Knowing One from the Other by Jonathan J. Dickau

Thanks greatly Sreenath..

Your comments here are warmly appreciated. I'll see what I can find out about Thandava-Nruthya, through a web search, now that I know what to call it. Your insights complement my own, so I'm thinking I'd better read your essay through - so I may learn what other gems you have to share.

All the Best,

Jonathan

OK then Akinbo...

I shall attempt to answer your question with all due brevity, but an honest answer precludes that only yes/no replies are considered valid. This caveat is necessitated in part by the nature of your query and by essential information not provided (only some of which is commonly available), but it is also dictated by the fact that my circumstances are unusual or unique. There are some basic facts to consider, in the set-up of the problem. The largest bills printed were $10000 notes, and a stack of 100 would easily fit in most people's pocket, and the smallest are $1 notes, but it is ludicrous to assume that anyone's pocket has space for one million of them. So there are natural limits, or boundary conditions to consider. One important feature of this problem is that all denominations of money have discrete values, but there are a number of ways a one million dollar sum might be constituted, and a limited subset of these that would actually fit in a pocket. I reason that a stack of 1000 $1000 notes would be mighty a tight fit, for a fairly large pocket. And since the $1000, $5000, and $10000 notes are no longer printed this makes it harder to obtain a stack of 'crisp notes' that total one million and will fit in a pocket.

Assuming the above limits present no obstacle, we are then left with distinguishing and counting the notes found in our pocket. While the hand as detector might be able to reliably count the number of notes, and while someone with enhanced tactile skills might distinguish one bill from another in pocket; most people would pull the stack or wad of money from their pocket in order to count it, to visually inspect the bills for authenticity, and so on. I am like most people, Akinbo, and I would pull the notes from my pocket and count them. Then, even if I was urgently needed on the job; I would immediately go to the Bank or Credit Union - and make arrangements for them to authenticate and store or deposit my new found wealth - before I went about my business. Having done so; any later attempt to probe my pocket that comes up empty handed would convey no additional information beyond what was known - unless I had put the receipt in that same pocket. One might also have the earned expectation that more money would appear, because it already happened once, and in this case finding nothing would confirm or deny this expectation.

Of course; if I found money in my pocket, then just left it there and went about my business (unlikely), I would have been surprised it was missing later - and this would be new information. It is also true that if I took it out and counted it, then slid it back into my pocket, it would be a shock later - and losing it after realizing you had one million dollars would definitely confer information, which would almost certainly be unwelcome. So yes; there are instances where an empty pocket conveys new information, but the loose definition of the problem does not allow me to say whether the scenario in the previous paragraph or this one plays out. As far as going to work goes; I am here in the very same studio where I recorded Pete Seeger, and where if I peek around the corner I can see my Grammy award on the shelf, but this is my home too and the bed I slept in last night is right behind me. So there is seldom a time I am 'on my way back from work' - unless I do a remote session as on "At 89." My guess is that I would likely stash the cash before showing up for a recording gig, so it is far fetched that I would leave a million dollars in my pocket, then go to work with it, but if I did I'd expect to find it there later.

So ends part one,

Jonathan

As explained above;

The answer is 'yes' for 1) above IFF one left the money in one's pocket (in which case an exact accounting is lacking) or counted it and then returned it to pocket (assuming no further action was taken), so there would be a reasonable expectation to find something there.

The answer is 'no' for 1) above when one has removed the money from one's pocket, perhaps to count it, and subsequently acted to store the money elsewhere - leaving it out of one's pocket before going to work. An expectation more will magically appear does not justify being surprised by empty pockets, if one has deliberately set the money aside before work, though if a million appeared twice you would wonder.

There are some scenarios allowable by the problem description where only a partial answer is possible, the correct answer is somewhere between 'yes' and 'no', or the result is indeterminate, and so on. I'll say that aThe great majority of cases fall into one of the two categories above, but... A funny thing happened on the way to work... Anything can happen. Unless some details of the day's activities are known, an exact answer eludes us.

Regards,

Jonathan

Hello again Akinbo,

I will still attempt to get to specific replies for 2) 3) and 4), and I think my initial answer explains any variance.

All the Best,

Jonathan

Greetings My Friends,

This message was meant to be a reply to Akinbo (in his blog), but because it has more general relevance I am also posting it here.

While I acknowledge that sometimes life reduces choices down to either/or decisions, the tendency to assume this applies more generally is a harmful logical flaw prevalent in modern society, because it fails to ask "Is there a middle path?" In more detail; sometimes the middle is excluded erroneously, in other cases the fact there are multiple choices is not considered, and in some cases there is a virtually continuous range of choices - where sometimes our choice among these cases is determined by how we interact with the system. According to an article in August's Scientific American by Meinard Kuhlmann; that sometimes applies for the choice of 'particles vs vacuum' which begs the question "Is there a particle or no particle?"

I first read about the hierarchy of objects and spaces as a point made in passing by Alain Connes, in one of his papers about non-commutative geometry. Measurable is a subset of topological, which is a subset of smooth - in relating the categories of well-defined spaces. This point has more than passing importance, however, to people who study differential geometry and topology. In some cases; one can assert that the boundary between stable conditions or well-defined regions is a fractal. That is; there are interpenetrating regions of yes and no, or black and white, as in an M.C. Escher artwork. So while sometimes a simple yes or no will suffice; sometimes a more subtle answer is called for.

More to follow..

All the Best,

Jonathan

Here is the rest of the story.

There seems to be an erosion of our natural perceptual ability to distinguish shades of gray, as an effect on the human populace over time. I've written about this in editorials, but few scholars have speculated on its cause. I suspect migration of a large segment of the populace to cities might be a factor.

The studies begun at Tübingen, and run by the German Psychological Association for a number of years, showed a marked decline in perceptual acuity at discerning shades of gray and other colors, for people at the end of the study vs the beginning. Early on more than 200 shades were easily distinguished, and later participants could discern only half that - focusing mostly on bright colors. I would hate to imagine a world where everything must be reduced to yes or no, black or white.

So let's celebrate the world's colors and shades of gray, while we still can.

Have Fun!

Jonathan

Your answers are:

4) - I don't have a cat.

3) - If you gaze at a fog you will see it is not just a diffuse mass, but is in fact engaged in a flickering, fluttering, dance at all times - that pulsates with the slightest vibration. The same might be seen to happen for pure energy devoid of substantial mass (i.e. - in the massless regime near Planck scale).

2) - Call it what you will; emptiness it is.

1) - There is a figure called the 0-brane. Following the construction in analogy to the spheres used by Greene in "Elegant Universe" the 0-brane is actually two points bracketing a location in space, but it is usually seen to be a point like object that holds an instant of time, the instanton. This is the minimal case.

To explain; even a point in space is assumed to have duration, but a point in spacetime is a pure fiction as it has no extent in either space or time, and thus does not actually exist. Only things possessing duration can exist within time, or said differently they must possess a parcel of time to exist at all.

Have Fun,

Jonathan

Thank you very much Gene!

I do appreciate the kind remarks, and that my essay made you think. That was the desired effect. I shall look on your page to see how you replied shortly.

All the Best,

Jonathan

Thanks greatly John!

Your insights and praise are appreciated. I guess I'll have to take a look at your essay, and see what you have cooking. And I agree; the assumptions we need to change or challenge may not be the obvious ones, so we must call virtually all our assumptions into question. That is pretty much the approach I took in last year's essay. I really like your statement about the evolving observer, and that has links into some of my other work in progress. Are you familiar with The Reflexive Universe by Arthur M. Young? He elaborately explains why the evolution of consciousness and of the universe follow the same pattern.

I will have to look for more links between our work, when I read your essay.

All the Best,

Jonathan

Thank you greatly Sridattadev.

I find wisdom in your words, and I thank you for taking the time to read through my essay and comment. The idea that I is the nothing in everything, and it is therefore infinite, is quite profound. I shall comment further after taking some time to look through and work with your formula, to see what comes out.

Kind Regards,

Jonathan