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Department of Electrical Engineering and Computer Science
6S19-PLEX Undergraduate Seminar -- Room: 36-155 (Classroom)
PS86-10: Problem Set 10 -- For Date: Tue 8699 -- Due Date: Tue 86916P300
The purpose of this first Problem Set for the Fall ‘86 Plex Seminar is to get you started in the practice of noting down and critiquing your use of your investigative and critical faculties. All too often we rush through, making do with fleeting thoughts coming up with a conclusion, and then rushing on to the next. It takes only a little practice to develop the ability to be more aware of what is going on when we think. In parallel with the main train of thought, we can ask some whys and wherefores and get a much deeper appreciation of how solid and well-founded our conclusions are, and of how we arrived at them.
This is particularly important in the study of Plex, for often the conclusions we will reach are surprising. In order to be sure that a conclusion is right, we’d better be sure about how we arrived at it. If we succeed in verifying every step, then the surprise becomes an interesting fact that we accept, because of our careful reasoning. The fact may still seem surprising, but that feeling we have about it will only be an artifact of its collision with more familiar views we have held for a longer time -- views that may well not be as well-founded as the new fact we have carefully verified.
The opening lecture, PL86-8: Now Is Forever New arrives at some rather surprising facts in rather short order. Specifically, no specific thing can exist before its time has come, but once its time has come, it exists forever. In brief, whatever "it" may refer to,
I.e. it must come into being when its time has come, and furthermore, forever thereafter, it cannot cease being.
That is surprising -- if it is a fact. If it is a fact, there are other surprising consequences. For example, there must be some profound sense in which time is strictly linearly-ordered and one-dimensional -- and furthermore, is unique! How does that special "time" (which in Plex actually is called thime) relate to the relative "time" of the Theories of Special and General Relativity, which is assumed to be the "time" of Quantum Theory, as well? [Plex's thime concerns pure existence, where "there" (pre-space "place" of two-or-more-ness, for "here" settles for/on just one, so it's absolutely certain where that place IS) and "time" coincide, which necessarily means that what Plex basically talks about along this vein is a sub-physical level re Big Bang cosmology, as it now known -- but possibly supplying a reason for Inflation, Dark Matter, and Strings, e.g.] -- It also is a consequence that there must be only one, unique, possible existence -- and this is it! We ourselves, each of us, came into being when and as we did because it (the whole universe) had to be that way, then. There are many surprises if "It can’t not be" is a fact. Is it?
The only way to find out is to carefully check and verify the steps of reasoning that lead to it as a conclusion. That’s what this Problem Set is all about.
What does it mean, "To verify a step of reasoning"? What is required to be sure about it? First of all, we must have some notation by means of which can write down something that will denote, concisely and precisely, some piece of thought. That means that whenever we look at that notation, we can with certainty associate with it just that piece of thought. That will serve to capture the elements of those "fleeting thoughts" and make them repeatable. If we discipline ourselves to play the game fairly, the chosen notation will denote, by reacquiring in our mind, and freezing it, just that one, elemental thought. If you think about, it, that’s what is involved when we see, read, and understand the meaning of any piece of notation.
There is a difference between the denotation, the meaning, and the signification of a notation. Thus, regarding Plex Time notation (PL86-8.3), its denotation is a specific instant; when it is written down and then is seen and read, its meaning is that instant which it denotes; and when it is written down in your own handwriting, as specified, it signifies that you, yourself, were present when that instant was chosen to be written. Since the Plex Time notation was completely new to you when I introduced it, the fact that you see your own, handwritten Plex Time notation does not allow you to deny that <you were present and participated in our shared experience>. You must agree that that assertion also is a fact. You do
of what you wrote. You know that -- by the definition of Plex Time, which had to be definitive for you, because it was entirely new to you. That’s what page PL86-8.6 describes. Check it out.
Just as the instant is the instant, whether or not it is the denotation of any notation, the self-referent, self-definition of any non-nothing is itself, itself, whether or not there is any notation for it. But if each of us uses the loop notation derived on 8.10-12 and attaches our signed, Plex Time date stamp to it with a squiggle, as in 8.13a, then we have a Picture Language Model of us all sharing that shared moment. We also know that as a fact. We similarly could make a PLM of any other state of affairs. We could see, read, and understand such a PLM and use it to verify a step of reasoning. The interpreted picturing of the PLM notation gives evidence that can be checked and rechecked.
"Evidence" comes from the Latin root videre -- to see. To have evidence verifying a fact, there must be something existing to see. Thus the First Definition of Plex (page PL86-8.14)
is not a matter of fact. It is, and must be, a matter of definition. Similarly, any non-nothing, i.e. any thing, must also be a matter of definition -- for otherwise it would not be what it is, by its self-definition, (which is not nothing, by definition). It is what it is, if it is not nothing. And that means it exists. Some consequences are summarized in pages 8.14-18. Review them now.
Which of the following denote a thing? Explain each answer.
a) an instant b) a moment
c) you
d) your Plex Time date-stamped self-reference loop PLM
e) our "shared experience"
f) a unicorn
g) a breaded veal pork chop
Carry out your solution to this problem in accordance with the Honor System Problem Set scheme referenced in the Preface pages viii and ix. List questions and observations, with page numbers, as you go along. Add comments and corrections. Get used to writing down your thoughts. Then, when you are ready, draw a breakline across the page, and write up your solution neatly and completely. My solution appears on the next page.
The key reference is 8.14c, which states that any non-nothing thing does exist. Even though we may sense differences in existence, it is the mere non-nothing-ness that counts. For example, does a part have more or less existence than the whole of which it is a part? No. We don’t have enough modeling machinery set up yet to make the distinction we sense there. (But we will, later.)
Other key references are 8.16a, which links instant definitively to existence, and then 8.17c, which ties that to moment in just that way. Here we see the distinctions, but again, only non-nothingness counts. The differences are nuances of our terminology, getting ready for later stages where definitive distinctions can be made. But so far they have no meaning.
The nuances of meaning continue to grow in 8.18a, which introduces instance (which 8.18c points out is interchangeable with a thing and an existence), but still only non-nothingness counts! Only later uses of these terms can bring out those differences!
Now notice how these ideas go together. If no thing at all exists, 8.16a shows there is no instant, and 8.17f says there is no moment, either. But if so, we would use the term nothing in those cases. So instant and moment, properly used, do denote a thing. And notice that, with respect to PLMing, in order to
that "properly used" comes quite naturally, in this case. If there’s nothing to see in some fashion in a PLM fragment, we’re more likely to say "nothing" is there, than to call it an instant or a moment, improperly.
As to you (part c of the problem), you certainly are a non-nothing thing. And your <Plex Time-date-stamped <<self-reference loop> PLM>> does denote <<you>at that time> of our shared experience, so it, too, denotes a thing. But what about our "shared experience"? Is that experience itself a thing? It seems funny to say so, because we sense a distinction between all of us merely collected together at that time versus the same but with us experiencing the experience of noting that instant. But any such distinction again is beyond making, within the terms we have definitively available to us, so far. Yes -- part e of the problem again denotes a thing, even though we still have questions about how each of our individual PLMs (are they instants?) collectively model something (is that a moment?) which -- ?? (does it itself have an experience?), etc., etc. We simply have to get used to matching our aspirations to the strength of meaning and modeling available to us as we go along. These all are good questions, but for the moment (pun!), only non-nothing-ness counts.
The last two parts of the problem crop up various places in later Plex developments and appear here only to make a point about nothingness (rather than non-nothingness). A unicorn is an imaginary animal being and thus is nothing in a physical sense. But being so well defined in our imaginations that we easily accept pictures of the mythical beast, it is only another name for nothing, in the physical sense. Such <physical-only <nothingness>> is special. In Plex, a unicorn is called a name-only thing. But because of the irreconcilable clash of meanings between "veal" and "pork", the syntactically well-formed expression "breaded veal pork chop" is anathema, in Plex. It is not allowed any meaning at all. It doesn’t even denote nothing -- in any sense at all.
End 10.1 Solution
Grade 10.1 Solution. Now
Try your hand at grading your 10.1 working notes and solution. Be constructively self-critical. Add metanotes and cross-references. Get your ideas and observations expressed briefly on paper. Be a good, strict, schoolmaster on yourself -- for your own good. But also that means you should be liberal in your praise when you got things almost right. You’ll get better with practice.
End 10.1 Grading
That "all" really means ALL!
It’s the perfect example of how you are to come to feel the power of words used in Plex definitions. Just as soon as any circumstance allows any definition to apply (whether you see it applying or not!) it does apply, and that it is it -- by definition. In the case of the definition of <now>, there’s no way even the tiniest feature can escape or even delay being swept up by that ALL. If it’s not nothing, its in there already! That’s what 8.23a asserts. That’s simply the way it is. [See a deeper discussion in the P1-P5 Plex Tract.]
And then the rest of 8.22, with its very important definition of change as requiring non-change to have any meaning at all, follows immediately. And again, study carefully and really convince yourself about the last annotation there. Only <now> can
and, in fact, it must do (be) just that! -- by its very definition!!! There’s no place other than <now> to make a site where <now> is situated, so <now> can’t be totally replaced by something in its place that is all new [and do notice how tightly these words are woven], so the definition of "to transform" cannot apply to <now>. But that works out just fine, because all <now> can do is what it must do -- namely, change without change. Even though <now> can’t transform and "forget" anything at all -- even the tiniest iota must either be old and in non-change or it must be new and in the change that yields the new form of <now> -- that’s all that happens. The consequence simply is the fact that the universe never forgets its past. That’s what our careful reasoning concludes. That’s simply the way it is.
The remaining pages of PL86-8 simply put icing on the cake, by spelling out the consequences. Notice how strongly 8.24b and c carries out what I said about the instantaneous action of applicable definitions, in Plex. Item 8.24d spells this case out. Again I am at a loss to devise a problem to pose to you because I see only inevitability in these considerations -- no problem at all! The only problem I can pose to you is the problem you pose to yourself:
Do you
what PL86-8 is saying to you? Can you doubt it? (Or is whatever lingering doubt you may have a doubting of your ability to completely grasp it? That’s quite normal!) Our careful reasoning has shown that "It can’t not be" is a fact, by the Plex definitions.
The purpose of the study of Plex is to proceed to resolve those nuances of meaning we saw earlier by the evolution of more powerful and richer PLM expressions. As we do so, more surprises are in store, but as they build up, we acquire new depths of "mind’s-eye seeing" that begin to remove (or at least weaken) those doubts about our ability to comprehend what our reasoning shows to be fact. Whatever success each individual may enjoy in that regard, at every step of the way the full faculties of the mind are exercised in ways that are very rewarding. The Problem Set scheme allows you to get out of the study of Plex just as much (and maybe a bit more) as you choose to put into it.