Acronyms used in this page:
|CTM||- Classical Thinking Methods|
|ISM||- Suffix, e.g., realism, objectivism, positivism, etc.|
|M3K||- Our Millennium (ending year) 3000 crisis|
|MoQ||- Metaphysics of Quality (Pirsig)|
|QTM||- Quantonic Thinking Modes|
|SOM||- Subject-Object Metaphysics|
If you have read our SOM Connection, our Aristotle Connection, our Quantum Connection, etc., you know how we crusade against SOMthingk or what we conventionally call classical thinking methods (CTMs). We have another example for you which shows, again, why Quantonic thinking modes (QTMs) are superior to classical thinking.
In our web pages mentioned above, we show you why Aristotle's syllogistic laws become untenable in any quantum realm. We show how SOM believes that Aristotle's first syllogistic law, A=A, is 'true.' Then we provoke more general quantonic thinking and deny Aristotle's syllogistic laws, except within extremely naïve and simplistic axiomatic conventions.
We want to retrace our same provocative Chautauquas, but use a subtly different meme.
If we insist Aristotle's A=A fails to hold in general, then we should be able to show, too, that it fails specifically. Let's do it in a manner similar to examples you may have seen in school. Has anyone ever asked you to show how one does not equal one? In general, if you accept our notion that Aristotle's A=A fails, then you should simply accept our proposition that, in general, one does not equal one. But then, it would be unfair if we did not provide an example (we give ample quantum examples under page links above; William James' example from Chapter III of his infamous Some Problems of Philosophy looks like this: "Mathematically you can deduce [one] from [zero] by the following process: 0/0 = (1-1)/(1-1) = 1.").
We want to use a Quantonics' MoQ-based axiom as we proceed. Remember how we have shown you that most SOM ISMs are objective? SOM insists that we focus our attention on properties-attributes-characteristics of objects. SOM reality depends on us adhering this SOM axiom of substance. In Quantonics we adhere a different axiom, one that Robert M. Pirsig gave us in his Metaphysics of Quality. MoQ tells us that Value is not objective. It tells us that Value appears more as a kind of subjective commingling~unification of both ~subject and ~object which together we call Value or patterns of Value. Value lies not in substantial objects, but in interrelationships among patterns of Value. (See our recent, July, 2002, Quantonic Ensehmble Quantum Interrelationships.) If one studies neurophysics, one finds that all value (usually called "reflex" behavior) is ihn synapses, not in neurons. Value is in interrelationshipings, n¤t nodal media (e.g., neurons as "wires"). Ref. see Pribram, Sherrington, et al. Doug - 8Dec2008.
Given that, let us look at an integer version of classical mathematics' real number line:
Our real number line may be generated based on an assumption that Peano's principle of finite induction is valid (i.e., assumes a static, uniform, and objective induction modulus of one). It basically allows us to add one to any number, and iterate to generate a number line as we have illustrated above.
So we see many 'objects' in a sequential list. Each object is an integer number. Its properties are mathematically well known. But what about Value? Quantonics tells us to pay attention to interrelationships among patterns of Value. So we ask, "What is a way of thinking about our number line's Value? What interrelationship(s) show Value?" Answer: Think of interrelationships which show Value between patterns of Value.
Let's call each number a pattern of Value. What interrelationships show Value between our numbers? An obvious one is difference: subtraction. Summation obliterates Value between numbers summed by combining them. So, too, multiplication, i.e., products, and division, i.e., fractions. (Too, division may be thought of as recursive difference, then we may also perceive division as a way of accumulating Value.) So let's focus on simple subtraction difference as one means for assessing Value interrelationships on our number line.
Aside on a quantum notion of recursive difference:
We have shown elsewhere in Quantonics how quantum uncertainty may be coarsely represented using a quasi-classical notation like this:
Assuming we can use a recursive notion of quantonic omnifference, we can use quantonic script to show, again coarsely, what quantum recursive omnifferencings~heterogeneous_differencings might look like:
See Ensemble Attractors.
We have to keep, pragmatically~actively cerebral, a keen awareness that our recursion above is occurring in an animate EIMA quantum reality. That reality issi heterogeneous in comtextings and tihmings. Too, and comcomitantly, that reality issi quantum pragma-, poly-, paralogical. Also, our subscripts above may not be viewed classically, rather they must be viewed as quantum n¤mbærs. For an applied example, see our Hamiltonian hypercomplex quaternion.
SOM's convenient OGC and OGT simply do not 'exist' in that quantum reality, except as classical delusions and classical deigns to feign.
End aside - 19May2003 - Doug.
Now let's use what we know so far to make our point again. If we subtract any two consecutive numbers, larger minus smaller, what difference do we get? You say, "Doug, are you some kind of nut or something? We used Peano's axiom to generate our real number line. Of course, we get one!" And, classically we agree, but isn't there something subtle happening here which SOM and Platonic mathematics cause us to overlook? Isn't there something very, very important here?
What is 2 minus 1? One, right? What is 4079 minus 4078? Again, one, right? Agreed.
Classical mathematics tells us that we get identical results for both operations. Further it tells us both ones are identical. Good old Aristotle: A=A; 1=1.
But is 211 really identical to 407914078? Are those two ones really identical? Are they really same? Classical SOM says, "Yes! Emphatically yes!" Quantonics~MoQ say, "No! Really no!" See our August, 2000 News graphic of quantum oneness.
A phrase like 'one context' suddenly takes on new meaning now. Classical mathematics is 'one-,' i.e., uni-contextual. You disagree? Then please show how classical mathematics distinguishes 407914078 from 211. Guess what? You cannot. Classical mathematics assumes all ones are identical!
Quantum reality shows us all ones are not identical, and to assume they are is to commit a serious mistake in judgment. SOMthink does exactly that.
SOM's classical mathematics declares itself, "context free," meaning it will work in any classical context (or that it assumes there is only one global classical context SOM's). But we have just shown you that classical mathematics cannot even distinguish two ones in a most cherished bulwark: mathematics' real number line. Further, real quantum comtexts are not classical contexts.
Good old SOM. Good old uni-SOM. Good old one-reality-SOM.
Quantonics~MoQ~quantum science tell us comtexts are not absent as classical mathematics ideally propounds. Omnicomtexts are present and elicit omniValue interrelationships among all patterns of Value. As soon as one places Value above both SOM's unilogic and SOM's one objective truth, one may see new light. Value is not attributes, properties, and characteristics of SOM objects, Value lives both animate and commingling among Quantonic~MoQ animate patterns of Value.
A first year student of Quantonics, Bret from UFL, recently wrote us and asked us to watch a 1998 movie titled Pi, starring Sean Gullette. Bret saw some connections to William James Sidis and our work here in Quantonics. We watched it. Gullette plays Max, a gifted-genius number theoretician. Film's most Quantonic moment is near end where Max is under duress from an Hasidic Rabbi and his followers to give up 'the God number.' Max says, from our recall, "The number is not what is important. Numbers are not what is important. Interrelationships among numbers is what is important in nature." Max, we agree whole-heartedly. Value is in interrelationships: Quantonic interrelationships. Thanks Bret!
End aside 23May2001.
A one, twixt 3 and 2, is not identical to a one twixt 77 and 76! Interval 77-76 offers a different quantum comtext from interval 3-2. Platonically, these two classical contexts are identical. Quantonically they are omnifferent and changing! Let's now show our above examples using our new (1Sep2000) quantum ones:
Lack of human awareness of advantages of QTMs over CTMs is a very large issue for Millennium III. It is an item on our list of critical M3K problems. Any way we can hurdle this oneliest M3K problem? We can innovate a quantum one to replace Peano's loneliest one.
"One is the loneliest number..."
Thanks for reading,