Not just three — we can extend Cartesian System to show as many orthogonal coordinates as we like

Do you think, we can’t show more than three orthogonal coordinates through the Cartesian System which we have been using to show only the X-Y-Z coordinates of an object?

No, it is not so.

Not just three, we can display as many orthogonal dimensions as we like — through the same Cartesian System which we thought limited us to show just three orthogonal coordinates.

Let us see for instance, how we may show as many as “Seven parameters of time”, using the same X-Y-Z System of coordinates of which, we thought — can’t show more than three coordinates.

Representation of the “Seven parameters of Time” using the Multidimensional Version of the Cartesian System

Just look at any analogue clock you may have been using in the past or, possibly, maybe using even today.

It does not have more than three arms — the hours-arm, the minutes-arm and the seconds-arm.

We can very easily show the number 1~12 the hours–arm may be pointing toward along the X-Axis; the number the minutes-arm may be pointing toward along the Y-axis and the number the seconds-arm may be pointing toward along the Z-axis.

If we want to show the additional parameters of the time, say, the year, the month and the date also, it calls f0r showing as many as six parameters.

If we add even the system of time-measurement, say, whether we are referring to the Gregorian System of the time-measurement or the Hijri system of the time-measurement or say, whether the Samvat System (the Hindu System) of the time-measurement — it calls for displaying as many as seven parameters, which can be displayed as shown in the following diagram, using the Cartesian System of three orthogonal axes.

It shows the dimensions (D1~D7) of time along the following axes.

The calendar such as Gregorian is designated by D1 through a code such as “Gr”, or any other calendar along the X-axis.

The year is designated by D2 along the Y-axis.

The month is designated by D3 along the Z-axis.

The date is designated by D4 along the ZX-axis (X-branch of the Z-axis).

The hours are designated by D5 along the ZXY-axis (Y-branch of the ZX-axis).

The minutes are designated by D6 along the ZXYZ-axis (Z-branch of the ZXY-axis).

The seconds are designated by D7 along the ZXYZX-axis (X-branch of the ZXYZ-axis).

The Y-axis shows the years say, 2017, 2018, 2019, 2020 and so on.

The Z-axis of each year has twelve divisions — one division for each month.

Each division of Z-axis has an X-branch which has up to 31 divisions — one division for each date.

Each branch of ZX-axis has a Y-branch which has 24 divisions — one division for each hour.

Each branch of ZXY-axis has a Z-branch which has 60 divisions — one division for each minute.

Similarly, each branch of ZXYZ-axis has an X-branch which also has 60 divisions — one division for each second.

We can display even all parameters of the so-called Celestial Clock also, much the same way, in the following manner.

The manner in which we may display even all parameters of the Celestial Clock using Multi-dimensional Model of Cartesian System

When we had no analogue clocks, people used to define the time when some event may have taken place by telling the year, the month, the date, whether it was the bright fortnight or the dark fortnight and which House was occupied by the Sun (for the daytime) and which House (or which — Lunar Mansion) was occupied by the Moon or the planets such as Mars or Jupiter (for the night-time).

Though we can display the three arms of the analogue clock we have been using all along till the digital clock had not been developed even using the three axes (X, Y and Z) — the Hours 1~24 along the X-axis, the Minutes 1~60 along the Y-axis and the Seconds 1~60 along the Z-axis; unlike analogue clocks, the Celestial Clock has 9 geocentric planets, 12 astrological Houses, 12 Zodiac Constellations and as many as 27 Lunar Mansions (Fixed Stars) — totally, 60 parameters.

Do you doubt, it should not be possible to show many parameters using the Cartesian System?

If so, just recline on an easy chair and look at the following diagram.

This diagram shows not only the primal X and Y axes, it shows even the multi-dimensional axes YZ, YZY and four YZYZ axes.

The axis YZ sprouts out of the Y-axis, the YZY axis sprouts out of the YZ axis and the YZYZ axes sprout out of the YZY axis.

We may call this system “Multidimensional Model of the Cartesian System”.

Though only four planets have been shown in the diagram, we shall require similar YZYZ axes for the other planets also.

Much the same way, we may use YZYX-axes to display even the Lunar Mansions.