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The article “Atoms of Space and Time,” by Lee Smolin, in the January 2004 issue of Scientific American, attempts to answer a very fundamental question: is nature continuous or discrete? However, it appears that the author is already biased toward his hypothesis that nature is discrete.

Is matter discrete?

Smolin says on page 66, “the granularity of matter is old news.” Is that really correct? Has anyone proven that electrons cannot be broken into smaller particles? We have already seen that neutrons can be broken. It is only a matter of time when our technology will break electrons.

On same page Smolin asks, “…does the world evolve in series of tiny steps, acting more like a digital computer?” The digital computer is not a discrete device. Often we casually say that it uses only zeros and ones, but in reality it does not. If you put an electronic probe of an oscilloscope at any pin of a microprocessor you will find a continuous time electrical signal.

Are real numbers discrete?

On page 69 Smolin writes, “…the volume could be any positive real number.” He used such statements in several places. It seems that the author thinks real numbers are discrete. In fact hey are not. In all mathematics we use finite precision representation of numbers. But that is not the true representation. The integer 2 is really the real number 2.0000…000… with an infinite number of zeros. When we say 2.00124 we really mean 2.0012413568…9457… with an infinite number of decimal places, but our number is accurate to only five decimal places, so we do not write the rest of the digits.

Or he should treat all finite precision numbers of his equations as open intervals around the specified point. For example he should treat the integer 2 as an open interval (2-, 2+) where is a very small number.

Is calculus continuous?

Surely Smolin has used lot of calculus to justify his theory. But is calculus continuous or discrete? Consider the Derivative operator D[xn]. It produces nxn-1. Is this a continuous operation? No. If you plot the graphs of xn and nxn-1, you will see a large gap between them. The Derivative operator D peels off a function in discrete steps. This Derivative cannot be used to analyze the discreteness of nature. It is too gross for the author’s subject.

Are limits correct?

The concept of limits was visualized using a figure drawn on paper. In describing this figure we have used two contradictory notions. On one hand we said we are approaching a limit and on other we still used the same gross level view of the figure. When we approach a limit we must also magnify the figure to see exactly what is happening. If we approach 100 times closer to a point we should magnify the figure by 100 times or a thousand times to see the result. To observe microscopic things we need a microscope. It is the same thing as saying that we are moving closer and closer to a distant star and still thinking that the star will maintain the same small size. So we see that the fundamental notion of calculus, the limit, has failed to treat continuous and discrete behavior of nature in a consistent way.

Is Derivative a tangent?

Consider how we proved that the derivative is a tangent. Imagine the figure, a circle, and a line OP, starting at O on the circle, intersecting at Q and extending beyond to P. If we keep the point O fixed and move the point Q closer and closer to O along the circumference, then the line OP will move and become a tangent at O. We see the same fallacy here; we are not using a microscope. As the point Q moves towards O we must magnify the figure. If you do that then you will see that the figure is basically not changing, only becoming bigger and bigger, and the line will never become tangent. Thus to analyze atoms of nature we cannot use this derivative to represent rate of change of variables or tangent to a function. That will lead to inconsistent results. ]]>

The fact that something keeps you on this continuum at a consistent place is essentially the magic fact that somehow or other, when you look at it from far enough away, it looks like a continuum; when you zoom in very closely there’s no obvious reason why it should do that, and even less why the continuum it forms should have nice properties like one time direction and three space directions. ]]>

which means that the rip in the fabric of spacetime exists only as long as there exists energy to maintain it

btw, you can just tell me that I’m full of shite and I’ll shut it

another tack on whether or not time exists:

my watch works

i exist in the now

and not in the has-been or the will-be

and that’s pretty consistent

if time doesn’t exist

then something keeps me on this continuum

at a fairly consistent pace

observable to me ]]>

As in, if you look at a bitmap image closely enough, it’s a mess, but if you step back far enough that the discrete changes are smaller than your ability to measure them, it looks nice and smooth?

Or more like how the energy released from electrons dropping valences (light emitted from a flame) is in discrete pieces that corresponds to the drop to a lower, more stable orbit? But that at some point, the size of the energy being released compared to the size at which your point of view is becomes so great that everything gets blocky and non-continuous? But at our massive pov, it’s all very smooth, because we can’t tell that it’s a bunch of different discrete bits all mashed together?

(I’m grossly simplifying into HS/first-year engineering college chem/physics). I’ve yet to finish Greene’s “Elegant Universe”… ]]>