Two dimensional time 5.2.2

time direction ~ direction of change

multiple time directions ~ multiple directions of change

— Me@2019-12-22 04:38:47 PM


the first dimension of time ~ direction of change

the second dimension of time ~ direction of change of changes

— Me@2019-12-22 04:46:47 PM



2019.12.22 Sunday (c) All rights reserved by ACHK


And what of that truth which more than anything else gives me confidence in Hong Kong? The truth is this. The qualities, the beliefs, the ideals that have made Hong Kong’s present will still be here to shape Hong Kong’s future.

Hong Kong, it seems to me, has always lived by the author, Jack London’s credo:

“I would rather be ashes than dust,
I would rather my spark should burn out in a brilliant blaze,
Than it should be stifled in dry rot.
I would rather be a superb meteor,
With every atom of me in magnificent glow,
Than a sleepy and permanent planet.”

Whatever the challenges ahead, nothing should bring this meteor crashing to earth, nothing should snuff out its glow. I hope that Hong Kong will take tomorrow by storm. And when it does, History will stand and cheer.





— Christopher Francis Patten



2019.10.13 Sunday ACHK


Event Realism | 事件實在論 6.1


exist = can be found


— Me@2013.09.25


If the consequences of an event cannot be found anymore, that event no longer exists.

— Me@2019.09.05


The surprising implications of the original delayed-choice experiment led Wheeler to the conclusion that “no phenomenon is a phenomenon until it is an observed phenomenon”, which is a very radical position. Wheeler famously said that the “past has no existence except as recorded in the present“, and that the Universe does not “exist, out there independent of all acts of observation”.

— Wikipedia on Wheeler’s delayed choice experiment



實在 ~ 堅實地存在



— Me@2019-09-05 09:08:41 PM



2019.09.05 Thursday (c) All rights reserved by ACHK

Visualizing higher dimensions

The trick of visualizing higher dimension is: not to visualize it.

— Wikipedia

— Me@2011.08.19


Besides trying to visualize, there are other methods to understand higher dimensions.

— Me@2018-10-28 04:28:01 PM



What is the meaning of visualization?

— Me@2018-09-02 4:35 pm


feel ~ receive all the data at once

(This definition is not totally correct, but is useful in the meantime.)

visual ~ feel at once through eyes


you can visualize a 3D object ~ you can see all of a 3D object at once

you cannot visualize a 4D object ~ you cannot see all of a 4D object at once


Actually, you can only visualize a 2D object, such as a square.

You cannot visualize a 3D object, such as a cube.

That’s why the screen of any computer monitor is 2 dimensional, not 3.

— Me@2018-10-28 04:32:41 PM



2018.10.28 Sunday (c) All rights reserved by ACHK

Life, 3

生命 3


We exist in time because time is change.

Growing is part of the definition of life. Growing is a kind of change.


Also, without time/change, there would be no thinking and no thoughts.

— Me@2017-12-26 11:42 am

— Me@2018-05-23 10:05:03 PM


time ~ change


Time is logically necessary if change is necessary.

— Me@2018-02-04 09:07:48 PM



2018.05.23 Wednesday (c) All rights reserved by ACHK

The language of Change 1.2

Energy conservation, 6.2 | Energy 5.2


time ~ change

energy ~ the ability of _keeping_ changing


constant velocity ~ the amount of an object’s change of position, measured with respect to its observer’s unit of change, is constant

s = \Delta x

v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}


kinetic energy ~ the amount of the ability of keeping changing an object’s position

\frac{1}{2} m v^2 ~ the square of (the amount of change of position, relative to the observer’s unit of change)



Energy difference is _not_ exactly a measurement of the amount of change, time interval is.

— Me@2018-02-20 09:39:30 AM



2018.02.20 Tuesday (c) All rights reserved by ACHK

The language of Change

Energy conservation, 6 | Energy 5


time ~ change

energy ~ the ability of causing change


1. a system of one single particle

2. has only kinetic energy

3. and that kinetic energy is conserved.

conservation of energy ~ an object’s potential amount of change of position, measured with respect to its observer’s unit of change, is constant

s = \Delta x

v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}

— Me@2018-02-15 02:21:20 PM



The above argument has a bug:

If the mass m is constant, the kinetic energy E_K should be proportional to velocity squared v^2, instead of velocity v.

E_K = \frac{1}{2} m v^2


However, the above argument is still technically correct:

When E_K is constant, v^2 is constant. In turn, the magnitude of v also remains unchanged.

— Me@2018-02-19 09:37:24 PM



2018.02.15 Thursday (c) All rights reserved by ACHK

Euler Formula

Exponential, 2


general exponential increase ~ the effects are cumulative

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

exponent growth

e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n

~ compound interest effects with infinitesimal time intervals

multiply -1

~ rotate to the opposite direction

(rotate the position vector of a number on the real number line to the opposite direction)

~ rotate 180 degrees

multiply i

~ rotate to the perpendicular direction

~ rotate 90 degrees

For example, the complex number (3, 0) times i equals (0, 3):

3 \times i = 3 i
(3, 0) (0, 1) = (0, 3)

multiplying i

~ change the direction to the one perpendicular to the current moving direction

(current moving direction ~ the direction of a number’s position vector)

exponential growth with an imaginary amount

e^{i \theta} = \lim_{n \to \infty} \left( 1 + \frac{i \theta}{n} \right)^n

~ change the direction to the one perpendicular to the current moving direction continuously

~ rotate \theta radians

— Me@2016-06-05 04:04:13 PM
2016.06.08 Wednesday (c) All rights reserved by ACHK

注定外傳 2.6

Can it be Otherwise? 2.6 | The Beginning of Time, 7.3











— Me@2016-05-18 11:40:31 AM

2016.05.18 Wednesday (c) All rights reserved by ACHK