uniform motion, we can reduce this grammar:
I.e: There is uniform motion between EM, ES.
There is non-uniform motion (ellipse with epicycle) between EV.
This gives us a grammar of two rules: one with two parts and one with one part.
However, if we ascribe rest to the Sun instead of anything else, we can eliminate the non-uniform motion, explain all the data with just uniform motion again, and reduce the original grammar even further:
I.e: There is uniform motion between SE, SV, and EM.
This gives us a grammar of one rule with three parts. Being simpler, it is therefore the better grammar, having captured more powerful generalizations, that is, deeper levels of generalization (or despecification) that still account for all the data - and can generate potential data that we can now look for.
(See Chomsky's Syntactic Structures for this grammar&rule talk and the concept that the best grammar is the one with the fewest rules because it reveals the "most powerful generalizations." Furthermore, we believe that Chomsky's thinking here reveals the mechanism of the repeated extension of self-interest, a vital process in human progress, since "there is no such thing as altruism or selflessness but only specifiably extended self-interest," or in scientific terms, "there is no such thing as objectivity, only specifiably extended subjectivity" or viewpoint, etc.)
Also, in M=mv, where M is momentum, m is mass and v is velocity, we have a generalization of the first half of Einstein's famous e=mc2, rewritten e=mcc, generalized to e=mvv, and split into e=Mv" and M=mv'. Note that c is the velocity of light, and as such, it differs from a generalized dimensional concept by having a specific value: 186,000 mi/sec. So the sixth dimension, energy, at least in Einstein's supposedly relativistic conceptualization, is tied to his absolutization of the fastest human medium of perception, sight (and light).
The best way to regard time is as a plateau concept like line, area, volume, mass, momentum and energy, rather than as a transitional concept like length, width, height, density, velocity and celerity. However, although on the same plateau level as momentum, time is a special case of momentum, and momentum is a general case of time.
Time is a reference momentum similar to the reference mass embodied in the platinum-iridium pound cylinder maintained in London or the platinum-iridium kilogram cylinder maintained at Sèvres; that is, time is a special case of momentum, with its reference mass, surface mark and reference-line termini neglected, specifically (in the small unit, the day), a rotational momentum referenced to the mass of planet Earth as measured by an arbitrary reference mark on its surface, the Greenwich meridian, and a reference line between its center and an arbitrary outside point, the shadowless noonday sun - that is, the reference mass of planet Earth and its rotational velocity judged to be constant enough by the passage of Greenwich directly under the noonday Sun, have been neglected to the point of partial amnesia, but with standardization and repeated refinement based on observation, averaging, and now, particle decay.)
Time, as the all-pervasively, comprehensively quantifying measure, is also the Great Integrator and Equalizer and Leveller. As the Great Leveller, time answers the same question of all deeds, great or small : "how long did it last?" and it treats them all the same way it treats inactivity : "how long did it last?" It treats the lives of great people the same as ordinary people - "how many years did they live?" It treats the lives of people the same as insects - "how long do they live?"
In our opinion, Einstein mistreated the concept of time dimension. Our argument goes like this.
"Relative" and "absolute" are opposites. "Relativity" and "absoluteness" are opposites. But Einstein betrayed his Theory of Relativity when he absolutized the speed of light, regardless of viewpoint, or speed and direction of viewpoint, relative to, for example, a photon under observation (though obviously photons have to be observed in a faster-than-photons medium). Basically this was a type of anthropomorphism or anthropocentrism (in psychologeze, "projection") because it absolutized our best (fastest), commonly agreed, human perceptual sense, namely, sense of sight.
Einstein's fundamental metaphor, riding on a light beam, got him off to a bad start because it mixed together and merged subject and object, observer and observed, and confused all subsequent thinking by essentially introducing a second unacknowledged viewpoint, the viewer astride the photon (and the viewer watching the photon-horse whizzing past). And significantly, in entertaining this fundamental metaphor, the mind (dba viewpoint) slides unaccountably back and forth between the ridable photon and a standpoint from which the fly-by can be viewed. This introduced a huge too-obivious-to-notice unaccountability, as when a child asks 'why?' and a parent says, 'because I say so.'
To absolutize, or constantize, the energy dimension in terms of light energy, Einstein then had to move the flexibility-adjustability-variability somewhere else, and he wound up sacrificing the constancy (in terms of the unidirectionality and irreversibility) of the time dimension and thereafter coming up with all kinds of nonsense, like arriving back from a light-speed trip before leaving, etc. And it is an embarrassing disgrace to contemporary physicists including Stephen Hawking that they are not onto this can of worms and dismissing time travel out-of-hand.
Another way to cut to the root of Einstein's nonsensical foundation for time travel is to point out the misleading functioning of the time line metaphor. An earlier metaphor was the circle or cycle, which facilitated the unchanging repetitiveness of human life in the feudal and prior periods. This circular metaphor was reinforced by the sundial and the clockface and the dial of the analog watch, especially in the case of one-handed clocks and watches (still *available!). In moving beyond the feudal period, we should have moved from repetitiveness to progress by combining circle and line into spiral, but it can't be a loose spiral: it has to be a tight spiral with ordinarily negligible sideways displacement of the circle, as that of the rotating Earth around the Sun. This ordinarily negligible displacement is the key to EInstein's mistake, however, because it means that the clock we use to measure travel has to be on the same scale as the travel; for example, Earth surface travel can accurately be measured by comparison to the Earth-rotation clock. However, intergalactic travel has to be measured, if multiple-decimal accuracy is desired (as in the claims of arriving before departure). by comparison to the MilkyWay-rotation clock or the local-galactic-cluster rotation clock. Why? Because in doing his calculations, Einstein failed to account for the series of teensy, ordinarily negligible displacements inherent in the scaling-up of the tiny Earth clock as it revolves around the Sun and of the Sun clock as it revolves around Sirius (if Ouspensky- and through him, Gurdjieff-pupil Rodney Collin is correct in his Theory of Celestial Influence) and of Sirius as it revolves around MilkyWay center and of MWcenter as it revolves around localcluster center... Another angle? Reverse (or accelerated) time travel would involve reversing (or accelerating) every motion in the Universe, from the nanocosm to the megacosm = not gonna happen. Anyway, the sturdy time metaphor of a spiral within a spiral within a spiral, all tight spirals, brings up the possibility of loose spirals and/or roughly 90-degree tight-spiral displacement, and takes us to the next sense of measurement, or "dimension," the sixth.
5 to 6: momentum x celerity (non-uniform, unbalanced velocity) = energy.
Note also that the shortcut span from dimension 4 to 6 is given by the general form of Einstein's famous equation,
e = mc2 or mc2=e or mv2=e.
Note also that a skewed traverse of the span from dimension 4 to 6 is given by:
mass x acceleration = force, which may be regarded as a 1-1/2 level climb from 4 to 5-1/2.
force x displacement = work (i.e: vectored energy), which may be regarded as a 1/2 level climb from 5-1/2 to 6.
If Newton had completed the three-set, his third definition, instead of changing the subject, would have been something like the following: The quantity of unbalanced motion is the measure of the same, arising from the [unbalanced] velocity and quantity of balanced motion conjunctly, or
The quantity of energy is the measure of the same, arising from the celerity and quantity of balanced motion conjunctly.
If Newton had only made this progression from dimensional level 5 to 6 his third definition instead of doubling back and doing 5 to 4 (in the reverse direction), we might have avoided a lot of the subsequent confusion based on Einstein's thrusting momentum or balanced motion aka time into the 4th dimensional slot instead of its proper 5th slot.
Note that this extended version of the dimensional paradigm accountably relates, indeed interweaves, the four modern "elements" of space (3rd), time (5th), matter (4th) and energy (6th). (Recall the four ancient "elements" of air, earth, fire and water.)
In supporting Newton's identification of mass rather than Einstein's convenience of time as the fourth dimension, and identifying time, non-arbitrarily, as a special case of the general fifth-dimensional variable, momentum, Volume I is potentially the most sensational of the three volumes. The book then explores some light that the now-established standard dimensional hierarchy of the six basic senses of measurement alias "dimensions" can cast on human progress, and its potential coincidence with social evolution as divided into six great social-science ages (discussed in Vol.II).
On the fourth dimension, see also websites -
On the sixth dimension, see also websites -
[we haven't even begun on this one, so again, let us know at firstname.lastname@example.org if you find some good websites.]
Note the economic connection here:
the Market is a great natural organism whose 24/7 function it is to reconcile every level and type of self-interest. The Market is the agora, the meeting place, where to the little marked pieces of metal and colored pieces of paper called "money" is extended the respect that each human has for his/her own life, quantified in time units. So the Market is where time units are converted into monetary units; that is, units of time or standardized momentum (5th dimensional, not 4th) are converted into units of money or standardized energy (6th dimensional), in accordance with translating and unpacking e=mc(2) where c=speed or unvectored velocity in a fixed large quantity, into e=mv(2) or mv(2)=e, where v=velocity or vectored speed in a variable large quantity, and then into mv=M (momentum) and Mv=e. See booklet Defining Time. This special case of momentum aka time is essentially just a standardized measure based on standardized motions (Earth rotation, Moon revolution, Earth revolution) which have been abstracted (i.e., generalized/despecified by fractionalizing and/or multiplying) for use in measuring stillness as well as motion/movement, or inactivity as well as activity. The hubbub of multiple exchanges of services/products for symbols (& vv.) giving rise to an economy-defining currency (stable symbol) is parallel to the hubbub of Earth and Moon motion generalized into multiple repetitive satellite and planet motion giving rise to a way to a solar system, or megastar system (if Rodney Collins is right and there's an intermediate center between Sol and MilkyWay-center), or galaxy, or galactic cluster, or universe. And functioning 24/7 as it does, the Market is the economy's heart, and when it stops ... no economy.
Now an attempt (a work in progress beginning 4/4/2015, cuz just found Gleick's "Isaac Newton" last Sun.3/29 @ Barrow Bks, Concord) to reconstruct the full six-dimensional paradigm from Newton's actual formulation of the 4th and 5th dimensions in his definitions I and II of the Principia:
(4) The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.
(5) The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.
4. The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.
3. The quantity of space is the measure of the same, arising from its area and height conjunctly.
2. The quantity of area is the measure of the same, arising from its line and width conjunctly.
1. The quantity of line is the measure of the same, arising from its unmeasurable unity and length conjunctly.
It's really difficult to imagine what wording Newton would have used in the runup to writing the Principia, but this attempt may alert Newton scholars in poring over his voluminous notes, and they will find such a scheme, hitherto unrecognized for what it is. E.g., it may just be in the form of a list or table of words.
5. The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.
6. The quantity of energy is the measure of the same, arising from the projecticity and quantity of motion conjunctly.
7. The quantity of power is the measure of the same, arising from the abeyance and quantity of energy conjunctly.
Newton played around with climbing/descending terms that had opposites, as gravity-levity, density-sparsity, velocity-tardicity, so projecticity-retracticity, abeyance-activation... I think he had a kind of silliness, different from Mozart's but just as necessary and generative of 'creative' = precedent-extending thinking, reflected in his conceiving "a series to square the hyperbola...and carried out the calculation to 55 decimal places: in all, more than 2000 tiny digits marching down a single-page in [his "Waste Book"] (Gleick, 39) so that "Years later he recalled: 'I am ashamed to tell to how many places I carried these computations, having no other business at that time: for then I took really too much delight in these inventions.' " (Gleick, 210). Of course, this could be called with anachronistic hindsight "obsessive compulsiveness" but such tasks function as reassurers, confidence rebuilders after sorties into the unknown, And to what audience was he recalling with shame, or was he smiling when he said "I am ashamed to tell to how many places..."? And in those later years, what if anything had taken the place of those too-far compulations? And are we not being a little naive in painting him now as asexual in view of his handsomeness, his 2-3 stepsisters, his sins including "peevishness with his sister(s)" (Gleick,p.__) and a list that includes "uncleane thoughts words and actions and...learning pleasure more than Thee" (Gleick,p.21) and the survival of only one piece of family correspondence, which includes "your sisters present thai[r] love to you" (Gleick, 33), What did the lost letters include granted correspondence may not have been too private in the 1600s and therefore self-censored?
I feel I should be able to position 'gravity' somewhere in this paradigm.
What if, in running the paradigm in reverse (doable in Newtonese??), "up": mass x velocity = momentum; in reverse ("down"): momentum x (uniform) tardicity = mass, what if we said,
momentum x gravity = mass?
Then standard "up" would be:
mass x levity = momentum, and uniquely,
momentum x velocity = energy,
(reversal: energy x tardicity = momentum)
thus avoiding the inelegant use of "velocity" at two different levels as some people use "length" (lxl=area).
(This implies that much of the quest for the GUT = grand unifying theory, at least the "Integrate Gravity!" part, is the kind of terminological sloshiness that confronted Newton, as described in Gleick's "Isaac Newton" around p.44, and that Newton did not completely clear up. And as usual, the confusion is compounded by the involvement and instirring of our own viewpoint according to the rule, 'The closer, the harder to see clearly.')
This could imply a reperception of momentum as non-moving motion, since it's moving, sortof, but still in the same general place; compare the boomerang. This is in line with the self-denial of every dimensional climb, the general feature of each being "minimal necessary departure from status quo," or "being as similar as possible without just being the same."
And "levity" is sortof the minimal oomph needed to just "get it up" - no complicating thisorthatwaying needed or wanted. What do they call it when eg: the Moon always has its same side toward us? "Tidal locking" or "gravitational lock" or "captured rotation"?
Then the directional connotation of "velocity" that differentiates it from "speed" comes in to direct the definitional component of "energy" in a (relative-to-immediate reference moon, planet, star...) "straight" or tangential line, in distinction from rotation.
And what compounded our confusion was the deceptively simple-sounding statement that "a body remains in a state of rest [mass] or of uniform motion [momentum] unless acted upon by an 'external' force." Because this is actually a 5th to 6th dimensional statement, and "state of rest" should not be included without a correction of the terminology to:
"A body remains in a state of 'rest' = relatively stationary positioning unless acted upon by an 'internal' force = a force internal to the mass or gravitational system of which the body has been an integral albeit separable part."