Insight Manuscript A version of chapter 5.
Archival Number: A404
Author: Lonergan, B.
pt 141, l. 1 of text (ts 1): ts has no comma after reasons
pt 141, l. 8 (ts 1): ts has four, crossed out and replaced by five.
pt 142, l. 6 (ts 1): ts has crossed out at end of this paragraph: `The reason why some expressions is [sic] invariant is easily discerned.'
pt 142, l. 12 (ts 2): ts has `Since the laws ...'
pt 142, l. -3 (ts 3): ts has `Descriptively, then, a duration ...'
pt 146, l. -14 (ts 6): ts has `Now mathematical expressions ...'
pt 148, l. -9 (ts 8): ts: `experience'
pt 150, l. 12 (ts 9): Paragraph began `The abstract intelligibility immanent in' This is crossed out and replaced by what is in pt.
pt 150, l. 16 (ts 9): ts had `may be named geometries.' This is changed to `are geometries.'
pt 150, par. Moreover (ts 9): Several stabs at this paragraph appear in ts, all crossed out. They read:
Moreover, the expression of the principles and laws of any geometry may be expected to be algebraic or, at least, to admit an algebraic formulation. Algebraic formulation seems to admit geometrical interpretation only through the use of reference frames and, in any case, unless
Moreover, a geometry applicable to
Moreover, if a geometry is to be applied to Space or Time, the application will occur through the use of a reference frame. For without any reference frame
pt 151, end of 3.1 (ts 10): ts had another paragraph here, but it is crossed out:
There is a further corollary. The validity of Euclidean geometry does not become a question for physical investigation in virtue of an interpretation of geometrical coordinates in terms of physical rods and clocks. Euclidean geometry, as a geometry, is valid independently of physics. But no unverified geometry is the intelligibility immanent in concrete extensions and concrete durations. And the task of determining the verifiable geometry falls to physics, not as an inquiry into rods and clocks, but in virtue of the empirical canon of complete explanation and in virtue of the involvement of physical principles and laws in spatial and temporal relations.
pt 153, l. -12 (ts 12): There is a first stab at the paragraph `First of all.' It is crossed out. It reads:
First of all, the existence of the problem should cause surprise to every follower of Galileo. For after all, Galileo had distinguished between the real and objective and, on the other hand, the merely apparent, and his criterion was the primary qualities
after all, the problem of distinguishing the merely apparent from the real and objective had already been undertaken by Galileo, and his solution was that colors, sounds, heat, and the like were merely apparent secondary qualities, while the mathematical dimensions of matter in motion were real and objective primary qualities. Now, however, it would seem that the eminently mathematical trajectory of a falling penny happens to be a multiplicity, and so there arises the question of distinguishing between the one real trajectory and the many merely apparent trajectories. Evidently, Galileo had
pt 154, l. 14 (ts 13): ts has `when we treat the notion of objectivity in Chapters 12 and 13.' Changed by hand to what is in pt.
pt 156, l. 5 (ts 14): ts adds to this paragraph: `Moreover, the only way to settle this issue is to determine what exactly one means when one uses the expression `at the same time.' This is crossed out.
pt 156, l. 13 (ts 15): several stabs from `he takes to cross' appear in ts, crossed out. They read:
he takes to cross. What comes first is an awareness of the duration of my own watching, and only in and through that duration do I apprehend the duration of his crossing
he takes to cross. The reason for this is simple enough. For, while the whole distance traversed is all at once there to be inspected, the duration of traversing is there to be inspected, not all at once, but only in successive bits. Nor is this all. If one supposed the possibility of a timeless inspection, one would infer
pt 157, l. -14 (ts 16): ts has `durations which we do not experience yet we do relate to the concrete durations that are experienced.' No change in ts, but changed by hand in B.
pt 157, l. -3 (ts 16): The following appears in ts, crossed out:
not exist. A statement of simulaneity is a statement about particular events at a particular time. There is no reason to expect such statements to be, not relative, but invariant. For invariance of expression rests upon the abstractness of what is expressed; and no abstract proposition refers to particular events at a particular time. Still, the demand for an objective, real, true simultaneity that is unique is, in more elementary terms, a demand that statements of simultaneity be invariant
particular events at a particular time. If it were true that events, simultaneous for one observer, must be simultaneous for all observers, then expressions of simultaneity would be invariant. They would fall in the same class as the expression, Twice two are four. They would not fall in the same class as the expression, John is here now.
pt 158, l. -12 (ts 17): ts had: `Time must be one, and so he appealed to the primum mobile, that grounded all other movements in the sky and on earth. The local movement of the primum mo
This is crossed out and text continues, but reads: `Time must be one, and so he appealed to the primum mobile, the outermost celectial sphere. There was only one such sphere, and it had only one local motion.
pt 159, l. -2 (ts 18): Several paragraphs are crossed out as an earlier version of at least part of section 3.6. They read as follows:
3.6 Still, the theory of special relativity has its paradoxes. If the distance between two points in one reference frame is measured by some number, S, then the distance between the same points in a relatively moving frame will be some other number, S'. Similarly, if the time interval between two instants in one frame is measured by some number, T, then the interval between the same instants in a relatively moving frame will be some other number, T'. Finally, there will be a similar difference between the numbers measuring in different frames the velocity of the same moving body. See Lindsay and Margenau, pp. 337 ff.
In so far as this paradox generates a problem in the conception of measurement, it provides the topic of our next section on Rods and Clocks. For the moment, however, we wish to restrict attention to the origin of the paradox in the relativity of simultaneity.
When we speak of the distance between two moving objects, we mean the distance between their simultaneous positions. Thus, the distance between two planes flying in the sky is, not the distance between the present position of one and a past position of the other, but the distance between the two at the same time. But, if simultaneity is relative, then different observers will select different positions as simultaneous and so arrive at different distances between the two moving objects. Accordingly, relativity of simultaneity involves relativity of distances; similarly, relativity of distances involves relativity of velocities; and relativity of velocities involves relativity of measurements of time intervals. Such is the general origin, then, of the paradox. But, the special theory of relativity supposes a relativity of simultaneity; it deals with reference frames which are systems of moving points; and it incorporates in the specifications of the points the consequences of the relative simultaneity that it supposes. Not merely does it effect synchronization in every reference frame by the formula, 2t = t' + t", but also it imposes on the coordinates of every distant clock the condition that
x2 + y2 +z2 = c2T2
where (x, y, z) are the coordinates of the clock and T satisfies the equation, 2T = t" - t'. In other words, the possibility of effecting synchronization in the same manner in all reference frames is that in each reference frame the coordinates of each point satisfy the requirements of the light-signal distance from the origin to the point.
pt 161, l. 5-6 (ts 20): ts has `any number of values'
pt 161-64 (ts 21-23): the ts had an earlier version of this section, now in A 383 (insitem4). See that locus for details.
pt 163, footnote: this note is part of the text in ts.
pt 165, l. 1 (ts 24): Ts has earlier attempts at this paragraph. They read:
Now the principal technique in effecting the transition from description to explanation is measurement. If we get beyond things as related to our senses, it is not by some preternatural gift of new senses, but by a pedestrian use of the senses we already have
only by introducing a new technique in the use of the senses we happen to have.
not by some praeternatural gift of new senses, but onlyby introducing a new technique in the use of the senses we happen to have.
We move away from colors and shapes as seen, from sounds as heard, from heat and pressure as felt. We seek relations between data. We evade the necessity of merely sensible relations between merely sensible terms by measuring and relating the numbers named measurements.
pt 165, l. 16 (ts 24): ts has `Thus, instead of noting that Tom is 1/10 taller than Dick, Dick 1/20 shorter than Harry, and Harry 1/20 of Dick shorter than Tom, ...'
pt 167, l. -12 (ts 26): ts has `bored. There is also an internal variation that is independent of our subjective states; and is measured roughly in terms of the length of days a process may be prolonged or quickly end by a dilatoriness or expeditiousness of its own; and so the size of a year is much greater than the size of a day. There are also ...'
pt 167, l. -10 (ts 26): ts has `jail' for `prison'
pt 168, l. -10 (ts 26: ts has `There remains measurement. It is a number that stands to unity, as the length of a measurable magnitude stands to the length of a standard unit There remains ...'
pt 169, l. 1: A discarded version of material from this point to the end of section 4 appears in Insitem4, A 384.
pt 169, l. 14 (ts 273): ts had `... that simultaneity is identical ...' changed by hand
pt 169, l. 18 (ts 273): ts had `... it may be expected that simultaneity is analogous to such notions as "now: and "then."' The change to `... it may be expected to be analogous ...' is made by hand, but there is no change of `then' to `here.'