http://rstb.royalsocietypublishing.org.unr.idm.oclc.org/content/369/1658/20130394
]]>Harmony in Chopin, Cambridge University Press, 2015. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/knowledgecenter/detail.action?docID=2056036.
]]>took a 250 yr old piano book (hummel) to motivate the distinction by *name* of harmonic vs melodic minor
]]>all the books show no spine/cover. What does it mean?
]]>Assuming that the whole playing-arm is in the balanced-armature position (like the old record player needle arm) contacting is a tiny amount of flexion. The force becomes an “biomechanical action” when it has to overcome the friction of the key surface.
Of course, the friction is tiny and this means that the flexion amount can be tiny. As every action has a reaction there has to be a compensating movement in a lever – or two-lever binding -earlier in the linkage chain. In this case, there is compensating stretch of the opposite extensor tendon, most obviously visible as a tiny depression of the metacarpal bridge.
With key up, there are two actions ongoing, and their two parallel reactions. The first pair is maintaining the balanced armature. The second pair is contacting.
With key down there are the same two actions and reactions ongoing. However the first balanced armature pair has been reweighted to overcome the tiny upward force exerted by the depressed key.
—
As a five year old boy learning piano I recall even now the friction-feel of my teachers (old world) piano which had ivory keys. I would contrast this with my Piano at home – with its plastic keys. Since one of keys had a tiny imperfection in the moulding (which feels large to the finger pad of a five year old) i remember running my finger over this tactile-imperfection – located towards the front of the black b-flat key, where my right hand index finger would normal lie at rest.
So why was that my resting position? Because my 15-year-old sister taught me only one piece. To use Taubman language it was a series of single rotations from d-flat to other black notes (only) above and below d-flat.
Being self taught I had a pinky centric orientation to my hands.I would jump to the thumb rather than jump away from the thumb. Probably here where I learned to do backwards rotations, between fingers one and two in particular – as they jumped and then struck d-flat, e-flat d-flat sequences.
Even with that simple piece, one learns to internalize different fingers as distinct pivot points ( for single rotations) , Especially after a lateral adjusting motion to change resting hand position.
It was not long before I also learned to distinguish hand touch from forearm touch. As I would swing my elbow in and out from my torso it would activate the forearm touch as the elbow swing changed direction. I learned that elbow swings and pivot points related in an irregular fashion, fitting the pending direction of the consonancy, raised/lowered nature of keyboard keys, and the desire to tie rotations to desired rhythmic accents.
I’m pretty sure Chopin taught himself the same material. He was just fortunate enough not to go to a professional piano teacher! He got to stay away from the C major all white note scale! He Never lost the naturally coordinate movement of elbow-swinging forearm touch distunct from hand touch, combing with rotations (and this taubman-evil backwards rotations)
]]>2-343434-5
This of course builds in rotations – remembering that that basic hand is well titled to the right. Played lightly, you get lots of bounce from the flexors.
And there no trying to pronate from a taubman classic hand. (Note taubman folks do advise that taubman hand/arms can be at an angle ti the keyboard, provided its still stays straight!)
For the chromatic scale, one simple uses chopin fingering – so the back notes are now incorporated … always on your long third that is generally always flexing while also pronating- whether ascending or descending
]]>here is my list – as it comes to my mind.
we have to skip. Just as we did when 10 years of age.
Three. Play a drum roll of fingers
1. With the right thumb aimed at f, play at the bottom of the swing.
2. The thumb should hit the key at the bottom of the swing.
i. The thumb strikes at the bottom when landing on the forward swing.
ii. The thumb strikes at the bottom when landing on the backswing.
iii. This is just “in and out”. Note in and out is swinging (in and out, back and forth).
1) Note we play 1-2-3 whether we are the bottom of n back swing or the bottom of the fore swing.
3. Each finger should land as the swing continues BEYOND the bottom, as the swing is coming up from bottom. It should be a rat-a-tat machine gun sound when all fingers are done. Ba-ba-bum for the back swing (fingers 1-2-3) and ba-ba-ba-bum for the fore swing (fingers 1-2-3-4)
Four. Add elbow arcs (= wristcircles)
1. Now do the cross-body swing again, starting as above.
2. Be conscious that your shoulder muscles are actively moving your elbow from its elbow-out location to its elbow-in position (as it slaps the torso)
i. This plays you the fore swing 1-2-3-4
3. Now reverse that on the back swing
i. This plays you the back swing 1-2-3
ii. Goes from the elbow-in to elbow-out (as you do complete the back swinging).
iii. Be conscious that your shoulder muscles are actively moving your elbow from its elbow-in location to its elbow-out position (as it slaps the torso of your duet partner on the same piano bench)
4. If you can think elbow in/out (distinct from in and out, as used by Abby)
Five. Now think scales
1. Start the swingin process AT the far end of the swing
i. (do a pretend fore swing to get there, f you want)
2. Perform a 1-2-3 backswing…
3. And as you reach the limit of the backswing, actively “push” a foreswing.
i. This “continues” the 1-2-3 (already played) with another 1-2-3-4
ii. Of course there is tiny time gap between 3 (end of 1-2-3) and (start of 1-2-3-4).
Six. Start skipping!
1. Do the above lots of times, one after the other.
2. You should feel a skip (in your arm), like you skipped as a kid with your hips and legs.
3. Skip along the octaves of a 4-octave scale!
At the last skip *as you “turn” to come back skipping down the octaves, change 1-2-3-4 to 1-2-3-4-5-4-3-2-1
“CHAPTER 4: Chopin Etude #1 Chopin Etude #1 is in C major and is influenced by Bach’s Prelude #1 in the Well Tempered Clavier. In both pieces Arpeggios are used to create a texture in the piece. The contrast is evident… Bach sounds Angelic and quite peaceful, while Chopin sounds dramatic and strong. Chopin completely changed the way the pianist plays the piano forever.”
Start reading this book for free: http://a.co/2ekfLy
]]>Start reading it for free: http://a.co/8jWLUM4
]]>The blind is basically two sequences of fingerings: 12345, 678. The 12345 sequence is an in and out sequence, Starting on the first chord and landing on the middle chord. Its rhythm is; Ya ta Ta ta Tat. The 678 sequence has the rhythm pattern: de de de.
In The language in and out spirals The sequence 12345 are the circle and the sequence 678 is the small-loop.
Going up the Op. 10 number two scales we have three in and out sequences, remembering that each one in and out of sequence has two patterns: 12345, 678. The 678 of the very last sequence is distended.
When going down the Op. 10 number 2 scale we also have several in and out sequences. However these are descending with the circle heafing right to left descending
]]>MLA Citation
Helmann, Jacob N. The Consciously Controlled Piano Tone: Most Natural Approach to the Problem of Artistic Piano Playing. 2d ed., enl. and rev. n.p., 1969.
Warning: These citations may not always be complete (especially for serials).
]]>Chopins description is better – for learning how to deliver them:
]]>I love this – especially its pertinency to op 10 no 2
I love that his crab and scorpion sting follow at the end. We use these below (dog paw is his crab and sting us three/four finger pre-extension with masking pedal).
Try this blend:
Flat fingers, first: giving gravity tap. This is taubman.
dog paw on the first of the kernel – thinking it as the last (chord) tone of the kernel pattern . You end up here that is (back in dog paw repose). Its a little counter intuitive. So ignore how you were taught to think of beat notation!
Wrist is low at the end (preparing for an extension to follow in the next kernel). Yes that means the very first chord is wrist-low! Play the kernel leading up to it without sounding, to get into the kernel-rhythm.
To set up the following 7tap kernel (the last of which is that wrist chord in paw position), extend the paw by simply extending the forearm (raising wrist) while also extending three and four fingers as a unit (without playing). This opens the hand (as a sideeffect of extending three over a raised wrist. Formally, you get palm extension (without abducting 1 and 5)
Pedal while you are doing this – to hide the non legato! Thats what chopin means, by his short pedal point.
The phrase “always legato” in this piece refers to chopins terminology (of how to deliver his taxonomy of articulations). The exception to the general rules is as above – for advanced students only. See last post. As taubman said, thats what the pedal is for! (Simulating legato, in gravity-tap playing)
So what is the middle chord within the kernel there to teach? Its teaches chromatic hand and arm, to use the taubman language. Mild rotation, in a flat finger tapping, in a post extension kernel heading for palm flexing (dog paw) will set up a bounce reflex on some of the taps. When accelerated with rotation, this propels the lateral movement (within the kernels scale, or monodic consonances – to use a chopin era phrase). The forearm will auto adjust – responding to the reflex – giving you proper taubman hard and arm.
Im not too surprised that the golinsky teaching fails to deliver all this! Its difficult to communicate. Mix it with chopin teaching method, it all hangs together.
And don’t forget the “arcane” flat finger technique – well written up for bel canto cantabile on a piano. Without it, its hopeless to do what chopin intended in this excercise
But thats not to say u cant also play it as abby whiteside taught. That works too (mechanically and in the no injury sense). but it fails the cantabile test! Elements of the pieces muddle section demand white-side technique, mostly to rest a moment once all the kernels start to change direction so much.
Font forget to thump out a strong beat in the left! Its cut time really. Rubato in each of the upper hands intra-kernel passages is fine, but keep the beat in the left. Its your self conductor waving his baton to sync up the band of players!
As you get good you can string the kernels together in longer phrases. Then you will use the left hands own very cannily crafted rhythm to feel an almost latin groove to this piece! Long live el commandante (che, castro et al etc) enabling cuban rhythms to remain free from yanqui jazz!
The middle section is the mist fun, since chopin adds in those specifucally chromatic modulations (augmented sixth giving a submediant enharmonic shift point). No doubt he was just learning those formally in his theory class, feeling them out as tonal shifts. Provably influence by bach’s pure mastery of these, here, in oratorio and chorale form.
Rambling now…
]]>What Chopin meant here was that the pleyrl action was responsive to his gravity-tap . Other “lesser” keybeds/actions didnt give any bounce-feedback (making chopin touch ineffective). He was left only with striking the key, getting whatever “standard” tone was built into the mechanism.
Now given the pleryl action he still had to find his own “form” – namely gravity-tapping. When out of form he played with fingers (vs gravity-taps)
The comment about strength refers to his muscular torsi strength needed for belly breathing. This suspends his coughing (since it minimizes air flow induced by classical breathing) and of course the now primed torso sets up a fluid whole arm response …able to sense and react to gravity tapping.
]]>Second, on the way up (only), apply Edna’s notion of “in and out” to each octave’s (extended) appegio. The in and out element of the “kernel” movement is really a dumbed down version of the mechanism required for the seventh etude in the series.
If you are throwing your fifth finger forward always onto the 10th from the root, you have the essence of the motion. (You don’t also throw the first finger, unlike in the seventh study). The in and out will follow automatically. It’s easy to justify stressing the fifth finger since there is a stress mark in the notation!
Third, the thumb direction is very-out on the first kernel and a little-out on the subsequents (of each phrase). Its rhythmic role is different, the first time! Don’t forget to walk hand and arm, and switch (complex phase) by 180 over the last octave (encompassing a 1-extended-octave ascent plus its descent)
Fourth, on those heading-up (and around) extended-octave motions, remember the “steam train” metaphor for the shoulder and the top of the humerus. Its vital for enabling the “free” taubman” forearm.
You need the forearm to be a “free linkage” (and thus you need the shoulder rotator to be specifically eccentric, to deliver the freedom to the link rod). This caboodle makes the whole mechanism respond/react to the bounce-signal from the keybed as the finger is being tapped. The “systems” reaction to that (tiny) signal will be next finger lifting! (It will lift with subconscious in and out or rotation added in to that custom-lift.) This corrects for the positional-eccentricity induced by the last fingers tap – as it hits the designated note (at some custom angle). Strike too had, the signal is lost in the overload.
In short, going up and around uses a self correcting two-eccentric-rotator rod-linked system, with the shoulder rotator i) responding to the (non linear) linear-direction movement of the main steam piston and ii) reacting to the imbalance induced in the wrist double-hinge!
This is just classical steam train mechanical engineering, for delivering (somewhat irregular compression power) over a bumpy track! There needs to be lots of slack (and re-balancing focused “eccentric weighting”).
On the way down, its mostly right hand (descending) easy double rotations, with hand and arm covering the distances between fingers. Obviously there us a snappy single rotation as you play 1-5, resetting the kernel motion.
Here is an eccentric system – self balancing (reno rodeo carnival):
]]>“CHAPTER 4: Chopin Etude #1 Chopin Etude #1 is in C major and is influenced by Bach’s Prelude #1 in the Well Tempered Clavier. In both pieces Arpeggios are used to create a texture in the piece. The contrast is evident… Bach sounds Angelic and quite peaceful, while Chopin sounds dramatic and strong. Chopin completely changed the way the pianist plays the piano forever.”
Start reading this book for free: http://a.co/bqg2NMa
Annoying. Play it right, it’s just as tranquil
]]>took a physicist to explain the chopin etude middle section design ! (Cycles through all 12)
]]>The key technical requirements are exactly those proposed by White side. In addition, you have to play with the cut time rhythm. This means, every two notes is in March Pattern, with the stress on the second note. Apart from those indications, always use Chopin’s fingering.
]]>every north African congo drummer knows this.
]]>Be interesting to know how they describe the hand/finger patterns. May have “alternative” description.
Start reading it for free: http://a.co/6wcchQx
]]>
here is my list – as it comes to my mind.
we have to skip. Just as we did when 10 years of age.
Rotation – in its non initial but final form – is easy to describe.
Why folks make it so mysterious i don’t know. Conjecture will run wild…
In pc games you are used to moving the joystick (and screen character) as does a pilot flying a plane: in 3d. Up/down, forward/back, left/right.
After a while you learn to use your upper arm with forearm and hand (plus finger) joints to also trace a curve in 3d space in front of your nose. You cannot fly a plane without doing this!
Rotation -for real – is moving the “next support point” in the hand to that 3d point , per above, where it will be, once that to-be supported finger plays down (and needs the support).
This creates a pico-pull on the connecting tendon back on that finger still releasing from the last played note. The release io that pico-pull (as you fully release then extend the new finger) gives the feeling of slicing through butter, when timed “just right”. You typically need to do it for an entire ripped chord (or two) to feel it. Its a standing wave – out of phase by one half wavelength. (Ignore if too much data…)
It helps if you can alternate wrist circles too. It needs speed and “coordination”.
Just imagine playing a fast scale on a newborns head. You stroke…
Another metaphor! Old computer disc drives used to create an 3atom high air cushion between the fast-rotating magnetic disc and the fixed ( in 2d but not 3d) reader head. The head would bounce rapidly at these micro distances, synced to the tiny variations of pull/repel from the magnetism deposited “across the air gap”
Got it?
Not telling you how to get there. Telling what it is (once you get there).
]]>This is not as nutty as it sounds. After all i advocate Using the elbows drawing bone (as an orthographic amplifier of micromovements). If you can use two levers even more back (your torso) good for you. Mini , to micro, to pico, …
For me the torso is restricted to using the intercostals (aka alexander technique) for synchronous belly breathing (synced with a coordinated set of rotations, both left(s) and right(s), or interleaved. This happens to squeeze in the upper arms, which is just another means to influence the elbows.
Just do Chinese calligraphy; or greek clay writing. Advanced virtuoso piano is just those movements, made micro. They are what every 12 year old prodigy uses, having honed his/her reflex bouncing tendons.
]]>The result was the movement of a stylus through the wet clay. Just like taubmans moving piano hand through butter.
It was better than Egyptian clay calligraphy!
]]>I think about drawing a tiny lower greek sigma, using my drawing bone. Thats the other downward facing bone you hit when not hurting your elbow bone. Sit at a bench and hold out your hand. Now draw circles with your drawing bone, best done on the bench itself. Your wrist move the same (but in larger circles) . Its just greek geometry…
Draw a lower case sigma next (really tiny, at your elbow/drawing bone) ! This accomplishes the required in and out motion when amplified to the (right) wrist. If you draw the right facing sigma end flourish, you will draw in and out with underflow.
Just ensure, as when performing Chinese calligraphy, to reflect the circular part in the wrist but the flourish across the well aligned knuckles.
Remember : the correct way is to chop (or more likely roll) through the knuckles. Align the thumb joint out and higher, just before you start.
The last point makes more sense when thinking of doing backhand undercut chop or roll, in squash. You learn fast to get your thumb joint out of the way (since otherwise racquet handle following through with the under-roll hits it, with dislocation a possibility) . Forces in squash are bigger than their micro versions used in virtuoso piano play.
]]>Taught wrong, or learned wrong, the elation of grasping just what is meant by Chopin’s flowing wave contrasts with the forearm pain that builds up rapidly.
If you induce the standing wave – think science – from the wrist you perform exactly the movements that induce injury.
If you induce the wave across the knuckles of the hand, it all works. You have both grasped and perfected the chopin hand (not wrist) wave. A throwaway line in an excellent phd dissertation alerted me yo the right/wrong wave mechanics.
Im enjoying university styled pedagological piano learning – books plus thinking and reasoning from controlled experimentation – vs follow some piano performer blindly.
would
]]>Scruffy wuffy had-no hair
Now say it a four beat. Accent on the first, as usual.
One SCRU-fy.
Two WUF-fy.
Three WAS-a.
Four BEAR.
Ie SCRU-fy WUF-fy WAS-a BEAR
1. 2. 3. 4.
Now syncopate it. The first accent lands on the FY of scuf-FY
Scru-FY wuf-FY he-WAS a-BEAR
Scruf-FY wuf-FY he-HAD no-HAIR
IE scruf FY-wu FFY-he WAS-a BEAR
NOW you can play Chopin op 10 number 2 etude!
The trick is to play interlaving that SYNC rhythm pattern with palm thurst on the first chord (scr￼u) and a elbow dig on the second chord (FY). Similarly thrust on he and dig on BEAR
1 234-5 678-1 234-5 6xx
IE A 16/4 RHYTHM
palm thrust on 1 and elbow dig on 5.
]]>The first 60s of the video are about playing 5 notes.
For right hand (backswing and then forward) 12345.
For right hand (forward then backswing) 54321. For left hand (forward and then backswing) 54321. For left (backswing and forward) 12345.
Think like this (for right hand, playing 12345 backswing)
first swing a squash backhand, powering the ball down the left hand side of the court. You strike the ball with your piano arm racquet as you create tone with your fifth. Your fingers are the string of the racket. As with squash, You first anticipate a little racquet/arm height (Upper arm pulls thumb back making tone and jets wrist up a little, automatically), you then let gravity take (your forearm weight) but you catch it (as you single rotate and land the second finger). Next you take the remaining caught momentum and power through the upper arm swing making (double rotation) tones with 3 and 4. At this you are swinging the racquet/arm upwards as you are about to hit the ball. That you do as you double rotate 5.
But we are not finished. We have to (backhand) topspin as we tone 5. This is that tiny muscle jerk as we now bounce off the key bed (only on 5) and induces a reflex that has the upper arm pull the whole arm/racquet into the air. This is also a squash jump back to balanced karate kid pose, ready for what comes next. That’s the much misunderstood AW torso action, for piano. It’s a mix of the tiniest possible key bedding reflex and tiny push up from on right seating bone.
You can figure the forehand next, for 12345 right arm.
Now repeat for the other three cases, each a sequence of backspinning backhand or top-spinning forehand (or vice versa order). For extra credit learn the right backhand chop (for piano) too. It’s puts your final pose orienting down keyboard instead of up.
I think Taubman would have loved this thinking. Pretty sure Edna will hate it. You can add belly breathing to it too, if you want. That’s more AW torso. Rhythmically expanding your legacy gills!
]]>The elbow joint is 3d circular, much like a character in s 3d game
Move you wrist around each axis!
The sparkler. Make in o in dark when holding a sparkler firework. This is rotation around the the z axis
Turn the Ferris wheel. (Using the knob on the reel). This is rotation around x.
Run around the flag, at the olympics. This is rotation around y
Now you have grasped what she meant!
]]>Folks doing cryptography in the 1950s didn’t need to be mathmaticians. They simply needed to understand a particular set of algorithms (that happen to be derived from math theorems).
The https://www.safaribooksonline.com/oriole/probabilistic-programming-from-scratch-1-a-b-testing-with-approximate-bayesian-computation teaches you what a cryptanalyst learned in cryptographics 101, circa 1950. Little had changed since 1943.
If I said this a few years ago, Id be shot. Now its all laid out…
The teacher is good. He’s a total natural. When he says that the hardness of the problem is basically how wide is the distribution of guess, for the count fairs jar of coins, he is exactly right. now one gleans just why, back in 1944 colossus, one is driving the uncertainty out to the very extremes of the deviations … so that one has maximally learned from the simulated data, from guesses, how to minimize the variance from all the trials. That’s a fancy way of saying … the data now supports the conclusion!
In 1943, with ships sinking (at obvious cost) and time being of the essence, one needed means to decide which path to take (when attacking cryptograms). one sees how such entirely qualitative factors could be added to an otherwise quantitative search, to help direct the machine search.
The following address tunny (rather than enigma); but the general principle is the same!
]]>The nsa doublespeak
]]>Thats because “targets” of spying are no longer @customers@
Its lying by definition
]]>Now one sees tunny rectangling as de
]]>Post war turing on cpu instruction set design knew how to leverage convolutionsl computation graphs – documented in the tunny report – to leverage conditional branching for cryptanalysis.
Even i was taught, in first year cd computer science computer architecture courses how the microcode behind each type of conditional branch instruction leverage amore basic computing model : handling the instruction pipeline itself.
What folks need to know is that the fixes indicate the wider problem: microcode download (for good or evil, or good again tomorrow when gchq releases its (well known) targeted spying patch
So what surprised me? That the precisely editions didn’t first require another zero day exploit, compromising the formal kernel security boundary
Gchq going for the user mode exploit is just brazen
]]>In the dream I am explaining that there is little difference in spirit between George Washington’s plantation (a place you are worked to death, raped for breeding and generally oppressed by terroristic white overseers and their nazi bosses making money from race slavery) and Belsen. The essence is the same: mass murder (by forced labor). There is no out given to Washington (oh he was nice and freed his house slaves after his death).
A group of students then go on a field trip, in a giant trailer that flys through the sky (in England). They fly over and in where the next group of reprobates are to be gassed, since society has returned to gassing folks. They are quite nonchalant about the whole experience, as they expect folks to be gassed (since its normal .. and they are not in the gassing class).
You know its a dream because as the trailer full of older students flys – like a 747 – two of the students are outside, like a couple of elves on santas sleigh. But in the dream its normal to be outside at 30k feet!
Well its normal until, as the “plane” is flying over its route and banking at the Isle of White (where some military area is seen, according to the announcer), the sleigh riders start to zombify. They are being gassed (and it happens just before the rest of the class are gassed in the flying rv). Yes its an accident. The flying protocol was mistakenly set as a gassing class ride.
Im flying on the next ride, and as we get on we see body parts being handled as the ride is being prepared – evidence of the last gassing run. On the trip, I and others remark and how unfortunate it is that the wrong group get gassed – specially as they were all well heeled, private school students from wealthy families. But… here we are on the same trip – in a nazi society that has accepted such things as normal.
ok. so I know why these themes come up in the dream – given certain recent reality events that are still present in recently-augmented memory. But its still fascinating to see how the brain concocts a mis-reality given the limited ability of memory and cognition to cooperate as the chemistry of the brain areas each return from sleep state.
]]>Not me!
]]>I fixed the FIRST BIT OF bit rot by replacing no-longer available cardboard sdk imports with an import of the relevant assets from the (older) cardboard unity project… also mentioned in the article. I say “import” – but in reality I used windows explorer to drag/drop the cardboard folder from its source to the assets directory of the unity project.
with that you can at least wander around the scene in the PC unity’s play mode.
]]>which is terrible
]]>And that is every deportee (who returned).
so the rumor is true. Ice will use this as a funnel (for the felon-to-be class). And that’s a lot of folk.
At a policy level I cannot disagree. At a practice level, ice have to do better in leveling. The storm shelter program and red cross Assistance is just another tool (to keep roundup costs low and ice staff safety high).
]]>What did you do !!
]]>Just sad. As in trump sad. But very very American.
]]>It’s like me sayin there are no tapes of my phone and I made none knowing full well NSA tapes everything on my phone and died the taping).
But “i” don’t do it
Classic American disinformation
]]>View the outer bits of the nibble widths box as a third input to the medium that is subject to phase inversion, as a mathematical Kerr effect doubles and triple the balancedness … which drives the number of times the inner bits are inverted. That is data driven computation of the symmetric and asymmetric spin similarity and difference, applied to mixing the round function.
It n feistel analysis term, we are amplifying the rate of confusion per bit in proportion to the information content
Tempting to see this as a repelling process. But once you add the wider Hamiltonian cycles of the p&s with the balacedness generator you get more of chaotic attractor for those (theoretical) bent functions.
Now Turing already taught us to generate custom operator norms, that evolve with the plaintext information content. Using the similarity/dissimilarity basis of the quaternion algebra to tease out the information and use it to generate a data-aware averaging norm that is a masks to both linear and differential comparators, one gets self evolving computation of an operator norm that generates a bent function.
With the feistel network and the des era spn the complexity goes beyond the limit available with a simple sequence of rotors with quaternion group wiring. One gets now to tangent spaces of much finer granularity.
Nsa head – Henry’s spymaster (domestic and foreign)
Cia head – Henry’s assassin and torturer
Fbi – Henry’s secret police (for nobles)
Irs – Henry tax collector
Given Washington’s intentional creation of a slaving state, one should see north america in medieval terms (Canada and modern Mexico aside)
Speaking as a vassal.
]]>Sad as in scientology sad.
Don’t be duped on the corporate practices in (non insurance) billing.
It was interesting how for six weeks folks lied (badly for the most part). Finally a matured sailor fessed up, a bit like the scientologist finally admitting to the theory of aliens taking over the planet (in order to work a familyfirst insurance non billing scam).
Did I say that I love family first’s chiro methods? I can even live with the hardsell (its bot worse than orthopedics hard sell) . I cannot live with the intent to deceive the off plan insurance cases though.
Amazing that a profitable brand has not found it it the right time to ban the internal practice, though.
]]>“Thus, the Fisher information may be seen as the curvature of the support curve (the graph of the log-likelihood).
Near the maximum likelihood estimate, low Fisher information therefore indicates that the maximum appears “blunt”, that is, the maximum is shallow and there are many nearby values with a similar log-likelihood. Conversely, high Fisher information indicates that the maximum is sharp.”
So what dat all mean , I say?
That support is just log likelihood is the first take away
That max has a couple of variant cases is the next. Read carefully.
We already saw how in affine combination spaces one can calculate likelihood functions in terms of log addition. That is, calculate in the algebra of likelihoods (rather than in the algebra of frequency probabilities).
Any gambler should know that in a run of similar results that there is , despite the run, no memory property in the frequencies observed. Thus likelihood is clearly distinguished from frequency.
But what is information and how did Turing apply it to cryptanalysis – knowing it to be yet further distinguished from probabilities and likelihoods both?
The answer lies in the Monte Carlo example. While an unbiased but unbalanced roulette wheel may offer exploitable information about the frequencies observed (the outcomes) it still does not change the likelihood of any particular event.
so what is the exploit value of information?
In the roulette wheel case, it tells you how long you must play the runs before the unbalacedness will show up in the statistics … And improve your return.
The property tells one something about the underlying mechanisms – generating the likelihoods. It tells one about the underlying group and its symmetries ;or lack thereof) used to generate a run, rather than run properties. In roulette wheel terms, it tells about unbalancedness of its mechanics.
In modern cipher design one learns about those boolean functions which are both balanced and non linear (being at a distance as far as possible from specifically affine combination functions.)
Or in pure information science terms, there must be no information from the run about the generators of the likelihoods.
And just as there must be no information flow from the product about the design So there must be no further meta information from the design about the designers (and their intellectual background). The secret of the cipher is not in the algorithm but in how the design impacts complexity.
The easiest way to think about information is to think about the complexity of the machine needed to compute the probability space. Known in the 1930, folks designs ciphers to need more compute power than was available – as measured by the information properties.
Now apply that to 1970s des where dengineers designed resistance to only a certain quantity of mechanical
The last point to note is that the tractability of non linear mappings of spaces (that appear to resist diffrential cryptanalysis) can depend on whether they are generated by linear like vector spaces (keyed by cryptographic parameters). Just as the exponential map links probability spaces to likelihood spaces, so lie groups are related to lie algebras through the exponentiation of (lie) matrices
]]>If u look at the four 1 dimensional representations of the quaternion groups, one has all four combinations of 2 bits.
When wheel breaking a tinny wheel, with its constraints on patters that influence which bit value in the sequence follows its prior, it’s crucial to cast such bit pairings and their biases in abstract terms, for which the quaternion groups 1-dimensional representations fit perfectly.
One has to recall how differential cryptography was conceived then (vs now).
Deltaing allowed convolutions of the “hermitian (quadratic) form” to amplify the bias, allowing reinforcement of biases when (delta’ed) streams are added
They thought of it all as a faltung (vs a generalized quadratic form) for which 2 binary digits are a special case.
Now if one was charged with finding machinery to assist in wheel breaking, being done manually but at high time cost, then noting that a system of suitably wired wheels (wired according to the quaternion group algebra) could represent an ideal set of likelihoods would give rise to it, when suitably biased as a detector of correct wheel patterns
That it all applied to enigma key/wheel breaking (as well as tunny) is still a secret!
Now one can see the algebra of bulges as an arithmetic of semi simple irreps, expressed in the quaternion group basis.
That the groups geometry happens to slightly with an affine simplex allowing limiting convergence of sequences of good guesses is also another secret
]]>It’s common to use Q as the letter for positive definite forms. And one then uses it to average over the group.
There are many Q, since the domain can be over 1 letter back in the cipher text, or 2, or 3… as his Lemma was pointing out (v obliquely). They are all the same, since it’s the invariance one is relying on.
Also see now the basis for his argument why some generators are 1 while the rest is 0.
Same as McCullough but easier!
]]>Even simpler presentation
]]>At the same time, it’s fascinating to see how folks in 1940 arrived at the same theory
The rest of the series looks just as interesting.
Because it opens their field to a hundred million open minded computer science students, eager to unify.
Put Clifford algebra into the heart of year two cs math, its game over.
]]>Sunday reading. So well written
]]>How I’ve been thinking of the fano plane
]]>Turing’s fbar is 1
]]>Now we know why!
]]>Contrasts nicely with the stats motivation that is the background to the (colossus aided) counting attack on Tunny cipher (and certain aspects of enigma too)
]]>So does a us president have the power and/or authority to “arrange” for the @incidental collection” of every collectible communication of us person #99?
Yes.
And yes gchq assist is that @arrangement”
]]>We have yet to see a Newman/Turing analysis (or topology applied to either enigma or tunny (or Italian heybern)) yet.
I see why it would still be seen as sensitive.
]]>It’s clear that the Truisms of all American (cum British) lying are abound; with definitional lying at the fore.
In my Era, pre 911, via 2 layers of Anglo-American (unofficially well coordinated) small contractors, each agency would have the other (small contractor) do metadata collection (on each other’s citizens)
This all went away post 911, when each agency could do it officially (whereas before metadata was legally grey)
What was retained, post 911, was the apparatus of grey ness.
Beware trump, with his CIA and NSA versions of his preatorian guards. Now beholden to the new emporer, the old guard may be lynched; Such is the nature of raw naked (super secret) power.
]]>As I recall when deniability is required, that’s when NSA induced gchq to do the spying on Americans (contact with foreign targets, of course)
Trump must be up by now on how and what NSA do!?
He won’t be as adept as Obama. But give him time. The absolute power of secret spying will either tame his dictatorial impulses or get him rapidly impeached.
]]>Id figured a while ago that he was interested in the shuffle around 1.
But now we get that in eigenvector explanation (which is better than the shuffle!)
any distribution is the sum of 1/n of the 1 eigenvector + a superposition of weighted others.
]]>Professional version of my similar drivel at https://yorkporc.wordpress.com/2013/10/10/turings-quantum-of-informationa-typex-wheel-wiring-plan-predating-shannons-information-theory/
]]>This is the second paper with modern presentation of two of the argumentation devices Turing used in on permutations. First we finally understand the why of wanting to establish that the math power of d generator is always positive 1. And second, we see why his lemma a is concerned with a power of four.
See paper for other examples of both argumentation devices.
]]>see 3.4 log signature s
]]>he really says that g has subgroup h which inturn has a centralizer subgroup h1
see http://www.turingarchive.org/viewer/?id=133&title=29
see also k:
This distribution can be generalized to more complicated sets than intervals. If S is a Borel set of positive, finite measure, the uniform probability distribution on S can be specified by defining the pdf to be zero outside S and constantly equal to 1/K on S, where K is the Lebesgue measure of S.
from https://en.m.wikipedia.org/wiki/Uniform_distribution_(continuous)
]]>https://case.edu/artsci/math/esmeckes/Haar_notes.pdf
i like this writer. she doesnt lose the point with endless symbols.
]]>recall turing used a doubly transitive operator to mix the plaintext differentials within the output space
]]>Center and zero
More great Turing
View as CPU design, instruction set for rational – i.e. Probability densities seen in cryptanalysis
View in terms of early comp sci, searching for a computable group (suited to improbability calculus)
]]>Relate center to quotient as Klein.
We saw this in tunny
]]>Contrast with fano plane which holds for octionions
]]>http://math.stackexchange.com/questions/866026/quaternion-group-as-permutation-group
]]>His system is still constrained to be looking at lambda2 (max difference from constants etc).
Interesting also that the inner product norm is to him just a (easy sum of squares) measure of the squiggle path one takes, with respect to another vector (including his eigenket vectors, k).
]]>as turing was taught it.
]]>Back to the future
Gives a nice notion of distance for measurable probability densities such as those found in Markova ciphers resisting 1943 era differential cryptanalysis
]]>Simple groups
Now we see why Turing left unstated the relationship to differential cryptanalysis.
]]>Link needed.
Because NSA objected and , just as with the dhs attempt to usurp NSA role earlier, was able to state why things must remain with NSA. ;and that’s not even discounting the alternatives lack of deployed capability).
The emotional reason doesn’t take a lot of understanding (and even trump – t for torture and p for pussy, recall – understands that without control over the metadata, you cannot spy. And that means spying as much on congress as vlad the impaler.
At this point NSA will be pitching trump on how they validate and protect him (oh king, imperatur) as the preatorians. At his level of paranoia it will be doubly effective.
]]>ie the screen is the torus surface
we want the circle packing to measure the embedding into spectral uniformity
we want gap minimzed when number of tangents on bith torus are equal
What’s is interesting will be to relate light cones and Padic labeling to the n particle case of the des e functions “slit”, as subkey expansion evolve the positions of the slits, and thereby imposes a discriminator (attacking des)
]]>What is cute is the very simple way the evolution shifts (the distances between the transformed state).
]]>S box nibble sized graph evolution (with quantum coin from support between pairs of plaintext chars).
Distinguished from e(), that de-localized flows, simulating quantum coherence
]]>We even get (after 3 years) why the tunny alphabet was ordered the way it was, when applied to cryptanalysis. See spectral partitioning and the way in which nodes were ordered.
]]>As we will see in a later lecture, there is a nearly linear time algorithm that finds a vector {x} for which the expression {\delta} in the lemma is very close to {1-\lambda_2}, so, overall, for any graph {G} we can find a cut of expansion {O(\sqrt {h(G)})} in nearly linear time.
…for any tunny “run” known to exhibit a stats measurable bias, through just counting (on colossus).
Think of each std deviation worth of amplification as refining the cutset And tuning to the ciphertext, to best decide between improbably candidates (wheel s that in x or still in the edge expansion set)
]]>U also look at the area of each as probability (of the event space). Noting obviously circle is less than triangle.
This is highly pertinent to quantum walks.
Now in terms of resistance to differential cryptanalysis one has to think of tunny attack: which wanted to chose just that cutest (between circle and triangle) that allowed a decision on two hypothesis tied to the improbability of each.
To resist D.C., the weight difference between the two h must be within the spectral gap.
Do I get the two sides of the des design argument. We are requiring the quantum random walk but also needing it amplifications to evolve the density to within the spectral gap do that h cannot be weighted in an attack.
Ok so I was right on my intuition, the other day. Now we have histologucal and pure math support.
]]>So imagine you are studying the infamous quantum mechanics 2 hole screen – separating electron gun on the left from intensity screen. Or the 1 hole. Or the two holes shifted up (or down) a bit on the grate.
Oh and don’t forget that we can flip the grate, should we want the gun on the right (and the screen on the left).
After all like des, quantum mechanics is inevitably reversible, since “information” is conserved.
Now imagine that the e function of des is the grate.
And 2 of the six input bits of the current sbox are the slits in the grates.
The purpose of the way the e function shift inputs left (and right) is to simulate shifting the slits in the grate ip and down.
Why?
So that the qm normal density is shifted.
Our goal is to uniformly fill an intensity space, on the screen. Or better, average the left and right intensity screen (per the classical functional form.
Now, even though we shift our normal curve up and down (as the number of supports in the pair wise plaintext’s chats induce a key particle to move 1,2 3… lambada from the center, within the normal curve (and while constructing/destructing as we go) we still need the addition of intensity curves to uniformly fill the output space.
And here is where comes in the particular key schedule. It’s particular sequencing moves the grate around not only so feistels multiplexor covers all subpace but does so in such manner that guarantees that the concentration of intensity at any point (in 2d intensity space) is never more than the second eigenvalue gap.
Now recall that des does not have reversible sboxes. But we don’t need them! After all we have interleaved diffraction grates, since left 2 right we have half s des round and (right 2 left) we have the other half.
Now view the des subkey generatio functions own (highly programmed) bit duplication as a means of subtly (at huge granularity) measuring the quantum effect, thus influencing just how the left and right particle motions occur – giving a characteristic.
And ensuring that there exists no matrix representation of the same graph.
]]>If the permutations in C are all even, then we say that C is an even conjugacy class. If the permutations in C are all odd, we say that C is an odd conjugacy class.
For n≥5, the subgroup generated by C, denoted by C, is Sn if C is odd, and An if C is even.
now we understand how turing thought about avalanche -and the significance of 4. he used gccs terms, like beetles….
]]>I you were 1920 trained math person, you be trained in such “strange” log tables – and such mechanical devices with vertical wooden “rods” bearing abacus like beads. The latter could compute, using the log basis in question.
So think! Tunny back to rods.
And from rods we get back to enigma/Hebern crytanalysis, and isomorph searching.
Of course, rods in enigma algebra are less about logs and more about relative automorphisms (as one computes conjugates).
But you see the eureka transitions.
Once turing and co figured that a discriminator could exist for a rotor set, now one can leap to its log (and an algebra of bulges).
What unclassified docs don’t say is the parallel analysis going on with quantum mechanics calculations, given the parallel effort going on with the ;mostly compartmentalized) atomic bomb making efforts (circa 1944).
Must have been fun to be thinking about the ” potential” of the electron cloud in a colossus tube/valve and that similar controlled electron (well neuron) flow used to accelerate a uranium chain reaction.
]]>The kind trapdoor I’d want is to probably abandon a given key before having to
Complete all rounds, putting that key at the back of the queue. Given the cost of io in a cluster and the accounting, I want every key derived from that candidate by key schedule to similarly get filtered out of the early trials
So now imagine your field had a special precomputation area with electronics dedicated to the subkey scheduling. So what would that look like?
Look at today’s general purpose CPU pipelining for a good clue on how such custom vlsi was built then.
Also? Since io is the main impeder, think of clustering that is centered on the accounting and queue. One thinks of a giant ram cache… so how do multi cores today share gigs of ram? Probably sane back then…
]]>And hadamard gates implement conditional qbit operations.
Even in 1940 thinking, multiplying u by r meant figuring what the ciphertect would have been should the rotor have rotated the u.
What we want after n rebounds of des is that if u consider each round output to be ur then ur and ur2 differ as do rows on the hadamard matrix.
Ie half the bit differ.
Which is more tangible than “avalanche” since now we had a limiting condition – when the sequence of conditionals has induced the cipher text itself to be/become an action matrix ;that only produces outputs indistinguishable from uniformity)
In q terms, the data under a long sequence of qbit manipulation has itself evolved to become a hadamard action…
Ok so that means we have a replicating group. We have an expander whose action is to output a (key/plaintext parameyerizrd) expander code that is itself an action…
]]>An expander is that set of graph that assures that the maximal use of edges will occur (diffusing Bayesian factors) And the profusion of edges for almost all cliques will quickly move one out of a local cycle to wider cycles more globally afield. Moreover as the edges cross the boundary between the clique and all the other potential rods, one wants the transitioning action to replace codependency on plaintext bits with dependency on key bits.
In a crypto avalanche one wants an average result that a change of one unit of distance in key or plaintext chooses half the edges that flip the cipher text bit on the next round. That is key and plaintext become isomorphs with even one bit flip inducing acting as an initial condition that causes an increase in uniformity.
So while the rotor wirings may be inducing long sequence of quantum conditional operations that preserve the dependency of each plaintext bit on key bits And preserve the randonmness of the key bit throughout, it’s the function of the expander to be guiding the walk through the qbit space.
Sent from my iPhone
]]>The side effect of the expander code is to deliver an diffusion engine that enables a sparse matrix to redistribute the Bayesian factors of each nibble over the entire vector space, in random directions and distance.
You can see the Hamiltonian graphs as the wiring of rotor cores in the rotor versions of des.
]]>The sub is compressing but the per distributes (randomly) so eventually you have covered the entire data space.
]]>Last night it was both : a partial NSA affiliate hiking, where the steps of the intricate inca path represented the inner story on how and why the des key schedule provides strength.
Go figure. It was more tangible than the previous one where I was looking at a meta magical wAterfall (on the mythical NSA campus) that expressed des (while trying not to get the hall cleaner into trouble…)
Tis true that (10 years later) today I found out just why Msft added mscep to their cert server (circa 2006). Hopefully I’m not dreaming pkcs7 or xml, tonight!
]]>