http://tech.groups.yahoo.com/group/Number_Theory_group/message/233
Can anyone help me with this?

I need to get the product of

{(1-1/(x/ln(x))*(1+(1/ln(x)) + (2.51/ln(x)^2))) : 30457 <= x <= 30676, x
integer}.

Perhaps that can be done using Wolfram Alpha?

With thanks in advance.

Z

Re: One for Wolfram?
Posted by: "Ross Millikan" millikan.ross@...
rmillika@...
Wed Mar 14, 2012 5:04 pm (PDT)


Here is what I got in Excel:

30457

1.120030187

30458

1.120029741

30459

1.120029294

30460

1.120028848

30461

1.120028402

30462

1.120027955

30463

1.120027509

30464

1.120027063

30465

1.120026617

30466

1.12002617

30467

1.120025724

30468

1.120025278

30469

1.120024832

30470

1.120024385

30471

1.120023939

30472

1.120023493

30473

1.120023047

30474

1.120022601

30475

1.120022155

30476

1.120021709

30477

1.120021263

30478

1.120020817

30479

1.120020371

30480

1.120019924

30481

1.120019479

30482

1.120019033

30483

1.120018587

30484

1.120018141

30485

1.120017695

30486

1.120017249

30487

1.120016803

30488

1.120016357

30489

1.120015911

30490

1.120015465

30491

1.12001502

30492

1.120014574

30493

1.120014128

30494

1.120013682

30495

1.120013236

30496

1.120012791

30497

1.120012345

30498

1.120011899

30499

1.120011454

30500

1.120011008

30501

1.120010562

30502

1.120010117

30503

1.120009671

30504

1.120009226

30505

1.12000878

30506

1.120008334

30507

1.120007889

30508

1.120007443

30509

1.120006998

30510

1.120006552

30511

1.120006107

30512

1.120005661

30513

1.120005216

30514

1.120004771

30515

1.120004325

30516

1.12000388

30517

1.120003435

30518

1.120002989

30519

1.120002544

30520

1.120002099

30521

1.120001653

30522

1.120001208

30523

1.120000763

30524

1.120000317

30525

1.119999872

30526

1.119999427

30527

1.119998982

30528

1.119998537

30529

1.119998092

30530

1.119997646

30531

1.119997201

30532

1.119996756

30533

1.119996311

30534

1.119995866

30535

1.119995421

30536

1.119994976

30537

1.119994531

30538

1.119994086

30539

1.119993641

30540

1.119993196

30541

1.119992751

30542

1.119992306

30543

1.119991861

30544

1.119991416

30545

1.119990972

30546

1.119990527

30547

1.119990082

30548

1.119989637

30549

1.119989192

30550

1.119988748

30551

1.119988303

30552

1.119987858

30553

1.119987413

30554

1.119986969

30555

1.119986524

30556

1.119986079

30557

1.119985635

30558

1.11998519

30559

1.119984745

30560

1.119984301

30561

1.119983856

30562

1.119983412

30563

1.119982967

30564

1.119982523

30565

1.119982078

30566

1.119981634

30567

1.119981189

30568

1.119980745

30569

1.1199803

30570

1.119979856

30571

1.119979411

30572

1.119978967

30573

1.119978523

30574

1.119978078

30575

1.119977634

30576

1.11997719

30577

1.119976745

30578

1.119976301

30579

1.119975857

30580

1.119975412

30581

1.119974968

30582

1.119974524

30583

1.11997408

30584

1.119973636

30585

1.119973191

30586

1.119972747

30587

1.119972303

30588

1.119971859

30589

1.119971415

30590

1.119970971

30591

1.119970527

30592

1.119970083

30593

1.119969639

30594

1.119969195

30595

1.119968751

30596

1.119968307

30597

1.119967863

30598

1.119967419

30599

1.119966975

30600

1.119966531

30601

1.119966087

30602

1.119965643

30603

1.1199652

30604

1.119964756

30605

1.119964312

30606

1.119963868

30607

1.119963424

30608

1.119962981

30609

1.119962537

30610

1.119962093

30611

1.119961649

30612

1.119961206

30613

1.119960762

30614

1.119960318

30615

1.119959875

30616

1.119959431

30617

1.119958988

30618

1.119958544

30619

1.1199581

30620

1.119957657

30621

1.119957213

30622

1.11995677

30623

1.119956326

30624

1.119955883

30625

1.119955439

30626

1.119954996

30627

1.119954552

30628

1.119954109

30629

1.119953666

30630

1.119953222

30631

1.119952779

30632

1.119952336

30633

1.119951892

30634

1.119951449

30635

1.119951006

30636

1.119950562

30637

1.119950119

30638

1.119949676

30639

1.119949233

30640

1.11994879

30641

1.119948346

30642

1.119947903

30643

1.11994746

30644

1.119947017

30645

1.119946574

30646

1.119946131

30647

1.119945688

30648

1.119945245

30649

1.119944802

30650

1.119944358

30651

1.119943915

30652

1.119943472

30653

1.11994303

30654

1.119942587

30655

1.119942144

30656

1.119941701

30657

1.119941258

30658

1.119940815

30659

1.119940372

30660

1.119939929

30661

1.119939486

30662

1.119939044

30663

1.119938601

30664

1.119938158

30665

1.119937715

30666

1.119937272

30667

1.11993683

30668

1.119936387

30669

1.119935944

30670

1.119935502

30671

1.119935059

30672

1.119934616

30673

1.119934174

30674

1.119933731

30675

1.119933289

30676

1.119932846

I think he is looking for 30456?
Where the product goes below one.
FullSimplify[
   ExpandAll[(1 - 1/(x/Log[x])*(1 + (1/Log[x]) + (2.51/Log[x]^2)))]]
(-2.51` + (-1.` + x - 1.` Log[x]) Log[x])/(x Log[x])
f[y_] := Product[(1 -
      1/(x/Log[x])*(1 + (1/Log[x]) + (2.51/Log[x]^2))), {x, 30457, y}]
Plot[f[y], {y, 30457, 30676}]
Table[f[y], {y, 30456, 30457}]
{1, 0.9996202123558691`}
But the first Prime in that region is: 30467
   Flatten[Table[If[PrimeQ[y], y, {}], {y, 30456, 30676}]]
   {30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529, \
30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, \
30661, 30671}

http://www.wolfram.com/news/wolfram-education-portal.html
Wolfram Offers Next Innovation in Education Technology with Wolfram
Education Portal

January 18, 2012—Wolfram today announced the launch of the Wolfram
Education Portal, providing teachers and students alike with a new way
to integrate technology into learning.

The Wolfram Education Portal, available at education.wolfram.com, comes
equipped with dynamic teaching tools and materials such as an
interactive textbook, lesson plans aligned to the common core standards,
and many other supplemental materials for courses, including
Demonstrations, widgets, and videos, all built by Wolfram education experts.

"Wolfram has long been a trusted name in education, as the creators of
Mathematica, Wolfram|Alpha, and the Wolfram Demonstrations Project,"
says Crystal Fantry, Senior Education Specialist at Wolfram. "We have
created some of the most dynamic teaching and learning tools available,
and the Wolfram Education Portal offers the best of all of these
technologies to teachers and students in one place."

The Education Portal, currently in Beta, contains full materials for
Algebra and partial materials for Calculus, but will continue to grow
and improve. Wolfram plans to expand the Education Portal to include
community features, problem generators, web-based course apps, and the
ability to create personalized content.

Wolfram developed the interactive textbook by working with the CK-12
Foundation, a nonprofit organization with the mission to produce free
and open-source K–12 materials aligned to state curriculum standards and
customized to meet student and teacher needs. The available Algebra
textbook takes CK-12's Algebra I FlexBook and makes it dynamic with
Wolfram technologies, including Wolfram|Alpha widgets, Wolfram|Alpha
links, interactive Demonstrations created in Mathematica, and the
Computable Document Format (CDF).

Wolfram has a longstanding commitment to providing educators and
students with the highest quality products and materials to enhance the
learning experience. These resources include Mathematica, Wolfram|Alpha,
CDF, the Demonstrations Project, and Computer-Based Math, as well as
Course Assistant Apps. Each Course Assistant App is custom-designed
specifically for today's popular courses, using an intuitive interface
that guides users through the coursework to help solve problems, not
just give answers.

CK-12 currently provides free STEM content for middle and high school.
Offerings include FlexBooks® digital textbooks, an SAT prep site, and an
interactive Algebra 1 curriculum. CK-12 is in the process of providing a
next-generation system for learner-focused features like guided
learning, analytics, and feedback for students. To learn more, visit
CK12.org.

For more information and to explore the Wolfram Education Portal, please
visit the website.

The Product is Tanh like:
  From 2 to the cutoff at 30456 it is one.
  From larger numbers to Infinity it is very near zero.
Where is the function exactly 0.5?
Something like :
f[y_] := Product[(1 -
      1/(x/Log[x])*(1 + (1/Log[x]) + (2.51/Log[x]^2))), {x, 30457, y}]
FindRoot[f[y]==1/2,{y,2*30456}]

Might work.
I'm running a correlation dimension for a second time
as I had the scale wrong the first time.
Takes a real long time for the 10000 value type.
Roger Bagula

f[t_] = Cos[t]/Max[Cos[t], Max[Cos[t + 2 Pi/3], Cos[t + 4 Pi/3]]]
g[t_] = Sin[t]/Max[Cos[t], Max[Cos[t + 2 Pi/3], Cos[t + 4 Pi/3]]]
gw = ParametricPlot3D[{f[t]*f[p], g[t] f[p], g[p]}, {t, -Pi,
     Pi}, {p, -Pi, Pi}, PlotPoints -> 90,
    ViewPoint -> {6.022, -4.428, 5.012}, Axes -> False, Boxed -> False,
    Mesh -> False, ColorFunction -> "Rainbow"]

http://library.wolfram.com/infocenter/MathSource/4945/

1. Description
2. Features
3. Requirements
4. Screenshots
5. Manual
6. .mp3 Projects
7. .mov Projects
8. Download
9. Registration
10. Contact

Virtual Composer (VC) is a multiple track graphical music sequencer acting as a QuickTime Musical Instruments (QTMI) interface for the Macintosh, designed for perfect execution of complex polyphonic music using either QTMI's libraries or using custom SoundFont libraries.

VC is intended mainly for performers who want to generate high quality musical executables acting as a musical renderer and sequencer. It is thus predominantly performance-oriented. It is not intended as a musical notator as it contains only a minimal (but sufficient) set of notation capabilities, but can be used as such for simple scores.

Playing is effected via the QTMI synthesizers or via SoundFonts so no MIDI cables or external devices are needed. All upsampling and downsampling is done automatically by QuickTime.

Features

1. Sophisticated playback using QuickTime or SoundFonts.
2. Asynchronous animation during playback.
3. Linear channel editor with chords^[1].
4. Channels can be disabled individually both in editor and during playback^[1].
5. Local and global QuickTime controllers.
6. Baroque and modern ornaments with alternate durations^[2].
7. Advanced channel heuristics.
8. Plays in alternate temperaments^[3].
9. Exports in a variety of formats^[4].
10. Help window and balloon help.
11. Debugger.

Requirements

1. A fast color Macintosh (clock speeds higher than 120 MHz strongly recommended).
2. MacOS 7.x-9.x or OS X.
3. At least 5 Megabytes of RAM.
4. QuickTime version 2.1 or later (QuickTime 4.1.2/6.x/7.x recommended).
5. The font Petrucci (provided in the distribution package).

Screenshots

You can view program screenshots here.

Manual

The program manual is included with the download in .pdf format and describes the program's more elaborate program functions. You can read it here.

.mp3 Projects

The projects below have been created by exporting VC scores into .aiff's and then encoding them as .mp3's at 128/112 kbits and 44.1 kHz, using QTMI version 4.1.2. Click on an project to download:

1. Crux Voudon by Aeon Music Productions (128 kbits, 0.9 MBs).
2. Don Juan by Aeon Music Productions (128 kbits, 1.2 MBs).
3. Etude No. 5, opus 25 by F. Chopin (128 kbits, 2.6MBs).
4. Gigue from Partita No. III by J.S.Bach, (128 kbits, 1.2 MBs) (arranged by the author).
5. Prelude & Fugue No. 2 from the Well-Tempered Clavier by J.S.Bach (128kbits, 3.6 MBs).
6. Prelude & Presto from Lute Suite BWV 996 by J.S.Bach (128 kbits, 1.6 MBs).
7. Same Prelude (as above) from Lute Suite BWV 996 by J.S.Bach, using a custom Lute-Harpsichord instrument, created by VC with samples extracted and multisampled from a Hungaroton commercial CD, featuring Gergely Sarkozy's own Lute-Harpsichord (128 kbits, 0.8 MBs), (consult section on CD Multisampling for details).
8. 3 Part Sinfonia No. 9 by J.S.Bach (112 kbits, 3.4 MBs) (arranged by the author).
9. 3 Part Sinfonia No. 14 by J.S.Bach (128 kbits, 1.1 MBs) (arranged by the author).
10. Goldberg Variation No. 5 by J.S.Bach (128 kbits, 1.2 MBs).
11. Nighfall - Starfall - Abyss by Aeon Music Productions (128 kbits, 3.8 MBs).
12. Fugue No. 4 from the Well-Tempered Clavier by J.S.Bach (112 kbits, 2.6 MBs) (arranged by the author).
13. Fugue No. 5 from the Well-Tempered Clavier by J.S.Bach (128 kbits, 1.2 MBs), using a coupled harpsichord custom sample.
14. 3 Part Sinfonia No. 7 by J.S.Bach (128 kbits, 2.7 MBs) (arranged by the author).
15. Sonata K 224 by Domenico Scarlatti (128 kbits, 1.3 MBs).
16. 3 Part Sinfonia No. 15 by J.S.Bach (128 kbits, 0.9 MBs), using a coupled harpsichord custom sample.
17. Walz No. 11 by Johannes Brahms (128 kbits, 1.3 MBs).
18. Fugue for Prelude BWV 999 by the author (128 kbits, 1.3 MBs) (the score for this fugue can be downloaded here in .pdf).
19. Fugue for Prelude BWV 999 by the author on Church Organ (128 kbits, 1.4 MBs) (the score for this fugue can be downloaded here in .pdf).
20. Four Voice Orchestral Fugue by the author (128 kbits, 1.9 MBs) (the score for this fugue can be downloaded here in .pdf).
21. Four Voice Organ Fugue by the author (128 kbits, 2.1 MBs) (the score for this fugue can be downloaded here in .pdf).
22. Source Unknown, opus 4 by the author (QTMI 4.1.2, MacOS 8, 128 kbits, 1.2 MBs).
23. Source Unknown, opus 4 by the author (QTMI 7.6.6, Win, 128 kbits, 1.2 MBs).
24. Echoes from the Deep, opus 5 by the author (QTMI 4.1.2, MacOS 8, 128 kbits, 1 MB).
25. Echoes from the Deep, opus 5 by the author (QTMI 7.6.6, Win, 128 kbits, 1 MB).
26. Soli Deo Gloria Fugue, opus 6 by the author (128 kbits, 2.3 MB) (the score for this fugue can be downloaded here in .pdf).
27. "Joke" Fugue, opus 7 by the author (128 kbits, 2.7 MB) (the score for this fugue can be downloaded here in .pdf).
28. Passacaglia I on Source Unknown, opus 8a by the author (128 kbits, 11.3 MB).
29. Passacaglia II on Source Unknown, opus 8b by the author (128 kbits, 11.3 MB).

.mov Projects

The projects below have been created by exporting VC scores into QuickTime movies, hence are playable on any system that has QuickTime installed, with its version of QuickTime Instruments. Click on a project to download:

1. Fugue-Sonate III by P. Hindemith.
2. Fugue No. 10 from the Well-Tempered Clavier by J.S. Bach.
3. Don Juan by Aeon Music Productions.
4. Prelude from English Suite No. IV by J.S. Bach.
5. Complete Lute Suite BWV 996 by J.S.Bach.
6. Complete Set of 3 Part Sinfonias by J.S.Bach.
7. Sarabande & Coupled by J.S.Bach.
8. Sarabande & Coupled by G.F. Haendel.

Depending on your System, you must download and install:

Latest version is 3.5.9, build #0 for MacOS 9 and 3.6.1 for MacOS X.

Registration

VC is freeware. Donations through PayPal are appreciated, but are not necessary. You can email the author and he will send you a registration number by email which you can use to activate the saving function of VC(X).

Contact

The author can be contacted here.

Notes

1. Making VC particularly suitable for fugue composition and counterpoint.
2. Making VC particularly suitable for analyzing the works of J.S. Bach.
3. Equal, Pythagorean, Modified Pythagorean, Ptolemaic (Just), Mean-Tone, Kirnberger III, Werckmeister III, Kellner Wohltemperirt, Custom.
4. .aiff, standard midi (smf0), abc, text, executable, QuickTime movie, disassembly dump, MusicXML.
5. The table above assumes that you are booting into the indicted OS. The VC applications are not guaranteed to work if you are booting into a different OS or if you use the applications in Classic mode emulation from OS X.
6. Downloading the application and fonts without the supporting files or the opposite (the supporting files without the application and fonts) will be an exercise in futility/frustration. You need to download both, for the corresponding version of your OS.
7. You may need to install a different QuickTime version depending on your System configuration. For more details, consult the program manual.
8. The fat application is identical to both 68k/PPC versions and is provided for people who don't know if they are running on a 68k or a PPC machine (it will run on both). If your machine is a PPC, download the PPC version to minimize download times.

Copyright © 1998 - 2011, Morpheus, Inc.

Here is how Mathematica replaces Musica:

Clear[a, c, b]
a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[5] = 1; a[6] = 1;
a[n_] := a[n] = a[a[a[n - 1]]] + a[n - a[a[-3 + n]]]
c = Table[Mod[a[n], 12], {n, 1, 300}]
b = Sound[
    Table[SoundNote[Mod[a[n], 12], 0.2, "JazzGuitar"], {n, 1, 300}]]
Export["trirecusiveJG.mid", b]
b1 = Sound[
    Table[SoundNote[Mod[a[n], 12] - 24, 0.2, "ElectricBass"], {n, 1,
      300}]]
Export["trirecusiveEB.mid", b1]
b2 = Sound[
    Table[SoundNote[Mod[a[n], 12] - 12, 0.2, "Marimba"], {n, 1, 300}]]
Export["trirecusiveM.mid", b2]
b3 = Sound[Table[SoundNote["MidTom", 0.2*a[n]/72], {n, 1, 300}]]
Export["trirecusiveD.mid", b3]

Based on an infinite Prime group that behaves as a zeta function s=2:
Solve[1/(1 - x^2*Prime[n]) == 1/n^2, x]

   {{x -> -(Sqrt[1 - n^2]/Sqrt[Prime[n]])}, {x -> Sqrt[1 - n^2]/
     Sqrt[Prime[n]]}}

a[n] = Floor[(n^2 - 1)/Prime[n]]

Table[a[n], {n, 1, 200}]

   {0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, \
6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, \
10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, \
13, 13, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, \
15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, \
18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, \
20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, \
22, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, \
25, 25, 25, 25, 26, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, \
27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 30, \
30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32, 32, \
32, 32, 32, 32}

ListLinePlot[%]

http://forums.wolfram.com/student-support/topics/25932

06/21/11 10:28am

There is an old package at
http://library.wolfram.com/infocenter/MathSource/4945/
that might be useful. If you come up with a modern (i.e., Mathematica 7
or later) MIDI importer, please consider submitting it to
library.wolfram.com so others can use it.

There are freeware/shareware applications available on the web for
translating among audio formats. Caveat Downloador.

http://books.google.com/books?id=ewr685ME-E0C&pg=PA100&lpg=PA100&dq=import+midi+\
into+mathematica&source=bl&ots=oFmHgmHQJy&sig=Mh8rh0o6aI4HZtUWzJUVvzLfSHI&hl=en&\
sa=X&ei=UeFoT82FKueKiAKZ_MivBw&ved=0CEsQ6AEwBTgK#v=onepage&q=import%20midi%20int\
o%20mathematica&f=false

Question:How do I import midi files into Mathematica?
Answer:
Seth Chandler • What about using some external midi to XML converter
such as http://en.nemidi.com/conversor/mid2xml.html and then importing
as XML for data analysis. It may not be elegant, but the XML data
structure will be a lot more pleasant than MIDI for most data analysis
purposes.
Here is what I did:
Clear[a, newdata]
(*http://en.nemidi.com/conversor/mid2xml.html*)
(*upload a midi: \
download the xml file*)
(* take out the second line which gives the \
error:
During evaluation of In[2]:=XML`Parser`XMLGet::prserr:Expected a \
markup declaration at Line:2 Character:3 in \
http://www.musicxml.org/dtds/MIDIEvents10.dtd.During evaluation of \
In[2]:=Import::fmterr:Cannot import data as XML format. \
  >>Out[2]=$Failed*)
a = Import["astrangebluemelody.xml", {"XMLElement"}]
Length[a]
1
(* strip the tree*)
events =
Cases[a, XMLElement["Event", _, _], Infinity]
Length[events]
1092
absolutes = Cases[events, XMLElement["Absolute", _, _], Infinity]
Length[absolutes]
1092
noteons = Cases[events, XMLElement["NoteOn", _, _], Infinity]

Length[noteons]
1076
(* isolate the Channel/ Track : Here Channel ->1*)
channel1s =
Cases[noteons, XMLElement[_, {"Channel" -> "1", _, _}, _], Infinity]
Length[channel1s]
262
channel1sv =
Cases[channel1s, XMLElement[_, {_, _, "Velocity" -> "127"}, _],
Infinity]

Then I stripped out all the remaining "stuff" by hand to get just the
note values:
I sure did this the hard way, but I got a simple tune in: 26.2 seconds,
it was easier to compose than to get into Mathematica...
The Midi note values seem to be about 60 =5*12 higher than Mathematica;
Clear[a, b, c]
a = {65, 67, 69, 63, 69, 72, 76, 65, 63, 64, 65, 65, 69, 69, 72, 76,
79, 77, 72, 72, 76, 79, 84, 86, 81, 81, 84, 65, 67, 69, 63, 69, 72,
76, 65, 63, 64, 65, 65, 69, 69, 72, 76, 79, 77, 72, 72, 76, 79, 84,
86, 81, 81, 84, 84, 86, 81, 79, 76, 79, 77, 72, 72, 69, 63, 72, 72,
69, 63, 69, 64, 79, 76, 72, 76, 75, 76, 72, 69, 65, 69, 81, 72, 72,
69, 65, 62, 72, 69, 65, 62, 75, 81, 84, 84, 86, 81, 79, 76, 79, 77,
72, 72, 69, 63, 72, 72, 69, 63, 69, 64, 79, 76, 72, 76, 75, 76, 72,
69, 65, 69, 81, 72, 72, 69, 65, 62, 72, 69, 65, 62}
c = Table[a[[n]] - 60 - 24, {n, 1, Length[a]}]
ListLinePlot[a]
b = Sound[
Table[SoundNote[a[[n]] - 60, 0.2, "JazzGuitar"], {n, 1,
Length[a]}]]
Export["sbm_JG.mid", b]
b1 = Sound[
Table[SoundNote[c[[n]], 0.2, "ElectricBass"], {n, 1, Length[a]}]]
Export["sbm_EB.mid", b1]
b2 = Sound[
Table[SoundNote[a[[n]] - 60 - 12, 0.2, "Marimba"], {n, 1,
Length[a]}]]
Export["sbm_M.mid", b2]

I attached the original midi four track/ 4 channel
so you can compare and try it yourself.

ZetaZero[n]=1/2+I*b[n]
I got the Idea that this is cyclotomic as:( I use n+1 because of the logs)
Exp[I*Log[n+1]*b[n]]=Exp[I*2*Pi*(n+1)^k]

Clear[a, b, k]
l = 100
b[n_] = I*(ZetaZero[n] - 1/2)
k[n_] = (Log[Log[n + 1]*b[n]] - Log[2*Pi])/Log[n + 1]
a = Table[N[k[n]], {n, 1, l}];
ListLinePlot[Re[a]]
ListLinePlot[Im[a]]
ListLinePlot[Abs[a]]
c = Table[N[{Re[k[n]], Im[k[n]]}], {n, 1, l}];
ListLinePlot[c, PlotRange -> All]

The curves appear to be exponential decays
and it is complex for some reason or other...

http://www.electronicsweekly.com/Articles/22/03/2012/53268/science-pattern-maste\
r-wins-million-dollar-mathematics-prize.htm
Science: Pattern master wins million-dollar mathematics prize
Jacob Aron, New Scientist
Thursday 22 March 2012 00:01

Imagine I present you with a line of cards labelled 1 through to n,
where n is some incredibly large number. I ask you to remove a certain
number of cards – which ones you choose is up to you, inevitably leaving
ugly random gaps in my carefully ordered sequence. It might seem as if
all order must now be lost, but in fact no matter which cards you pick,
I can always identify a surprisingly ordered pattern in the numbers that
remain.

As a magic trick it might not equal sawing a woman in half, but
mathematically proving that it is always possible to find a pattern in
such a scenario is one of the feats that today garnered Endre Szemerédi
mathematics' prestigious Abel prize.

The Norwegian Academy of Science and Letters in Oslo awarded Szemerédi
the one million dollar prize today for "fundamental contributions to
discrete mathematics and theoretical computer science". His specialty
was combinatorics, a field that deals with the different ways of
counting and rearranging discrete objects, whether they be numbers or
playing cards.

The trick described above is a direct result of what is known as
Szemerédi's theorem, a piece of mathematics that answered a question
first posed by the mathematicians Paul Erdos and Pál Turán in 1936 and
that had remained unsolved for nearly 40 years.

Irregular mind

The theorem reveals how patterns can be found in large sets of
consecutive numbers with many of their members missing. The patterns in
question are arithmetic sequences – strings of numbers with a common
difference such as 3, 7, 11, 15, 19.

Such problems are often fairly easy for mathematicians to pose, but
fiendishly difficulty to solve. The book An Irregular Mind, published in
honour of Szemerédi's 70th birthday in 2010, stated that "his brain is
wired differently than for most mathematicians".

"He's more likely than most to come up with an idea from left field,"
agrees mathematician Timothy Gowers of the University of Cambridge, who
gave a presentation in Oslo on Szemerédi's work following the prize
announcement.

Szemerédi actually came late to mathematics, initially studying at
medical school for a year and then working in a factory before switching
to become a mathematician. His talent was discovered by Erdos, who was
famous for working with hundreds of mathematicians in his lifetime.

Modest winner

When Szemerédi proved his theorem in 1975 he also provided
mathematicians with a tool known as the Szemerédi regularity lemma,
which gives a deeper understanding of large graphs – mathematical
objects often used to model networked structures such as the internet.

The lemma has also helped computer scientists better understand a
technique in artificial intelligence known as "probably approximately
correct learning". Szemerédi also worked on another important computing
problem related to sorting lists, demonstrating a theoretical limit for
sorting using parallel processors, which are found in modern computers.

Speaking on the phone to Gowers after receiving his award, Szemerédi
said he was "very happy" but suggested that there were other
mathematicians more deserving than himself. Gowers told our sister site
New Scientist that Szemerédi was "very modest", adding that "he is a
worthy winner and a lot of people think this sort of recognition is long
overdue in his case".

http://en.wikipedia.org/wiki/Endre_Szemer%C3%A9di

I thought of looking at the results of behavior of individual primes:
Only two primes occur in four different finite differences Schwarzian
derivatives!
(*http://en.wikipedia.org/wiki/Schwarzian_derivative*)

f1[n_] = Prime[n + 1] - Prime[n]
f2[n_] = Prime[n + 2] - 2*Prime[n + 1] - Prime[n]
f3[n_] = Prime[n + 3] - 3*Prime[n + 2] + 3*Prime[n + 1] - Prime[n]
sf[n_] = f3[n]/f1[n] - (3/2)*(f2[n]/f1[n])^2
a = Table[N[-sf[n]], {n, 1, 100}]
(* staircase behavior of individual primes*)
b = Sort[Flatten[
     Table[If[IntegerQ[-sf[n]], {n, n + 1, n + 2, n + 3}, {}], {n, 1,
       500}]]]
{3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 13, \
14, 14, 15, 15, 16, 16, 17, 21, 22, 23, 24, 26, 27, 27, 28, 28, 28, \
29, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 32, 33, 34, 37, 38, 38, \
39, 39, 40, 40, 41, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 49, 50, \
50, 51, 51, 52, 59, 60, 61, 62, 63, 64, 64, 65, 65, 66, 66, 67, 69, \
70, 70, 71, 71, 72, 72, 73, 74, 75, 76, 77, 84, 85, 86, 87, 89, 90, \
91, 92, 97, 98, 99, 100, 113, 114, 115, 116, 116, 117, 117, 118, 118, \
119, 119, 120, 120, 121, 122, 122, 123, 123, 124, 125, 126, 127, 127, \
128, 128, 129, 129, 130, 132, 133, 134, 135, 142, 143, 144, 145, 148, \
149, 150, 151, 152, 153, 154, 155, 163, 164, 165, 166, 166, 167, 167, \
168, 168, 169, 169, 170, 181, 182, 182, 183, 183, 184, 184, 185, 202, \
203, 204, 205, 206, 207, 207, 208, 208, 209, 209, 210, 212, 213, 214, \
215, 224, 225, 225, 226, 226, 226, 227, 227, 227, 228, 228, 229, 231, \
232, 233, 234, 234, 235, 235, 236, 236, 236, 237, 237, 237, 237, 238, \
238, 238, 239, 239, 240, 243, 244, 244, 245, 245, 246, 246, 247, 253, \
254, 255, 256, 261, 262, 262, 263, 263, 264, 264, 264, 265, 265, 266, \
267, 276, 277, 277, 278, 278, 279, 279, 280, 285, 286, 286, 287, 287, \
287, 288, 288, 288, 289, 289, 290, 294, 295, 296, 297, 302, 303, 304, \
305, 313, 314, 315, 316, 318, 319, 320, 321, 322, 323, 324, 325, 325, \
326, 327, 328, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, \
343, 347, 348, 348, 349, 349, 350, 350, 351, 352, 353, 354, 354, 355, \
355, 355, 356, 356, 357, 357, 358, 361, 362, 363, 364, 366, 367, 368, \
369, 371, 372, 373, 374, 377, 378, 379, 380, 384, 385, 386, 387, 389, \
390, 390, 391, 391, 391, 392, 392, 392, 393, 393, 394, 404, 405, 406, \
407, 408, 409, 410, 411, 411, 412, 413, 414, 414, 415, 416, 417, 428, \
429, 430, 431, 438, 439, 440, 441, 444, 445, 446, 447, 447, 448, 448, \
449, 449, 450, 450, 450, 451, 451, 452, 453, 458, 459, 460, 460, 461, \
461, 462, 463, 466, 467, 467, 468, 468, 469, 469, 469, 470, 470, 471, \
472, 475, 476, 477, 477, 478, 478, 479, 480, 484, 485, 486, 487, 492, \
493, 494, 495, 498, 499, 500, 501}
ListLinePlot[a, PlotRange -> All]
ListLinePlot[b, PlotRange -> All]
(* frequency of occurrence of of one prime in an integer valued
Schwarzian derivative*)
Flatten[Table[If[Count[b, n] > 0, Count[b, n], {}], {n, 1, Max[b]}]]
{1, 2, 3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 4, 3, \
3, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, \
1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, \
2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, \
1, 1, 1, 2, 2, 3, 4, 3, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 3, \
2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 1, \
1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, \
3, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 2, 1, 1, 1, 1, 2, 2, 1, 1, \
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

A biscuit function that can be used to generate
fractal triangular waves:

s = N[Log[2]/Log[3]];
f[x_] = Sum[TriangleWave[2^n*x]/2^(s*n), {n, 0, 20}];
g[x_] = Sum[TriangleWave[2^n*(x + 1/4)]/2^(s*n), {n, 0, 20}];
ParametricPlot[{f[x], g[x]}, {x, 0, 2}, Axes -> False]
ParametricPlot[{(f[x] + g[x])/Sqrt[2], (f[x] - g[x])/Sqrt[2]}, {x, 0,
    2}, Axes -> False]

(*Cartoon definition*)
PiecewiseExpand[TriangleWave[x], 0 < x < 2]
\[Piecewise] {
    {4 (-2 + x), x >= 7/4},
    {4 (-1 + x), 3/4 <= x < 5/4},
    {4 x, x < 1/4},
    {-2 (-3 + 2 x), 5/4 <= x < 7/4},
    {-2 (-1 + 2 x), \!\(\*
       TagBox["True",
        "PiecewiseDefault",
        AutoDelete->False,
        DeletionWarning->True]\)}
   }

(* fractal triangular waveforms*)
Plot[{f[x], g[x]}, {x, 0, 2}, Axes -> False]
Plot[f[x], {x, 0, 2}, Axes -> False]


This really doesn't work if you substitute Mathematica's
SquareWave[]...
s = N[Log[2]/Log[3]];
f[x_] = Sum[SquareWave[2^n*x]/2^(s*n), {n, 0, 20}];
g[x_] = Sum[SquareWave[2^n*(x + 1/4)]/2^(s*n), {n, 0, 20}];
ParametricPlot[{f[x], g[x]}, {x, 0, 2}, Axes -> False]
ParametricPlot[{(f[x] + g[x])/Sqrt[2], (f[x] - g[x])/Sqrt[2]}, {x, 0,
    2}, Axes -> False]
Plot[{f[x], g[x]}, {x, 0, 2}, Axes -> False]
Plot[f[x], {x, 0, 2}, Axes -> False]

These two function TriangleWave and SquareWave
are new to me:
I've always had to generate my own Biscuit cartoon functions...

s = N[Log[2]/Log[3]];
f[x_] = Sum[SquareWave[3^n*x]/3^(s*n), {n, 0, 20}];
g[x_] = Sum[SquareWave[3^n*(x + 1/4)]/3^(s*n), {n, 0, 20}];

ParametricPlot[{f[x], g[x]}, {x, 0, 2}, Axes -> False,
   PlotPoints -> 1000]
ParametricPlot[{(f[x] + g[x])/Sqrt[2], (f[x] - g[x])/Sqrt[2]}, {x, 0,
    2}, Axes -> False, PlotPoints -> 1000]

Plot[{f[x], g[x]}, {x, 0, 2}, Axes -> False]
Plot[f[x], {x, 0, 2}, Axes -> False]

http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thre\
ad/45ca7b6a628749d2/3e68a229b9c4f4f4?hl=en#3e68a229b9c4f4f4

How do I import midi files into Mathematica?
Options

[Click the star to watch this topic]

            2 messages - 1 new - Collapse all  -
Report discussion as spam



Roger Bagula
View profile
       More options Mar 22, 11:34 pm
I asked this in a Mathematica help group
and came up with an xml conversion of midi
that Mathematica will read, but stripping down the xml tree
is hard and I missed the pauses on the first successful track.
Do anyone else know of a better method to
get a midi track into a times series in Mathematica?

      Reply     Reply to author      Forward



markholtuk
View profile
       More options Mar 24, 12:03 am
On Mar 23, 6:34 am, Roger Bagula <roger.bag...@...> wrote:

  > I asked this in a Mathematica help group
  > and came up with an xml conversion of midi
  > that Mathematica will read, but stripping down the xml tree
  > is hard and I missed the pauses on the first successful track.
  > Do anyone else know of a better method to
  > get a midi track into a times series in Mathematica?

This is something that I've been working on recently, so the code is
pretty nascent and has only been used on simple one track midi files
consisting of four bars of notes. It might be a useful spring for you
though.

midiIn=Import["file.mid","Byte"];

midiIn={77,84,104,100,0,0,0,6,0,0,0,1,0,96,77,84,114,107,0,0,0,255,0,255,3,7,66,\
76,95,52,95,67,0,0,255,88,4,4,2,36,8,0,255,88,4,4,2,36,8,0,144,60,95,36,128,60,3\
2,13,144,36,95,11,128,36,32,13,144,48,95,10,128,48,32,13,144,48,127,13,128,48,32\
,11,144,60,95,13,128,60,32,13,144,48,95,10,128,48,32,12,144,72,95,25,144,48,95,9\
,128,72,32,27,128,48,32,11,144,48,127,13,128,48,32,11,144,48,95,12,128,48,32,12,\
144,60,95,12,128,60,32,13,144,48,127,10,128,48,32,13,144,48,127,11,128,48,32,13,\
144,48,95,13,128,48,32,11,144,60,95,37,128,60,32,12,144,36,95,11,128,36,32,13,14\
4,48,95,12,128,48,32,11,144,48,127,13,128,48,32,11,144,60,95,12,128,60,32,13,144\
,48,95,11,128,48,32,11,144,72,95,26,144,48,95,9,128,72,32,26,128,48,32,12,144,48\
,127,13,128,48,32,10,144,48,95,13,128,48,32,12,144,60,95,12,128,60,32,13,144,48,\
127,10,128,48,32,14,144,48,127,10,128,48,32,13,144,48,95,13,128,48,32,0,255,47,0\
};
(*This is the imported data from a MIDI file that I have. Execute this
rather than the line above so that you can see how it should work. You
can also export this to see how it should sound. It's a modern
electronic bassline!*)

ch=1;     (*assuming a range of 1-16*)

noteonPos=Position[midiIn,143+ch];

noteoffPos=Position[midiIn,127+ch];

timeEvents=Flatten[Union[noteonPos,noteoffPos]-1];     (*These are
timing events since the last timing event.*)

realTimeEvents=Accumulate[midiIn[[timeEvents]]];     (*Time events are
accumulated to give actual timing events.*)

midi=ReplacePart[midiIn,Table[timeEvents[[i]]->realTimeEvents[[i]],
{i,Length[timeEvents]}]];   (*The original timing events are replaced
by the real timing events*)

extractEvents[data_List,{x_}]:=Extract[data,{{x-1},{x},{x+1},{x
+2}}];     (*This function is for extracting timing, note event, note
number, and velocity for each note on/off evnt*)

noteOn=Flatten[{#,extractEvents[midi,#]}]&/@noteonPos;     (*This
extracts each note on event and prepends with the events position in
the imported list*)

noteOff=Flatten[{#,extractEvents[midi,#]}]&/@noteoffPos;     (*This
extracts each note off event and prepends with the events position in
the imported list*)

notes=Table[{noteOn[[i]],First[Select[noteOff,#[[1]]>noteOn[[i,
1]]&&#[[4]]==noteOn[[i,4]]&]]},{i,Length[noteOn]}];     (*Pair the
correct note off messages with each note on message*)

Graphics[{Hue[0.8#[[1,5]]/127],Rectangle[#[[1,{2,4}]]+{0,-0.5},#[[2,
{2,4}]]+{0,0.5}]}&/@notes,Frame->True,AspectRatio->0.5]     (*Show the
notes on a grid*)

I should point out that the MIDI file that I have used here only
contains note on and off events and consists of only one MIDI channel.
There are no controller events present. If you want to work with MIDI
files that contain more than one channel and events other than note on
or off then you will need to significantly change some of this code.

Hopefully, this is a start to go on to bigger, better things! I will
try to incorporate controller events and multi-channel data myself at
some point.

Good Luck!

Mark

PlotPoints->1000 bombed well, LOL.

s = N[Log[2]/Log[3]];
f[x_] = Sum[SquareWave[3^n*x]/3^(s*n), {n, 0, 20}];
g[x_] = Sum[SquareWave[3^n*(x + 1/4)]/3^(s*n), {n, 0, 20}];
a = Table[{(f[x] + g[x])/Sqrt[2], (f[x] - g[x])/Sqrt[2]}, {x, 0, 2,
      2/10000}];
ListPlot[a, Axes -> False, PlotStyle -> PointSize[Small]]

http://www.wired.com/wiredscience/2012/03/ff_aiclass/all/1
The Stanford Education Experiment Could Change Higher Learning Forever

By Steven Leckart
Email Author
March 20, 2012 |
9:34 pm |
Categories: Biotech, Miscellaneous

Photo: Sam Comen

Sebastian Thrun and Peter Norvig in the basement of Thrun's guesthouse,
where they record class videos.
Photo: Sam Comen

Stanford doesn’t want me. I can say that because it’s a documented fact:
I was once denied admission in writing. I took my last math class back
in high school. Which probably explains why this quiz on how to get a
computer to calculate an ideal itinerary is making my brain hurt. I’m
staring at a crude map of Romania on my MacBook. Twenty cities are
connected in a network of straight black lines. My goal is to determine
the best route from Arad to Bucharest. A handful of search algorithms
with names like breadth-first, depth-first, uniform-cost, and A* can be
used. Each employs a different strategy for scanning the map and
considering various paths. I’ve never heard of these algorithms or
considered how a computer determines a route. But I’ll learn, because
despite the utter lack of qualifications I just mentioned, I’m enrolled
in CS221: Introduction to Artificial Intelligence, a graduate- level
course taught by Stanford professors Sebastian Thrun and Peter Norvig.
Magazine2004

Last fall, the university in the heart of Silicon Valley did something
it had never done before: It opened up three classes, including CS221,
to anyone with a web connection. Lectures and assignments—the same ones
administered in the regular on-campus class—would be posted and
auto-graded online each week. Midterms and finals would have strict
deadlines. Stanford wouldn’t issue course credit to the non-matriculated
students. But at the end of the term, students who completed a course
would be awarded an official Statement of Accomplishment.

People around the world have gone crazy for this opportunity. Fully
two-thirds of my 160,000 classmates live outside the US. There are
students in 190 countries—from India and South Korea to New Zealand and
the Republic of Azerbaijan. More than 100 volunteers have signed up to
translate the lectures into 44 languages, including Bengali. In Iran,
where YouTube is blocked, one student cloned the CS221 class website
and—with the professors’ permission—began reposting the video files for
1,000 students.

Aside from computer-programming AI-heads, my classmates range from
junior-high school students and humanities majors to middle-aged middle
school science teachers and seventysomething retirees. One student
described CS221 as the “online Woodstock of the digital era.�
Personally, I signed up to have the experience of taking a Stanford
course. Learning about artificial intelligence would be a nice bonus.
After all, if I’m ever going to let a self-driving car speed me down a
highway at 65 mph, it’ll be comforting to have a basic understanding of
what’s behind the wheel.

It’s not until the second week of class that I notice a small disclaimer
on the AI course website: Prerequisites: A solid understanding of
probability and linear algebra will be required.

Solid understanding? I majored in English. This makes me a “fuzzy� (what
Stanford techies call liberal arts majors behind their backs). And now
I’m trying to wrap my head around Bayesian probability, a branch of
statistics that in the past 25 years has revolutionized a dozen fields
from genomics and robotics to neuroscience. I’m told it all boils down
to this formula:
P (A|B) =
P (B|A) P(A)
P (B)


Apply this rule to a computational problem and you can make efficient
predictions based on otherwise unreliable data. Practical applications,
aside from programming autonomous cars, include calculating a woman’s
risk of breast cancer, analyzing DNA, and building a better spam filter.

That stuff’s all easier said than done. But the basics are actually
fairly basic. I manage to score 58 percent on this homework assignment.
I may not comprehend every which way to Bucharest. But in five weeks
maybe I’ll be ready to tackle a spam filter.

Sebastian Thrun stepped onstage at the March 2011 TED conference in Long
Beach, California. In a ballroom filled with 1,000 heavyweight thinkers,
the roboticist and AI guru offered a peek at his latest project at
Google: a charcoal-gray Toyota Prius outfitted with a laser range
finder, radar, and cameras. He showed video of the sedan navigating
through highway traffic, dodging deer on a pitch-dark road, and even
zigzagging down San Francisco’s Lombard Street—all without a human so
much as touching the wheel, the gas, or the brake. The applause roared.

You’d think that would have been Thrun’s favorite moment at TED. But it
wasn’t. Salman Khan also made a presentation that week. The founder of
Khan Academy, which wired profiled last August, told the story of his
nearly six-year-old website, which provides more than 2,800 tutorial
videos in subjects like science, math, and economics. Khan capped off
his talk by emphasizing how he’s growing a “global one-world classroom.�
Joining him onstage, Bill Gates called Khan Academy “the future of
education.� For Thrun, it was a full-on epiphany. “I was flabbergasted,�
he says. “I teach a lot of great students at Stanford. But the entire
world is out there.�

Even on a campus with 17 Nobel laureates, four Pulitzer Prize winners,
and 18 recipients of the National Medal of Science, Thrun has managed to
distinguish himself. In 2004, six months after arriving at Palo Alto as
an associate professor, he was named director of the Stanford Artificial
Intelligence Laboratory. The next year his team won the Darpa Grand
Challenge, a competition to build an autonomous car that can drive
itself across the Nevada desert. (Wired wrote about the 132-mile
robo-race in 2006.) For Thrun’s achievement, Stanford was awarded a $2
million prize. Today “Stanley,� Thrun’s self-driving Volkswagen Touareg,
lives at the Smithsonian. In April 2011, Thrun gave up his tenure at
Stanford to head Google X, a lab created to incubate the company’s most
ambitious and secretive projects. He was also free to pursue outside
ventures.

After seeing Khan at TED, Thrun dusted off a PowerPoint presentation
he’d put together in 2007. Back then he had begun envisioning a YouTube
for education, a for-profit startup that would allow students to
discover and take courses from top professors. In a few slides, he’d
spelled out the nine essential components of a university education:
admissions, lectures, peer interaction, professor interaction,
problem-solving, assignments, exams, deadlines, and certification. While
Thrun admired MIT’s OpenCourseWare—the university’s decade-old
initiative to publish online all of its lectures, syllabi, and homework
from 2,100 courses—he thought it relied too heavily on videos of actual
classroom lectures. That was tapping just one-ninth of the equation,
with a bit of course material thrown in as a bonus.

Thrun knew firsthand what it was like to crave superior instruction.
When he was a master’s-degree student at the University of Bonn in
Germany in the late 1980s, he found his AI professors to be clueless. He
spent a lot of time filling in the gaps at the library, but he longed
for a more direct connection to experts. Thrun created his PowerPoint
presentation because he understood that university education was a
system in need of disruption. But it wasn’t until he heard Khan’s talk
that he appreciated he could do something about it. He spoke with Peter
Norvig, Google’s director of research and his CS221 coprofessor, and
they agreed to open up their next class to the entire world. Yes, it was
an educational experiment, but Thrun realized that it could also be the
first step in turning that old PowerPoint into an actual business.

In June he took the next step: cofounding KnowLabs, which he funded with
$300,000 of his own money. He pulled in David Stavens, one of Stanley’s
cocreators, as CEO; he tapped Stanford robotics researcher Mike Sokolsky
to be CTO. They converted Thrun’s guesthouse into a temporary office.
Thus ensconced on a scenic hillside on Page Mill Road near Stanford’s
campus, the team began planning. They had eight weeks before the fall
term started—not unreasonable given the modest scope of the project.
Stavens thought they’d get 500 students. Sokolsky hoped for 1,000.
Norvig figured they might hit 2,000.
Fifty years from now, according to Thrun, there will be only 10
institutions in the whole world that deliver higher education.

In late July, Thrun emailed 1,000 members of the Association for the
Advancement of Artificial Intelligence, a group that had weathered the
AI winter of the 1980s and ’90s only to see the field later revitalized
by the likes of Stanley. By the next morning 5,000 students had signed
up. A few days later the class had 10,000. That’s when the Stanford
administration called. Thrun had neglected to tell them about his
plan—he’d had a hunch it might not go over well. The university’s chief
complaint: You cannot issue an official certificate of any kind. Over
the next few weeks, 15 meetings were held on the matter. Thrun talked to
the dean’s office, the registrar, and the university’s legal department.
Meanwhile, enrollment in CS221 was ballooning: 14,000, 18,000, and—just
two weeks later—58,000.

In all those meetings, not one person objected to Thrun’s offering his
class online for free. They admired his vision. The administration
simply wanted Thrun to drop the assignments and certificate. He refused.
Those two components, he argued, were responsible for driving the
sign-ups. Someone proposed removing Stanford’s name from the course
website altogether. Eventually they reached a compromise: (1) Offer a
Statement of Accomplishment, not a certificate, and (2) include a
disclaimer stating that the class wouldn’t count toward Stanford credit,
a grade, or a degree.

Thrun didn’t have time to celebrate. By mid-August, word of his AI class
went viral after a write-up in The New York Times. Enrollment
skyrocketed past 100,000. KnowLabs’ website had been built to handle
10,000 students. Class was starting in a matter of weeks. “That,�
Sokolsky says, “is when I stopped sleeping.�

Education, Mark Twain once said, is the path from cocky ignorance to
miserable uncertainty. By that standard, it seems I’m making progress.
After a month of CS221, I’ve come to dread the homework, especially when
I check back on my performance: 60 percent, 33 percent, 44 percent.
Technically, I guess you could say I’m failing. Few of the concepts in
CS221 click easily for me.

The videos, which are sometimes weirdly entertaining, do help. A unit
usually begins with a close-up of Thrun or Norvig in a makeshift studio
speaking directly to the camera. Then you see a tight shot of a drawing
pad and watch their hands write out variables, diagrams, and
calculations as they provide voice-over elucidation. It’s all recorded
with a DSLR camera mounted on a tripod. The videos are broken up with
questions, prompting students to engage, so the team overlays HTML form
boxes onto each video. This allows answers to be submitted directly into
the browser. The videos aren’t flashy or polished; they take their
inspiration from Khan Academy, which pioneered this technique of
intimate, direct instruction. It’s a stark contrast to MIT’s
OpenCourseWare videos, which mostly depict professors from afar,
scribbling on blackboards. Still, some of my classmates are
underwhelmed. “In a world of slick presentations and animated diagrams,�
one student blogs, “this looks a little homespun.�

But because CS221 seems like a work in progress, students are also eager
to help improve it. Early in the term, for example, Thrun and Norvig
decided to nix the programming exercises (a bummer to techies but a
relief to us fuzzies). The team at KnowLabs had enough on its plate. But
Vitalik Buterin, an 18-year-old high school senior in Toronto, stepped
in to help. He spent a few days creating an “AI playground� where
students could practice coding all those basic AI algorithms we’d been
hearing so much about. The site presents puzzles, such as asking for the
most efficient path from point A to B. Students can write a function in
JavaScript—testing out A* search, breadth-first, and naive Bayesian
analysis—and check their performance. “Find your way through a world
with deadly obstacles and uncertain senses and actions and make your way
to the goal,� Buterin’s site prompts students. Just like an autonomous
Prius.

Thrun is thrilled.His experiment is working. More than 20,000 students
have taken the midterm and are turning in weekly assignments. The
website’s stability is improving. CS221′s YouTube videos have been
viewed 5 million times. The team at KnowLabs has automated and ramped up
the workflow: film, edit, double-check the lessons, post, and monitor
the message boards to put out fires.

The course is hitting eight of Thrun’s nine educational components. Sure
there’s room for improvement. But what they’re building is starting to
look less like a whimsical one-off and more like a legitimate venture.
They’ve hired a second engineer, who also serves as a teaching assistant
to oversee the discussion forums. By November they’re staffing up again,
with a new video editor and a web designer to rethink the interface for
future courses.

Stavens is thinking about potential business models. Though Thrun
cringes at the notion of charging students, people might eventually pay
for add-ons—say, TA services, study aids, or offline materials. He also
considers other revenue streams. Near the end of the term, he emails his
top 1,000 students, the ones with perfect or near-perfect scores on
homework and tests. The subject: Job Placement Program. Thrun solicits
résumés and promises to get the best ones into the right hands at tech
companies, including Google. A recruiter who places a hire typically
earns 10 to 30 percent of an engineer’s first-year salary, which might
be $100,000. Stavens figures he could charge much less. After all,
KnowLabs discovers talent in the course of doing business.
My initial approach to the class turned out to be wrong. My grades are
low. I’ve never wanted a D-minus so badly in my life.

In December the company secures a sizable chunk of money from Charles
River Ventures, a VC firm specializing in early-stage investments. First
order of business: another hiring spree, which more than doubles the
staff, bringing it to 14. KnowLabs revamps its software from scratch and
starts to work on a full site redesign.

KnowLabs already has competition: At the same time as CS221, two other
computer science courses are being taught at Stanford using another
digital platform. (Neither has attracted near the number of enrollees as
CS221, but some students taking all three say the materials and website
for CS221 are less polished.) Two Stanford professors then develop that
platform into Coursera, an independent venture for serving online
courses. (They’re beginning with Stanford but plan to expand to other
institutions.) The plan is to offer 14 classes in 2012, including
cryptography, anatomy, and game theory. For now, these are all free.
Then MIT announces it is racing to catch up with Stanford by creating a
program called MITx, which will serve up a handful of online courses in
the fall of 2012. Enrollment and participation will be free, but to earn
a certificate of completion students will have to pay a “fairly modest�
but yet-to-be-determined fee.

Thrun isn’t worried that these respected universities or faculty will
crush his startup. He’s envisioning his own digital university, with a
less conventional curriculum, one based on solving problems, not simply
lectures on abstract topics. It would offer a viable alternative for
students of the global one-world classroom—particularly those who lack
the resources to move to the US and attend college.

Thrun decides that KnowLabs will build something called Udacity. The
name, a mashup of audacity and university, is intended to convey the
boldness of both Thrun’s and his students’ ambitions. His goal is for
Udacity to offer free eight-week online courses. For the next six months
or more, the curriculum will focus on computer science. Eventually it
will expand into other quantitative disciplines including engineering,
physics, and chemistry. The idea is to create a menu of high-quality
courses that can be rerun and improved with minimal involvement from the
original instructor. KnowLabs will work only with top professors who are
willing to put in the effort to create dynamic, interactive videos. Just
as Hollywood cinematography revolutionized the way we tell stories,
Thrun sees a new grammar of instruction and learning starting to emerge
as he and his team create the videos and other class materials. Behind
every Udacity class will be a production team, not unlike a film crew.
The professor will become an actor-producer. Which makes Thrun the
studio head.

He’s thinking big now. He imagines that in 10 years, job applicants will
tout their Udacity degrees. In 50 years, he says, there will be only 10
institutions in the world delivering higher education and Udacity has a
shot at being one of them. Thrun just has to plot the right course.

It’s a crisp and sunny December morning at Stanford—the last day of
class—and Thrun steps up to a podium to deliver the in-class lecture.
I’d pictured crashing a hall packed with techies, but only 41 students
out of 200 show up. Four stroll in late. Two fall asleep. Five leave
early. That’s not uncommon. There’s little incentive to come to class.
During the fall term, the Stanford students taking CS221 preferred
watching the KnowLabs videos. Thrun says this improved their
performance. In previous years his students averaged 60 percent on the
midterm; this time around they did much better. Thrun swears the exam
was tougher than any other he’s given at Stanford. My online classmates
averaged 83 percent overall. (I did not help the average.)

He doesn’t congratulate himself for long. Along with the technical
hurdles, including scaling up the website and staving off at least three
denial-of-service attacks, Thrun acknowledges some harsh feedback from
his students. “We made a lot of mistakes,� he says. “In the beginning I
made each problem available only once. I got a flaming email from a
student saying, ‘Look, you’re behaving like one of these arrogant
Stanford professors looking to weed out students.’ I realized we should
set up the student for success, not for failure.� KnowLabs tweaked the
software to allow students to keep trying problems.

My initial approach to the class was wrong too. At the beginning of the
term, I joined an offline study group in San Francisco and met with six
of my classmates at a pub. As I expected, discussing problems was very
helpful. Unfortunately, the group fizzled well before the midterm.
Agreeing on a time and location proved too difficult.

Online, of course, that wasn’t an issue. A dozen or more discussion
groups formed on Facebook, and students organized virtual study sessions
via Google+ and private IRC channels. I posed questions on the Q&A site
Aiqus and on Reddit discussion boards at all hours of the day and night
and received explanations and tips from around the world in near real
time. On Aiqus alone, more than 4,000 questions were posted, and they
received more than 13,000 answers. All that information was scattered,
though. I had to filter through a dozen comment threads on Aiqus and
open a dozen tabs in my browser just to solve one homework problem. It
was difficult to focus.

Filip Wasilewski, a 30-year-old IT consultant in Lodz, Poland,
experienced the same frustration. So he spent three nights coding a
piece of software to fix the problem. Wasilewski’s solution, a
JavaScript add-on to Google’s Chrome browser, fetched relevant Aiqus
questions and displayed them on the AI course website, right beneath the
corresponding video. I could scan discussion subject headings without
clicking on another tab. More than 2,000 students installed the plug-in.

Thrun expects such student- built innovations to multiply as Udacity
ramps up this year. In February it offered its first two eight-week
courses for free. These classes are not affiliated with Stanford, and as
of this writing, a combined 65,000 students have registered for CS373:
Programming a Robotic Car and CS101: Building a Search Engine. The
robotic car course, taught by Thrun, requires some math and engineering
chops. But the search engine class—helmed by David Evans, a professor on
sabbatical from the University of Virginia—was designed specifically for
people with zero background in programming. Thrun tapped Google
cofounder Sergey Brin to appear in a YouTube video promoting the class.
It worked.

An hour before that last lecture, I stop by Thrun’s office to say hello.
“We have a recipe that works,� he tells me proudly. “Putting these
ingredients together and working really hard to create good content and
a good experience for the students, we can break through.�

I have only a vague idea of how an autonomous car drives itself. I’m
nearing the end of CS221 and I’ve never wanted a D-minus so badly in my
life. Sadly, I don’t quite pull it off. My total score for the term:
52.7 percent. That’s 7.3 percent below passing—in other words, an F.
I’ve never failed a class before. If I were an actual Stanford student,
this would tarnish my GPA. It might wreck my chances of landing a summer
internship. It would certainly disappoint my faculty adviser.

But I’m not an actual Stanford student. I’m a gate-crasher. A fuzzy one.
At least I finished. That’s better than the 137,000 registered students
who dropped out. I decide to print out my Statement of Accomplishment.
Will I frame it and hang it next to the master’s degree in my office?
Maybe. Will I ever build a better spam filter? Probably not. Will I take
another online course? I’m no expert, but the probability seems high.

Correspondent Steven Leckart (@stevenleckart) wrote about Hackathons in
issue 20.03.

http://thestar.com.my/education/story.asp?file=/2012/3/25/education/10976617&sec\
=education
Star Education Fair
Sunday March 25, 2012
Award for Mathematics genius

A 22-year old who solved a difficult mathematical problem which had
puzzled the Maths community for over two decades, has been nominated as
the “Star of Hope”.

Liu Lu, a Chinese national, received the nomination for solving the
“Seetapun Enigma”. The ceremony will be held at the Peking University.

He drew worldwide attention last year by successfully solving the
complex problem, a conjecture put forward by English mathematical
logician David Seetapun in the 1990s. It is a problem of reverse
mathematics related to Ramsey’s Theorem.

Liu submitted his findings to the Journal of Symbolic Logic, an
internationally authoritative academic journal, and won praise from its
editor-in-chief, Denis Hirschfeldt, an expert in mathematical logic and
a professor at the University of Chicago.

As a result of the amazing mathematical achievement, he became the
youngest professor in China, upon his appointment as professor by
Zhongnan University in Hunan Province on Tuesday.

University head Zhang Yaoxue hoped Liu would acquire more knowledge and
dedicate himself to scientific research. – Bernama

s = N[Log[2]/Log[3]];
f[x_] = Sum[SawtoothWave[3^n*x]/3^(s*n), {n, 0, 20}];
g[x_] = Sum[SawtoothWave[3^n*(x + 1/2)]/3^(s*n), {n, 0, 20}];

a = Table[{(f[x] + g[x])/Sqrt[2], (f[x] - g[x])/Sqrt[2]}, {x, 0, 2,
      2/50000}];
ListPlot[a, Axes -> False, PlotStyle -> PointSize[Small]]

This kind of hurts my eardrums!
<< Audio`
Clear[x, b0]
b0[1] = 1; b0[2] = 1; b0[3] = 1; b0[4] = 1; b0[5] = 1; b0[6] = 1;
b0[n_] := b0[n] = b0[b0[b0[n - 1]]] + b0[n - b0[b0[-3 + n]]]
partialList =
   Table[{ b0[7 + n] - n/2 + 1/2,
      20 + b0[n]*((-1)^((Mod[n, 2]))*
           Cos[(n \[Pi])/3] + (-1)^((Mod[n, 6])) Sqrt[3]
            Sin[(n \[Pi])/3])}, {n, 1, 10}]/15
ListPlot[%]
sequence =
    Table[ListWaveform[partialList, 440 2^(n/12), 0.2], {n, 0, 16,
      16/48}];
Show[sequence]

Searching for Beauty in Music
Applications of Zipf's Law in MIDI-Encoded Music

NOTE: This page is superseded - see newer results in music and fractals.

[Overview]   [Background]   [Data and Results]   [Credits]   [Publications]   [References]

Overview    (top)

This project explores stochastic techniques to computationally identify and emphasize aesthetic aspects of music. Currently, we are studying ways to apply the Zipf-Mandelbrot law on musical pieces encoded in MIDI. 

We have extended earlier results (Voss and Clarke, 1975; Zipf, 1949) by identifying a set of measurable attributes of music that may exhibit Zipf-Mandelbrot distributions. These measurable attributes (metrics) include pitch of notes, duration of notes, harmonic and melodic intervals, and many others. Experiments on corpora from various music genres (e.g., baroque, classical, 12-tone, jazz, rock, punk rock) demonstrate the validity of the approach.  Currently, we are investigating ways to combine our metrics with AI techniques, such neural networks and genetic algorithms, to analyze and help generate music that sounds "pleasing, beautiful, harmonious." Related application areas include music education, music therapy, music recognition by computers, and computer-aided music analysis/composition.

Background    (top)

Earlier studies (Voss and Clarke, 1975) show that pitch and loudness fluctuations in music follow Zipf's distribution.  However they were unable to show this for note fluctuations. This work was carried out at the level of frequencies in an electrical signal. Eventually, Voss and Clark reversed the process so they could compose music through a computer. Their computer program used a Zipf's distribution (1/f power spectrum) generator to produce pitch fluctuations. The results were remarkable. The music produced by this method was judged by most listeners to be much more pleasing than generators that did not follow Zipf's distribution. They concluded that "the sophistication of this '1/f music' (which was 'just right') extends far beyond what one might expect from such a simple algorithm, suggesting that a '1/f noise' (perhaps that in nerve membranes?) may have an essential role in the creative process." [Voss and Clarke, 1975, p. 258]

We have extended these results by identifying a larger set of measurable attributes of music pieces on which to apply the Zipf-Mandelbrot law. These measurable attributes (metrics) include pitch of musical events, duration of musical events, the combination of pitch and duration of musical events, harmonic and melodic intervals, and several others.  After several manual experiments, which demonstrated the promise of this approach, we automated these metrics. Applications of these metrics on corpora from various music genres (e.g., baroque, classical, 12-tone, jazz, and rock) demonstrate the validity of the approach (see Data and Results).  

Current Directions

We are investigating ways to combine Zipf metrics with AI techniques such neural networks and genetic algorithms to analyze and generate music that sounds "pleasing, beautiful, harmonious."  Related application areas include music education, music therapy, music recognition by computers, and computer-aided music analysis/composition.  Currently, we are exploring three directions:

1) Classification of pleasant music through artificial neural networks.

2) Genetic algorithms for generation of pleasant music.

3) Development of Zipf-Mandelbrot metrics (an extension of Zipf metrics).  

Data and Results    (top)

Zipf's distribution in music

A study on a corpus of 220 pieces of baroque, classical, 12-tone, jazz, pop, rock, and random (aleatory) music, discovered near-Zipfian distributions across many of our metrics (melodic intervals, harmonic intervals, pitch&duration, etc.)  Also, certain patterns seem to emerge; for instance, we are able to automatically identify 12-tone music from other types of music (including random ones).  

Figures 1 and 2 below show an example from this study.  

Fig. 1. Pitch distribution for Bach's Orchestral Suite No.3 in D  '2. Air on the G String', BWV.1068.	Fig. 2. Pitch distribution for Random Piece No. 7 (white noise).

For additional information, see Manaris, Purewal, and McCormick, (2002).

Music Classification

Juan Romero and his group (at University of La Coru�a, Spain) used our metrics to train an artificial neural network (ANN).  This ANN was able to classify music by Bach and Beethoven with 100% accuracy.  This experiment was conducted on a corpus of 132 pieces by Bach (BWV500 to BWV599) and Beethoven (32 piano sonatas).  The ANN was trained on 66% of the corpus (97 pieces) and tested on the remaining 47 pieces.

Figures 3 and 4 show visualizations of six metrics that were identified by the ANN as the most relevant for differentiating Bach and Beethoven.  These metrics capture various statistical aspects of (a) pitch and (b) melodic intervals. In particular, the x-axis (blue) corresponds to significant metrics (1 to 6); the y-axis (red) corresponds to music piece (1 to 32); and z-axis (green) corresponds to absolute value of metrics . 

Fig. 3. Bach-scape - a 3D contour map of six Zipf metrics over 32 Bach pieces	Fig. 4. Beethoven-scape - a 3D contour map of six Zipf metrics over 32 Beethoven pieces

Incidentally, these visualizations help identify Beethoven's Piano Sonata No. 20 as an outlier.  This piece exhibits an "unexpected" peak of 1.7472 for metric #3.  Metric # 3 captures the Zipf balance of pitch regardless of octave (e.g., C1 and C4 are counted as the same note).  This indicates that Piano Sonata No. 20 is considerably more monotonous, in terms of pitch regardless of octave, than the other Piano Sonatas.  This may be accidental, or it could be the result of Beethoven trying something different when composing this piece.

In a preliminary, follow-up experiment, we have trained an ANN to classify music by Bach and Chopin with 98.69% accuracy. This ANN was trained on 300 pieces and tested on 153 pieces.  Additional ANN experiments are being conducted.

For additional information on these experiments, see Machado, et al. (2003).

Credits    (top)

The following individuals have contributed to this project (in reverse chronological order; students in bold): William Daugherty, Dallas Vaughan, Christopher Wagner, Penousal Machado, Juan Romero, Charles McCormick, Tarsem Purewal, Dwight Krehbiel, Robert B. Davis, Valerie Sessions, Yuliya Schmidt, James Wilkinson, and Bill Manaris.   

The project has received support from the Classical Music Archives and the College of Charleston.

Publications    (top)

1. Penousal Machado, Juan Romero, Bill Manaris, Antonino Santos, and Amilcar Cardoso, (2003), "Power to the Critics - A Framework for the Development of Artificial Critics," in Proceedings of 3rd Workshop on Creative Systems, 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), Acapulco, Mexico, Aug. 2003, pp. 55-64.

2. Bill Manaris, Dallas Vaughan, Christopher Wagner, Juan Romero, and Robert B. Davis, (2003), "Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music," EvoMUSART2003 - 1st European Workshop on Evolutionary Music and Art, Essex, UK, Lecture Notes in Computer Science, Applications of Evolutionary Computing, LNCS 2611, Springer-Verlag, Apr. 2003, pp. 522-534.

3. Bill Manaris, Tarsem Purewal, and Charles McCormick, (2002), "Progress Towards Recognizing and Classifying Beautiful Music with Computers-MIDI-Encoded Music and the Zipf-Mandelbrot Law," Proceedings of the IEEE SoutheastCon 2002, Columbia, SC, Apr. 2002, pp. 52-57.

4. Bill Manaris, Charles McCormick, and Tarsem Purewal, (2001), "Searching for Beauty in Music--Applications of Zipf's Law in MIDI-Encoded Music," 2001 Sigma Xi Forum, "Science, the Arts and the Humanities: Connections and Collisions" (poster and demonstration), Raleigh, NC, November 8-9, 2001.

References    (top)

1. Adamic, L.A., (1999), "Zipf, Power-laws, and Pareto - a Ranking Tutorial", www.parc.xerox.com/istl/groups/iea/papers/ranking/ 
2. Balaban, M., Ebcioglu, K., and Laske, O., eds. (1992), Dobrian, C. (1988), Understanding Music with AI: Perspectives on Music Cognition, AAAI Press and MIT Press. 
3. Dobrian, C. (1992), "Music and Artificial Intelligence", www.arts.uci.edu/dobrian/CD.music.ai.htm 
4. Elliot, J. and Atwell, E. (2000), "Is Anybody Out There? The Detection of Intelligent and Generic Language-Like Features", Journal of the British Interplanetary Society 53(1/2), pp. 13-22, www.comp.leeds.ac.uk/eric/jbisjournal2000.ps 
5. Glatt, J., "Tutorial for MIDI Users", www.borg.com/~jglatt/tutr/miditutr.htm 
6. Knuth, K. (1997), "Power Laws and Hierarchical Organization in Complex Systems-From Sandpiles and Monetary Systems to Brains, Language, and Music", CUNY Cognitive Science Symposium. http://bulky.aecom.yu.edu/users/kknuth/complex/powerlaws.html . 
7. Li, W. (2000), "Zipf's Law" http://linkage.rockefeller.edu/wli/zipf/ 
8. Mandelbrot, B.B. (1977), The Fractal Geometry of Nature, W.H. Freeman and Company. 
9. Schroeder, M. (1991), Fractals, Chaos, Power Laws, W.H. Freeman. 
10. Voss, R.F., and Clarke, J. (1975), "1/f Noise in Music and Speech", Nature 258, pp. 317-318. 
11. Zipf, G.K. (1949), Human Behavior and the Principle of Least Effort, Addison-Wesley.

manaris@....
Last updated on Thursday, November 06, 2003 06:08 PM -0500

http://en.wikipedia.org/wiki/Hilbert_series_and_Hilbert_polynomial

http://ckw.phys.ncku.edu.tw/public/pub/Notes/Mathematics/GroupTheory/Tung/Powerp\
oint/nb_6/CharacterTableStandAlone.nb
These go in your Appilcations in "Library" Mathematica directory:
http://ckw.phys.ncku.edu.tw/public/pub/Notes/Mathematics/GroupTheory/Tung/Powerp\
oint/nb_6/Group.m
http://ckw.phys.ncku.edu.tw/public/pub/Notes/Mathematics/GroupTheory/Tung/Powerp\
oint/nb_6/GroupBasics.m

From:
http://ckw.phys.ncku.edu.tw/public/pub/Notes/Mathematics/GroupTheory/Tung/Main.h\
tml

http://www.charlesperry.com/bio/
Charles O. Perry



BIOGRAPHY

Charles O. Perry (1929-2011) was a creator, an artist of many dimensions
who ponders the wonderful mysteries of the universe. His large scale and
monumental sculptures celebrate and question the laws of nature. His
intuitive investigation of nature's variables provides the springboard
for many of Perry's concepts. Believing that sculpture must stand on its
own merit without need of explanation, Perry's work has an elegance of
form that masks the mathematical complexity of its genesis.

Perry has always extolled the beauties of nature and the qualities of
materials, beginning with watercolors of his native Montana, inventing
equipment to improve his tour of duty in Korea, and celebrating Japanese
reverence for natural materials. He returned to America to study art and
architecture and explore the “what ifs” at Yale University in 1954.
While at Yale, Joseph Albers, Chairman of the Art School, encouraged
Perry to play with materials and to discover their true nature. As a
student, he pondered the nature of the rhombus, resulting in the
invention of a building brick that needed no mortar and was unrestricted
by the limits of size. The concept was intuitive, the result was visual
art. The piece was later shown at Spoleto's Festival, Italy, in 1969.

After graduating from Yale, Charles Perry practiced architecture in San
Francisco, California with the firm of Skidmore, Owings, & Merrill, from
1958- 1963. During his architectural career he had developed many
sculptural models and was offered a one-man sculpture show in San
Francisco. At the same time, he won the Rome Prize, a prestigious award
granted by the American Academy in Rome for two years study in Italy.
Prior to leaving for Rome in 1964, he had secured two major sculpture
commissions. "The basic difference in the discipline of architecture and
sculpture is that one can't force a solution in sculpture, whereas in
architecture, one can arrive at an apparent 'rational' solution through
continual work." For Perry, the appropriateness of the form is the
criteria for the final goal.

Since 1964, Perry concentrated on large scale public sculpture, the most
prestigious of which stands in front of the National Air and Space
Museum, in Washington, D.C. The piece, "Continuum", began as an
exploration of the Moebius strip, product of pure mathematics formed by
joining two ends of a strip of paper after giving one end a 180 degree
twist, thus creating only one edge. The center of the bronze sculpture
symbolizes a black hole, while the edge shows the flow of matter through
the center from positive to negative space and back again in a continuum.

"When I set off to be an artist, I would avoid the arbitrary, esteem the
orders of God in Nature, make forms that were beautiful, which appeared
to have no author, forms you thought you had seen before; entwined with
mathematics, geometry, topology, spinning, interlocking, always saying
thank you God."

Charles Perry's sculptures are located in public spaces at Dartmouth
College, Hanover, NH; Harvard University, Boston, MA; University of
Connecticut at Storrs, CT; Zeimu University, Tokyo, Japan; Indiana
University Art Museum, Bloomington, IN; General Electric headquarters,
Fairfield, CT; IBM headquarters, Charlotte, NC; Shell Oil, Melbourne,
Australia and Singapore. There are over one hundred major commissions
throughout the world.

As an industrial designer, Perry has invented three unique IBD prize
winning chairs. His patents on chair design are licensed to Krueger
International, Steelcase, and Virco. Perry has designed various forms of
art such as a collection of jewelry and silver objects for Tiffany,
puzzles for the Museum of Modern Art, and a chess set which is in the
Design Collection of MoMA. In recent years, Perry has frequently
lectured on mathematics and art, in conferences throughout the world.

1929 Born in Helena, Montana, USA
1952 Lieutenant, Artillery Forward Observer, Korea
1958 Master in Architecture, Yale University
Licensed and practiced architecture, San Francisco, CA
1964 First one-man show in sculpture, San Francisco, CA
1964 First sculpture commission, Fresno, CA
1964 "Prix de Rome" in architecture
1964 Moved to Rome, Italy, and practiced architecture and sculpture
1967 First one-man show in New York City, NY
1967 Chess set design and "Perrygons" a construction toy,
marketed by the Museum of Modern Art (MOMA)
1968 First outdoor sculpture show, "Festival of Two Worlds," Spoleto, Italy
1969 Artist in Residence at American Academy in Rome
1969 Venice Biennale, group print show
1973 Artist in Residence at Dartmouth College, Hanover, NH
1977 Returned to live in Norwalk, CT, USA
1979 First show in jewelry design, "Breakfast at Tiffany’s" New York, NY
1982 Puzzle designs marketed by MOMA, Smithsonian I., et al
1991 "Perry" chair design launched by Krueger International
1995 "Virtuoso" chair design launched by Virco
1997 "Uno" chair design launched by Steelcase, Inc.
1980-2003 Lecture participation in design, sculpture, symmetry, "art and
math,"
in USA, Australia, Argentina, Sweden, France and Italy — see Lectures
1970-2005 Installation of large outdoor and indoor sculpture — see
Commissions



• © Copyright 2000-2011 by Charles O. Perry •

http://www.usustatesman.com/professor-brings-mathematics-to-life-1.2724879#.T3yl\
pI73TWY
Professor brings mathematics to life

By ALLEE EVENSEN

Published: Wednesday, April 4, 2012

Updated: Wednesday, April 4, 2012 13:04



When James Powell was a child, his dreams were similar to many boys his
age. He wanted to be an astronaut, an engineer and a cowboy when he grew
up. However, it was early in elementary school when he decided he wanted
to do something slightly out of the ordinary.

“I actually decided I wanted to become a math professor in second
grade,” Powell said. “I remember (talking) with one of my buddies. We
were so excited about long division ... we were just having so much fun
with it.”

Though he said many aspirations have come and gone, math was the dream
that stuck. He has taught math for 25 years — nearly 20 of those at USU.

Marti Garlick has worked under Powell as both a master’s and doctoral
student for more than six years. Powell’s involvement and energy in the
classroom bring his classes to life, she said.

“(He’s) totally engaged,” she said. “(He makes) sure students learn
something.”

When a student makes a mistake in class, she said he often writes a
problem out on the board in order to show where the mistake was made.
This, she said, is one of the many ways he creates interaction in his
classes.

Powell said one of his primary goals in the classroom is to make math
apply to real life, something Garlick said she sees him doing on a
constant basis.

“The real world has to collide with the theoretical world (in math),”
Garlick said. “We actually have to have something that reflects
processes in the real world.”

Powell said he is able to the two worlds together by telling stories
that make what he’s explaining applicable. Sitting in an office
surrounded by boards of equations and graphs, it would be hard to guess
Powell once flirted — as a teenager and again in college — with the
notion of becoming an English professor.

He said he still sees the connection between the two.

“I don’t think there’s that big of gap,” he said.

Powell said he spent a lot of time writing in college, especially while
involved in various research projects. No matter what field a student is
in, whether it be business or science, it’s important he or she learn
how to write, he said.

While working with the honors program at Colorado State University,
Powell’s job was to review ACT scores after new student orientations and
flag students who would fit the program.

“The honors director at the time said, according to his analysis, the
biggest determinant for success in the honors program in math and
science and everything else was an ACT English score of 32 and above,”
he said.

When his students aren’t writing or doing hands-on experiments in
lab-based classes, Powell said he tries to engage them with conversation
to keep them actively learning.

Currently, Powell teaches a biology-based math class in which he said he
tries to get students involved as much as possible. This includes having
them create their own mathematics. He said the one thing that sets him
apart from other professors is the decibel level in his classroom.

“I’m louder and more ballistic than most professors are when they
lecture — particularly (professors) in mathematics,” he said.

Like many professors, Powell said the reason he teaches is because he
loves seeing “light bulbs illuminate” when his students understand
something.

He cited an example a few weeks ago when he was teaching a lesson on how
to fit curves and models to data, and a student who had been confused
suddenly understood what he was trying to say.

“The student just looked stunned like I had smacked him with a frying
pan … he had a little bit of drool,” Powell said. “Those are moments I
live for, when you really see students integrate whole bits of
knowledge. There’s a lot of those.”