I got a lot of work done on MathFuture, but given we were starting to argue about the Infinite Monkey Theorem, and given that's not a list designed for arguments, I felt it was time to get off.
NOTE: I acknowledge the case where we claim the proof is empirical,
because Shakespeare fits our definition of "monkey" for all intents and
purposes (so what about a few chromosomal differences, don't be so
picky). So duh, a monkey already *has* come up with Hamlet, a tale told
by an idiot, that monkeys also read. [post]
We were hitting too many hot button items, such as whether the Theory of Real Numbers is really sound.
Andrius, in Lithuania, clued me regarding the video below, which I'm still plowing through, as I get ready to teach a next class.
Bradford gave me some good advice, reminding me I wasn't talking to rank beginners.
The target audience for my Philosophy for Physics Majors is more like West Point faculty members (thinking of Dr. Bob Fuller). I shared it with the Physics listserv I'm subscribed to.
Anyway, the voltage was getting too high for such a village-level grid, where typical household voltages are more the norm, if I may be permitted such a metaphor.
Regarding Norman Wildberger's video, I've gotten up to 31 minutes, 16 seconds, where he covers the Infinite Monkey Theorem, par for the course (i.e. it often crops up in such
contexts).
He tries to shove that nonsense off onto Philosophy maybe, after getting
our agreement it's not Mathematics, however I'd say Philosophy grew up a
lot in the 20th century and what he's saying is not really Philosophy
either.
Yes, it might be cocktail conversation after a few drinks. I'd leave it at that.
I think the whole talk up to that time point demonstrates what
Wittgenstein observed: that mathematicians are singularly poor at avoiding pitfalls in
philosophy. I'll have to go dig that up and provide a proper citation.
Norman is trying to dig himself out of such holes, more power to him.
Here's a new Jupyter Notebook undertaking to compare the 4D IVM tetravolume measuring system vs-a-vis the 3D XYZ cubic volume system we all learn in school.
By 4D I don't mean "four mutual perpendiculars" but four rays from the origin through the corners of the topologically minimum container, the most primitive "cage" enclosing volume, a "simplex" of Euclidean dimension: Dim=3.
Think of the 4D as a "branding mark" signalling a different approach to 3rd powering. The Notebook expresses this difference in a way similar to the way Bucky does in Synergetics 982.44-47.
Imagine two sticks of varying length with a common origin, at any angle to start, and imagine an operation that connected the two tips with a 3rd segment, thereby marking off the area within.
This is "closing the lid" in the case of a triangle (Dim=2). However, leaving the angle unspecified fails to nail down the numeric results of the computation. We need to decide on a fixed angle to always get the same result.
Fixing the included angle defines a specific triangle (SAS).
In XYZ multiplication, that included angle is 90 degrees, upon which, after we "close the lid", we then multiply by 2, placing two of the resulting triangles on opposing sides of a shared hypotenuse, thereby defining a rectangle.
That's our standard algorithm for area. |A||B| is a rectangle, a square if |A| = |B|. We all know this cold by elementary school.
In the IVM (different scaffolding), the included angle is 60 degrees and upon closing the lid, we do not proceed further to double the resulting area.
That internal original area, of the triangle, is simply defined to be |A| x |B|, where |A| and |B| are the stick lengths. |A||B| is an equilateral triangle if |A| = |B|.
Moving on to volume (Dim=3)...
In XYZ we start with 3 sticks from a common origin (0,0,0) fanning out in a mutually orthogonal arrangement. Closing the lid begets a right tetrahedron that is only 1/6th of the total volume we come up with, by forming a rectilinear parallelepiped from these sticks.
|A||B||C| is a brick, maybe a cube.
In the IVM, three sticks from a common origin fan out along the imaginary edges of a regular tetrahedron, which
establishes relative direction.
The magnitudes are variable, so the resulting tetrahedron may not be regular. The angles at this corner remain fixed, as they do in the XYZ case.
We simply "close the lid" and call that the volume. The numbers stay the same. 2 x 4 x 5 = 40, same as before,
it's just that 40 is tetrahedron-shaped, and obtained from adding three sticks to the initial three, thereby forming a six-edged, four faceted shape, not a hexahedron as before.[1]
How might we bridge these two operations?
Taking our cue from Bucky, we construct a tetrahedron from four unit-radius balls, closest-packed, edges 1/2 D
where D = ball diameter. Saying the edges are 1 and the volume is 1, makes the cube in which said tetrahedron
inscribes = 3 tetravolumes.
That's a fixed and known relationship: the tetrahedron inscribed in a cube as face diagonals has 1/3rd the volume (this generalizes to any parallelepided).
However in XYZ this same cube of edges √2 (in R units) and face diagonals 2, will have a volume of 2.828427...
or √2 √2 √2 i.e. "√2 cubed".
So there's our conversion constant: 3/2.828.. or √(9/8).
Another way to think about it: the XYZ scaffolding or matrix consists of unit cubes of edges R. It wasn't originally developed with sphere packing in mind (unlike the IVM, which is the scaffolding associated with the FCC or CCP).
The unit R (2R = D) gives us R * R * R = 1 or R-cubed in XYZ (cube shaped), whereas D * D * D gives us 1 in
the IVM (tetrahedron shaped).
Using our conversion constant is like converting between currencies or energy values (joules, calories)
where the R-edged XYZ cube is about 6% bigger than the D-edged IVM tetrahedron. The two units of volume are somewhat close (like the Canadian and American dollar) but not the same.
If you know the volume in XYZ cubic units, multiply by √(9/8) to get the same volume in IVM tetrahedron units, or use √(8/9) to go the other way.
Why bother? What's the pay-off?
The tetrahedron of edges D divides thrice into a cube of face diagonals D (as we've seen) four times into an octahedron of edges D (its space-filling complement in the IVM), six times into a rhombic dodecahedron (space-filling CCP ball encasement), twenty times into a cuboctahedron (from 12-balls-around-1 and connecting corners).
The five-fold symmetric Icosahedron, Pentagonal Dodecahedron, and Rhombic Triacontahedron (RT) all fit in here as well, incommensurably in most cases.
The Jitterbug Transformation is used to connect the Cuboctahedron of edges D to a corresponding icosahedron of edges D.
Said Icosahedron of volume ~18.51, combined with
its dual, define a rhombic triacontahedron that, if
shrunk down by by 1/Phi (linearly) gives the RT
of 120 E-mods (60 left, 60 right-handed).
The RT sharing vertexes with the RD of volume 6 has
volume 7.5 exactly (IVM tetravolumes) and shrunk by
2/3 gives the RT of volume 5 exactly, and the 120 T-mods,
same shape as the E-mods but a tad smaller, by about .001%.
What David Koski does is phi-scale the E-mods to express volumes as a linear combination of mods of different
size (same shape).
A rhombic triacontahedron with a radius of ø¹, is dubbed the Super RT. The long diagonal of the rhombic face = 2, which is R.B.Fuller’s edge for the tetrahedron, octahedron, cuboctahedron or VE, and the resultant icosahedron from the Jitterbug transformation.
The volume of the Super RT is 15√2 or 21.213203 = 120E3 = 480E + 120e3 [tetravolumes].
The icosahedron with an edge = 2, inscribes within the Super RT. It has a volume of 5(√2)ø² = 18.512295. It has
an exact E module volume of 100E3 + 20E = 420E + 100e3. [tetravolumes]
That's about all the mathematics one needs to know, to understand about tetravolumes. It's not that hard.
We also get to think again about foundational matters, such as
what basic assumptions we might vary to produce interesting
new flavors of mathematics.
[1] Just for fun, lets compute the lengths of the "lid" edges and feed
these numbers to our Pythonic tetrahedron volume computer, same
one as in the Jupyter Notebook. Given edges a=2, b=4, c=5 I get d=3.46410..., e=4.582575..., f=4.35889...
for a volume of:
a = 2
b = 4
c = 5
d = 3.4641016151377544
e = 4.58257569495584
f = 4.358898943540673
tetra = Tetrahedron(a,b,c,d,e,f)
print("IVM volume of tetra:", tetra.ivm_volume())
Although superficially a light comedy and midsummer entertainment, this film gave me much to think about and when people asked me for my views, like my mom, I'd say "still thinking about it".
There's a lot about symmetry, left and right, dead and alive, with this bridging of two worlds. Male and female. Flipped roles. The receptionist is the airhead bombshell. The girls are geeking out.
Girls are good at geeking out, we knew that. I was probably more thrown by a guy bombshell. I tend not to see them that way, though I could digress into a longer psycho-social profile and make this review more of a selfie. I'll forgo.
Lets just say I identified with the dead behind the mirror. That goofy blob guy seemed to be having the most fun throughout the movie. Maybe I could be him.
Mostly what I learned about was New York (again) and the Victorian convergence of electricity and negative Universe (meant in a spooky sense). Edison was not the only one to think these phenomena might have something to do with the soul.
There's sense in that really, in that we're already bio-electrical devices in an Internet of Things, as high tech as we don't know how to make, which is the highest of all. Us, the not-ghosts. We think we're less spooky than if we floated. We're wrong.
Anyway, haunted world, and politics. The Mayor is as close to a father figure as we get, and he's savvy about (A) the need for ghostbusters and (B) the need to deny it. His operative, another smart cookie, keeps us attuned to another sense of "two worlds" (one to keep the public happy, another that's more real).
The physics lady, the first person we follow (omniscient camera), is caught in that bind between upholding Victorian science against the evils of abhorrent or heretical beliefs, and her actual experiences. What happens to Bill Murray's character again? How was his going missing smoothed over? Plot hole?
The mirror people remind me of The Zero Theorem, which I've been thinking about quite a bit. They get sucked down a vortex, but before long they've come back for more. There's an eternal return implied here.
But like I said, it's summer fluff and great ethnography, a memes-on-parade reminder of where we stand with the paranormal (or whatever) in 2016.
Probably an ideal job for me would be as tour guide through various storyboards from which hypertoons and other movies could be made.
Hypertoons consist of a wandering playhead making choices at each keyframe, about which scenario to follow, node-to-node. Keyframes are hubs, some are grand central stations. Many "time tunnels" (tubes) start and end at each one.
You've got triangular and tetrahedral numbers in there, just for starters. Pascal's Triangle: a grand central switch https://t.co/QxpVzAFyKY
I was mentioning to students tonight on my real time Python channel, that if we had truly driverless cars, then we could send them on errands sans any human passengers.
"Go get me breakfast" might send the car through a drive-through, where a robot would hand my menu selections through the window, as a bag for the driver's seat.
My topic was APIs or control surfaces. What controls are read-only and when might a user's choices be overruled?
Trying to change lanes with a car in your blindspot? The steering wheel locks up.
Back in the day, futurism, a subclass of science fiction, included so-called "mega-projects" by which was meant more than just more skyscrapers.
Whole cities might be planned and built according to plan, implementing smart house and grid technologies.
Whether jet packs were involved is up for grabs, but definitely people movers. A passenger would be delivered to a dialed-in destination without having to do any skilled driving.
Many big airports have these today, as trains connecting terminals. Elevators are also people movers. Neither of these is quite as private as the private car, not yet driverless.
Today, many civilizations have imploded or are imploding, meaning the individuals trying to make their way in these societies may be in need of rescue. We recognize physical disasters but some of the most acute are man-made.
A global network of Asylum Cities, geared to take a steady influx of people needing to start over, would provide cyber-identities that were difficult to steal and easy enough to manage in shared memory. Services such as healthcare and education would be provided.
One imagines people flocking to these cities even if well-provided for, however the familiarity of the known means less stress and less coping. Undertaking a brand new life in Asylum City is both work and a workout.
Valid identities that do not stipulate nationhood, at least at first, might be a first step. Having no documents proving citizenship need not result in random assignment. Feel free to move about, at least in Asylum Network, even minus a recognized homeland or nation.
As of this writing, Turkey is in turmoil, with massive layoffs amidst high levels of distrust. The need the New World served, in terms of receiving refugees, is still a need, even if no world is new anymore. Venezuela, South Sudan, Syria, Iraq, Libya... much of the world is falling apart.
Now that we're very clear on the finitude of our planet, it makes sense to sustain high living standards for as many as possible, as a best way of avoiding wars.
I'm only here for an afternoon, night and morning this year. Mary Klein, editor of Western Friend, and myself, Clerk of the IT Committee, thought up an Interest Group focusing on the experiences of Monthly Meetings using information technology, including social media. I'll post a separate journal entry on how that goes, still ahead as I write this.
On my way out here, driving alone, I veered off to visit monuments and memorials. My mind is hovering in that space between the two worlds, perhaps just a figure of speech. Sam Hill's Stonehenge, and the Washington State Veterans Cemetery, near Spokane, called me to pay my respects, and I obeyed.
I've been thinking about our global Iron Mountain economy, whereby so many find their daily bread, typically within the context of a male-dominated pyramid hierarchy. Has the nature of soldiering changed in any essential way, since the time of the Roman conquests? How do we define our terms? I know that was a preoccupation of former Secretary of Defense Donald Rumsfeld (definitions).
If it's true, as Bucky Fuller was fond of claiming, that we crossed a threshold in the 1970s, whereby taking care of the world's billions at a high living standard was in principle doable, does that change the context in any way?
One veteran I know was saying how welfare programs were failures because whole families just stayed home and became couch potatoes, unto a third generation, to which my response was "I have no problem with that."
In my mind's eye, I see a pilot in a souped up jet fighter, bombing some village, with the caption "Welfare Queen". Ditto drone pilots and their warlords. Not very nice of me to think that right? Families are proud of their generations of national service, regardless of nation.
Yes, the Iron Mountain shells out a lot to pay for such sacrifices, and the costs are much higher, but think how many paying jobs each bomb represents, not to mention all the work it takes to maintain such aircraft.
Staying home, watching TV, is of negligible cost in comparison, though maybe not if family members fail to exercise and require expensive medical interventions as a consequence. That's employment for medical professionals sure, but don't we want to focus on preventative care?
If said family has disposable income, they likely help keep the local stores and restaurants afloat.
I think about "programmable money" quite a bit. Food stamps are a step in that direction. Imagine a form of currency that was only good towards charitable donations, yet one still had discretionary powers over which charities.
My charitable video arcades or whatever we call them, wherein the winners engage in philanthropic behavior, are about developing awareness of what's out there, in terms of helping people. Choose where your winnings go, you just won the right to do so.
What makes living standards low today is precisely that so many suffer in ways we could prevent if not so stuck in our reflex-conditioning. South Sudan is but the tip of the iceberg.
Living standards occasioned by the displaced, those fleeing untenable / unsustainable theater, are low for everybody as a result, as we all share the same backdrop of Ghetto Planet or Looney Bin Earth.
If we were to eliminate death by starvation as in any way "natural" (as in "God's Will"), then living standards would increase even for those who've been in no danger of starving. The whole world would feel better off.
Thanks to my being a proposal reader for OSCON 2016 (and in some prior years as well), I was able to gain access to the recordings, as a way of getting feedback on our program committee's work.
Did we pick useful presentations for our conference goers?
Just as important: what is the state of the art in the world of computer programming?
In working through those videos, I came across Kirstin Hunter's talk on being a polyglot, (here's one like it on Youtube) in the course of which she introduces a modeling language called RAML (RESTful API Modeling Language)
Wow, I hadn't seen that before. I learned a lot from her talk, and tweeted my appreciation.
@synedra saw your Becoming a Polyglot talk @ OSCON 2016 on video yesterday, excellent and inspiring. Hey, I have a BA in philosophy too.
I've been diving into RAML ever since (i.e. since this morning), and now realize that a RAML specification of an NPYM.org API could be a next project for the NPYM IT Committee, of which I am clerk.
As shown below, I'd started on such a thing last year, but without knowing as much about API design as I do now:
The Youtube below, by one of the inventors of RAML, does a good job of advertising the power of thinking this way.
One of my goals for Quakerism is that it get up to speed on IT such that our volunteer roles become more rewarding in terms of the professional development opportunities they offer.
I wonder if any @MethodistGB churches are using RAML to define their APIs. I'm moving in that direction @npym_it
Greetings Brad. I was thinking
"circle and/or sphere and/or tetrahedron" through most of what I wrote,
and seriously thought of quoting some passages from Synergetics
associated with this Figure:
... then thought the better of it. Some other time maybe.
True, conflating spheres with circles is conflating 3D with 2D, and that might be a sin.
On
the other hand, Renaissance perspective is all about rendering 3D
vistas on a 2D canvas and as Joe points out, the 3D moon is a circle (if
full) in most children's books.
We play with that circularity, as in the DreamWorks logo (boy with fishing pole, sitting on a moon sliver).
The
basic idea is to establish in fresh minds (of any age) a semantic
network of related concepts that don't fizzle right away, as they too
often do, thanks to geometry being compartmentalized, something to put on a
mental shelf the minute we leave the classroom.
On the
contrary, V, F, E all follow us down the hall, as halls with doors and
lockers, the school itself (like a maze) is all Vs, Fs and Es, once you
start looking for them.
And yes, it's on a ball (Planet Earth),
which we might see using Google Earth on a flatscreen. The Little
Prince might feel right at home here (or not).
Circles have
a lot of the same properties as spheres, as you well know, and if we're
able to take advantage of this homomorphism -- the analogy (if not a
full isomorphism, congruent concept) -- so much the better.
The
circle has concave and convex aspects, just like a cave. People are
either inside or outside the circle, drawn in playground dirt, or "on
the fence", straddling, one foot in, another out.
That sense of
"container" -- which I'd consider at the root of conceptuality -- is
still there. Or we might use a square, or a triangle, to make our
boundary. Who's in? Who's out?
The semantic web I was building follows the Synergetics path of looking for "twonesses" (pairs of concepts that go together):
(i) spinning around an axis in either direction
(ii) growing and shrinking radially
(iii) having a macrocosm outside, a microcosm inside.
We might play this game with circles, not only balls. We might use a circle to represent a ball.
In
a Geometry of Lumps per Karl Menger, we have only "3D" as there's
always the observing camera, the viewpoint, separated from whatever's
observed.
The observer-observed is already an axis and its
context is always volume. There's 2D "in volume" and 1D "in volume" but
the context-container is always 3D. Everything is a lump. A circle is
a pancake, a disk. A line is a cylinder. We may dismiss "thickness"
as irrelevant but we don't appeal to infinity to make it disappear. A
plane is a sheet of paper.
In this geometry (non-Euclidean)
there's no need for either "infinitely thin" nor "infinitely wide" as in
Euclideans' metaphysical cartoons (lots of hand-waving). The word
"infinitely" itself as been largely deprecated as unnecessary.
Different
axioms and definitions, sure, but not entirely unfamiliar as its a
reality we may access experientially. Taking a page from the old
textbooks, we might say the omni-presence of 3Dness is "self-evident".
But then what about Time i.e. change, i.e. deltas? The movie moves. Stuff happens.
Going
deeper with the elementary topics, I introduced V + F = E + 2 and
Descartes Deficit of 720 degrees. You'll not find these in Common
Core.
My ethnicity, no doubt some religious minority or cult,
wants to share these generalizations in 3rd grade. Might we need a
special dispensation from the Governor? Must we keep our kids from
public school? I certainly hope not, fingers crossed.
In the
1980s, I wrote up much of the above for an archive in Bhutan, but I
doubt it met with Jesuit approval way back then. Malesh (means "oh
well" in Egyptian -- an acceptance of God's will).
Finally,
I want students (of any age) leaving my geometry classroom to keep
thinking about social networking, about graphs. Who is friends with
whom? Who consider themselves enemies?
I'm in need of such a
graph database myself. As I wrote to the director of the code school
(< guild />) this morning from Linus Pauling House:
I spent the night of the 4th at home studying history of
the French Enlightenment period. I had no idea that Hume, the Brit, and
Rousseau, the so-called romantic, had such a dramatic falling out. Such revelations make me want a graph database of "friends
and enemies through the ages". A great way to teach history to kids
(adults too): "if I were Thomas Jefferson on Facebook, who would my FB
friends be?" ...
Giving high school teachers free PD in Python etc. would be
a smart move, as a pilot program at least. I guess I'd consider myself a
lobbyist for such programs. I probably have natural allies in PSU I
don't know about, enemies too. History was ever thus. :-)
I'm also sporadically reading a fantastic book on Ada
Byron, the first computer programmer. She wasn't allowed to know who her
dad was until her 21st birthday, when his portrait was unveiled with
much ceremony. The mom didn't want her to have any contact with the guy.
PD = Professional development. PSU = Portland State University.
You
might see where high schools could relate to talk of "in groups" and
"out groups", the Venn Diagrams. That's what the #BigData and
#MachineLearning folks are studying too. Who's who, and who knows whom,
who works with whom etc.
The company Little Bird (here in
Portland) is one example, that's what they do for a living: find out
who is influential, based on network traversal. The theory is that, in
knowing all this, one becomes an insider in some way, like being in the
CIA in some science fiction.
My wish, then, is to
anchor a semantic web that doesn't fizzle when the mind turns to social
matters. Geometry doesn't just sit on the shelf.
Verifying the truth of a story, seeing if it all checks out, is "omni-triangulating".
We're building mental maps, mental models.
Yes, constructivism: we're each responsible for creating our own model.
Geometry supplies conceptual tools for doing that.
Improvements in speech and image recognition have caught the attention of BR (business religion), which is a little different than BI (business intelligence).
Those tracking the Deep Belief Net (DBN) algorithm, or really any neural net solution, know it's all about weights and biases.
BR is all about applying DBNs in an unsupervised learning environment and forming conclusions about the patterns it finds, locking those in, and defending them, creating a "hard shell" around a "nut" or "nugget".
Depending on the use case, said "nut case" (pun intended) will have a corresponding "half life" or decay curve, preceded by potentially sharp spikes or other growth patterns. Strong BR has the potential to form the nucleus of a "pattern integrity", to use the jargon.
The millions of customers using camping or other outdoor gear on a year round basis, abetted by sports campers, are stretching the borders of Cell World i.e. those parts of the biosphere served by cellular telecommunications technology.
GPS, news, weather and basic daily income (BDI) are examples of what some businesses circle as mission critical, either as customers or providers or both. The cell phone network is forming the B2B web that we hope has a safety net aspect where living standards are falling. What does BR say?
Note that Business Metaphysics (#BM as in IBM) and Business Philosophy (#BP) both serve as tags in this space, but really BI and MVC have more widespread circulation as concepts, the latter (model view controller) serving as a mirror for what many businesses see themselves to be.
Star Trek's Enterprise is MVC with VC concentrated on the bridge to interact with Spock's and Kirk's bionets (brains included, however a the whole body is trained, including glandular / hormonal systems; Spock's is built this way too even if he has more control of emotions).
We give BR a captain's role, whereas BI is the ship's computer, more like Siri. BI will take feedback from a Model up to the visualization phase, however only the captain and other bridge personnel have the weightings and biases to recognize what levels of risk might be acceptable or not, going forward.
BR is concentrated in the CRO (chief risk officer) in other words, the Klingon in our analogy. Klingons are on the lookout for shaky markets likely to flat-line, bubbles on the brink of bursting. Whereas some on the bridge might be looking to pump in some energy savings, their "get rich quick" short cut might best be tested on the holodeck first.
Speaking of the holodeck (simulation environment), although mostly used for entertainment on Star Trek, that's the training ground you'll want and need, when investing in role playing around new business models.
If you're a bank working with crypto-currencies, you'll want proto-customers to role play with actual devices. Pitch a tent right there in your 47th floor office if need be (don't start any fires) or find a prototyping camp that specializes in Deep Learning.
