Meg5. New Tables

Overnight lock first, then the table.

Instant is Strength, not duration.
(N^)/m⁽²⁾ at Instant is compressive strength of area itself. Value: infinite. The generator of the cone is a straight line top to bottom; it cannot buckle in-member; it carries (N) without end. Water’s geometric acceleration $σ_{R}$ = m/s^2 crystallises to static cube strength N/m⁽³⁾ (concrete). Instant time is that measure. Empty the duration seat here.

That steals (N^)/m⁽²⁾ from Simultaneous on the old strip. Simultaneous keeps m.s and N^m.s⁽²⁾(moment). Instant keeps Strength. Freeze that or the columns will fight.

Build table — Time Family first

Time Family	Units	Signs / symbols	Math set	Platonic (optional)
Now	T=0 Continuous Seconds	toggle; A ± / -· B – / –	choice; not a set	—
Imaginary	no units; spent	^i^	C stance; (i) carries ticks	point (unseen)
Instant	(N^) /m⁽²⁾ = ∞	Strength of area; cone generator straight	locked cell $ -1 $; kink >(	tetrahedron (fold from flat)
	k.g.s^{^2}	package; (g) = mass seat + clamp	—	—
	m^{^4}	centroid	φ m4	—
Simultaneous	m.s	duration along support	joint F<i>M	triangle, wrap dθ
	N^{^}.m.s⁽²⁾	moment	—	—
	$\sigma_R$ m/s²	ring; whip; 2^{^ –}	Fib spring	—
Real	(h) RealSec	packet	R,πR, E=m^{(c^2)}	square / disc
	m^{^2}	area	—	—
Observational	ContSec	blunt second	Algebraic Real; PCA (C)	cube (filed)
	m^	length	—	—
Arena	^s⁽³⁾/m⁽²⁾ or 3^/sqrt2 i m	can; Parts not joint	G naked; S=φ^m(4)	sphere S⁴ as m⁴

Notes under the table (short)

Now is more fleeting than Imaginary, but both live on the continuous second line: it is the toggle. No unit. You do not calculate in Time = Now; you choose.

Instant Strength $\infty$ means: do not put a duration in that cell. Concrete N/m⁽³⁾is Instant Strength after water has crystallised — one dimension added by the cube.

Platonic column is a teaching hook, not a proof. Drop it on the first drawing if it crowds. Keep Instant = tetra (origami start), Real = square/disc, Arena = sphere.

Empty-cell rule (for the later read-off sheet)

Do not analyse from this member.

Grey those cells. The first-year lives in Observational × Engineering. Tick $m^4$ only as a pointer into Instant / Complex. Do not read Strength $\infty$ as a ContSec coefficient.

Build from this. Read-off matrix last.

Previously…

Draft work for final to highlight discipline appropriate readings

Maths graph (simple)

Axes are the joint, not spacetime.

			
x     m.s          Simultaneous time (support; Abb. 9)
y     m            Observational length
z     s^2          Instant area-of-time; disc
α     tilt of that disc to the rim

Plot is a disc at $\alpha$ on the $z=s^2$ plane, radius from $y=m$, duration along $x=m\cdot s$. Complex row is entered by ticking $m^4$ into that disc (centroid). No coefficients on this sheet. Geometry only.

Physics table (PCA habit)

Columns — Time family (left = blunt, right = fine):

	Obs. ContSec	Real (h)	Sim. $m\cdot s$	Inst. $kgs^2$	Complex $^\wedge i^\wedge$

Rows — stance / set (top = practice, down = sets):

Row	Who	What they read
E Engineering 1st year	practice	$f=\mathrm{practice}$ ; $\sigma_R$ ; $pr/t+\sigma_R$ ; tick $m^4$ only as a pointer into the Complex column
M Maths	sets	$\mathbb{N}$ split; Fib; $\varphi\,m^4$ ; $1^{\land} / φ \Rightarrow φ -^{\land} 1$
P0 Observational physics	Algebraic Real	ContSec; $e^{μθ}$; SI if they insist
P1 Real	growth face	(h); $E=m^{(c^\wedge 2)}$; $e^\wedge$
P2 Simultaneous	joint	$N^\wedge/m^{(2)}$; $F\langle i\rangle M$; capstan $\sigma_R f/c$
P3 Instant	contact	$N^\wedge m/s^2$; $k\cdot g\cdot s^2$; kink $>($
P4 Arena	Parts, not joint	$\mathbf{G}$ (no units); (g) vs $\sigma_R$; $\rho_{Ross}$

PCA coefficients sit in E × ContSec and E × Sim cells — the old table, now with $\sigma_R$ instead of a nameless factor. Deeper rows do not invent new coefficients. They say which member that factor was hiding in.

How to read (student rule)

			
Pick row   = how deep you are willing to stand
Pick column = which member you are calculating in
Carry tick  = next move (count or exp)
Stop at E if you are building
Open M or P only if the coefficient will not sit still

		

Example: tank hoop.

			
E, Sim     σ_θ = pr/t + σ_R
E, ContSec same number filed as a PCA C
P2, Sim    σ_R f / c  =  e^{μθ}
P4, Arena  G naked; do not give g a second m/s² line

Cells to letter first (the “set” you can see)

	ContSec	(h)	$m\cdot s$	Inst.	Complex
E	PCA (C)	(f) if held	$\sigma_R$, $N^\wedge/m^{(2)}$	—	tick $m^4$ →
M	count $0^\wedge$	packet	Fib spring	$\varphi\,m^4$	$^\wedge i^\wedge$
P0	$T_0,\Delta T=k$	—	—	—	skipped Real (blunder)
P1	—	$E=m^{(c^\wedge 2)}$	—	—	$e^{i\pi_R}$ intra-band
P2	—	—	$F\langle i\rangle M$	—	angel check
P3	—	—	—	$kgs^2$, kink	—
P4	$\mathbf{G}$	$S=\varphi^{m(4)}$	Parts $g,\sigma_R$	$S^4$	spent

Empty cells are not missing physics. They are “do not calculate that member from this stance.”

Drawing order

Maths graph: three axes + $\alpha$ disc.
Table as a ruled sheet, E row heavy, P4 faint.
One arrow from E’s $m^4$ tick into the Complex column — that is the only bridge the first-year needs.

Yes: coefficients from PCA are the E-row readout. Physics rows are the maths sets, named as members. Depth is optional. The tick travels.

	ContSec	(h)	\(m\cdot s\)	Inst.	Complex
E	PCA (C)	(f) if held	\(\sigma_R\), \(N^\wedge/m^{(2)}\)	—	tick \(m^4\) →
M	count \(0^\wedge\)	packet	Fib spring	\(\varphi\,m^4\)	\(^\wedge i^\wedge\)
P0	\(T_0,\Delta T=k\)	—	—	—	skipped Real (blunder)
P1	—	\(E=m^{(c^\wedge 2)}\)	—	—	\(e^{i\pi_R}\) intra-band
P2	—	—	\(F\langle i\rangle M\)	—	angel check
P3	—	—	—	\(kgs^2\), kink	—
P4	\(\mathbf{G}\)	\(S=\varphi^{m(4)}\)	Parts \(g,\sigma_R\)	\(S^4\)	spent