Problem cruncher 20160803

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Problem cruncher: solving problems
which already have solutions
SharonXiaoLiu. 2016/08/03-Present.
Disclaimer:thougheveryefforthasbeenmade toensure correctness,Iacceptnoliabilityforany
lossesincurredasa resultof readingthisdocument.
Solutionsmustbe the same or betterthanthe original solution. Programmingsolutionsshouldrun
and produce the expectedbehaviour,donotsolve the problemif youcannotrunthe code. Findnew
waysof checkingyourwork.
Googledproblemsuggestions:programmingpractice problems,PHP codingchallenges.
Otherproblemsuggestions:Chineseessay,correctedby https://languagetool.org/ ,selectionof
wordsin Englishwhichneedtobe translatedtoChinese, JavaScriptproblemwhichincludescommon
JavaScriptfunctions,calculusproblemsfromabookwhichincludesanswers, Google:(mathstopic)
practice problems, copywritingproblemswhichare giventomumto review withamarkscheme,
website designsfromCSS ZenGarden,Upworkassignments,webbackendexperiments basedon
Magentoand WordPress,graphicdesignsforDeviantart,healthstatistics,satellite calculations,
strategystartlets,reactiontime tester,processdesign,explainapaperor opensource code files in
plainEnglish,answerquestionsfromStackOverflow orEngineeringStackExchange.
Analysingbusinessmodelsandsalestechniques.2017/03/13.
Modifying somebody else’s code
ModifyingWordPressorMagentocore.
KnownWordPressbugs. Contributingtoa programminglanguage.
https://core.trac.wordpress.org/report/1
https://make.wordpress.org/core/
Analyse Code
Take a sectionfrom Magentoand explainwhatitdoes.
Programming technologies list
Modify problemsfromUpworkassignments,make themharder.
Windows batch language: Clean up directories. 2016/08/17.
FindfolderswithDelete afterDate andif the date is olderthanthe currentdate,delete them.
PHP Test generator
Openbooktest,problemswithoutanswers.PresentCSScode asquestions,theninterpretinanswer
box.UploadCSS file fromCSSZengardenintestgenerator.Othersearches:CSSexample files,free
webdesigntemplates.PHP.HostinXampp.Alternatively,commentinaCSSfile.
<html>

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<body>
<?php
Crawl webdirectoryrandomlyandselectcssfile;
if (isset($tg-CSSFile)) {
Turn file into$tg-CSSFileAsVariable;
$tg-CSSFileInTestSections=Split$tg-CSSFileAsVariable accordingto"}";
$tg-CSSQuestion=Selectrandomelementfrom$tg-CSSFileInTestSections;
print$tg-CSSQuestion;
}
functiontg-ProvideAnswer($tg-CSSQuestion) {
Translate css to English;
}
functiontg-ProvideImage {
}
?>
</body>
</html>
Python: Automate The Boring Stuff practice questions. 2017/02/22.
Chapter 1. 2017/02/22.
Question 1. Which of thefollowing areoperators, and which arevalues?
*: operator.
‘hello’:value.
-88.8: value.
-: operator.
/: operator.
+: operator.
5: value.
Question 2. Which of thefollowing is a variable, and which is a string?
spam:variable.
‘spam’:string.
Question 3. Namethreedata types.
int,float,str.

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Question 4. Whatisan expression madeup of?Whatdo all expressionsdo?
An expressionismade of upvaluesand operators.Expressionsreduce downtoasingle value.
Question 5. Thischapterintroduced assignmentstatements, likespam=10. Whatis thedifference
between an expression and a statement?
A statementiseverythingthatmakesupa line orseveral linesof Pythoncode.Allexpressionsare
statements,butnotall statementsare expressions.
Question 6. Whatdoesthevariablebacon contain afterthefollowing coderuns?
bacon = 20
bacon + 1
The variable baconcontains20.
Question 7. Whatshould thefollowing two expressionsevaluateto?
‘spam’+ ‘spamspam’
‘spam’* 3
The two expressionsevaluate to‘spamspamspam’.
Question 8. Why is eggsa valid variablenamewhile 100 is invalid?
Variable namesmuststartwitha letterorunderscore.
Recognising 3D shapes in a photo. 2017/03/13.
Plotout a 3D shape usingcoordinates.Translate these into2Dimages.Compare these imageswith
the testimage.
Recognise characteristicsof the 3Dshape:is there a characteristicpartof the 3D shape thatis
alwaysthere.
Folding:write anunfoldingorfoldingcode.
CSS Coding Challenges
Strategystartlet.
CSS marionette.
SlidingCSSpanel.
HTML and CSS glassbutton.
Wireframesshouldcontaincontentthatyoucan learnfrom, or functional content,donotuse
fictitiouscontent.
The headline challenge. 2016/08/03-2016/08/10.
Put website wireframe onSlideshare.
https://en.wikiversity.org/wiki/Web_Design/CSS_challenges
Basedon https://freewebsitetemplates.com/website/knollwalters/
Funky. The imagesshouldincludehexagonsof variouspastel colours,mainlypeachandblue.The
plaincolouredcolumnshouldtravelslowlytothe rightwitheachscreen.Photopanel of smaller
photosto clickand enlarge tobringup a biography,whenhoveringoverthe photos,there shouldbe

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a white flagsayingthe name andjob title. Slideshow coveringthe entire page. Responsive web
design,fordesktopscreensand mobiles. Use semanticHTML5, use <section>.
Firstslide:Name of company,theirgoals,aspirations,function. Name isSpunRise.Panel of peach
flushtothe left,whichcanbe slidaside onhovertoreveal the goalsand aspirations. Panelissemi-
transparentandfont underneathlookslike patterning,withdividers.Panelof photographoccupying
the right handside,withthe functionof the company.Photographshouldbe of acircuitina
computer. Slide:news,e.g.expansionof the businessbybuyinganother similarbusiness,new
website launched,new employee. Newsshouldinclude date andbe inblue bullets. Slide:solutions
as to the scale of the webdesignproject withstandardprices,eachoptioninadifferentcolumn,
industriescovered, samplewebsites, sidetabsforeachsubpage.Industriescoveredisatable with
alternate cellshavingphotos,one wordtakingupthe whole of the cell. Slide:customers,show logos.
Slide:teammembers. Slide:contactform. Webdesignbusiness.
Differenceswithmobile website:nopanel of smallerphotos,justaseriesof photoswhichare
clickable tobringupthe biography. Javascriptmaybe required. Noslideshow coveringthe entire
page,as the entire page wouldnotbe bigenough,insteadthe designisscrollable. Solutionsslide:
clickable buttonsbringupa scrollable page.
http://www.w3schools.com/cssref/default.asp
Incorporate everyCSSfeature. Peachpanel hasaright-sidedoutline. Colourof the textoverthe
photoon the title slide iswhite withablackshadow. Peachpanel isslightlytransparent. The
photographto the rightof the title slide isabackgroundof a div,it isa fixedbackground.
Backgroundblendmode of the peachpanel ismultiply,colour ispeach. Photopanel has
background-positionascenter,background-repeat:no-repeat,background-clip:initial.Gothrough
and do the webdesign,thenaddthe extrapropertiessettotheirdefaultvalue,ora differentvalue if
applicable. Flex itemsare the photoicons,containedwithinanotherbox. Copyrightnoticeina
vertical textdirectiononthe title slide. Solutionslide asatable. Animationof the name of the
companyon the photopanel whenthe page loads,asa drop.Transitionof the name of the
company,to have an outerglowwhich subtly goesbrighteranddimmer. Translate the name of the
webproductpackages,to come infrom the left. The whole of the propertiescanbe implemented,
justthat some propertiesare commentedout,sotheyare not visible inthe final product.
The copyrightsymbol isinsertedafterthe companyname. Commentcontentbox isresizablebythe
user,withresize property. Putthe photoiconsandthe largerphotosintwo columns. Marquee at
the bottomof the title slide withTwitterfeed.
Use screenshotsof final productinaWord file forSlideshare.
Quickbridge
Choquet-BruhatY.IntroductiontoGeneral Relativity,BlackHoles&Cosmology.2015. Refertothe
bookas well asGoogle to helpyoudothe problems.
Exercise I.3.1. 2016/08/10-2016/08/15.
Checktensorsymmetryproperties,e.g. 𝑇𝑖𝑗 = 𝑇𝑗𝑖,are intrinsicproperties(i.e.independentof
coordinates). Thistensorisanorder2 tensor,ora 2-covarianttensor. Anorder2 tensorisoften
comparedto matrix.
https://en.wikipedia.org/wiki/Tensor#Notation

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https://en.wikipedia.org/wiki/Symmetric_tensor
Tensorsymmetryintrinsicproperty http://www.mx.iucr.org/iucr-
top/comm/cteach/pamphlets/18/node3.html
𝑇𝑖′ 𝑗′
ℎ′
is a 1-contravariant2-covarianttensor.
http://mathworld.wolfram.com/SymmetricTensor.html
If a tensorissymmetric,thisequationhastoapply:
𝑇𝑖𝑗 ≡
1
2
(𝑇𝑖𝑗 + 𝑇𝑗𝑖)
If co-ordinatesare swappedaroundfromIto j, the tensorsymmetrywouldstillhold.
Exercise I.3.2 2016/08/16-2016/08/31.
The image of a contravariant tensorfieldon V undera differentiable mappingbetween
differentiable manifolds 𝒇: 𝑽 → 𝑾 isnot necessarilya tensorfield on W unlessfis a
diffeomorphism.
Prove thisstatement inthe case of a vector field.
Replace “tensorfield”with“vectorfield”. A contravariantvectorexists.
The contravariantvectorsare tangentvectorsat 𝑥 ∈ 𝑉. V isa differentiable manifold. A manifoldisa
topological space whichcanbe charted. A differentiablemanifoldcanbe representedbyaline,on
whichone can do calculus.
𝑓 is a function. The colon: isusedto give a name to a map. W isanotherdifferentiable manifold.
An image isa subsetwithinthe domainWwhichisarrivedbyapplyingf tox in V.
A vectorfieldisanassignmentof avector to eachpointina subsetof space.
Vectorfieldsonsubsetsof Euclideanspace:assigningavectorto individualpointsinthatspace.
f the diffeomorphismisabijectionanditsinverse isdifferentiable aswell.
Maths mappingmanifolds.
Diffeomorphismisdifferentiable.
https://en.wikipedia.org/wiki/Diffeomorphism
If f is a diffeomorphism:
𝐷𝑓: 𝑇𝑥 𝑉 → 𝑇𝑓(𝑥) 𝑊
Where T is a vectorfield.
Give an example wherethe differentiable mappingbetweenmanifoldsisnotavectorfield.
Resultof differentiationof avectorfield.
http://www.math.illinois.edu/~verahur/18.024/notesDER.pdf
If 𝑔 ∘ 𝑓( 𝑥) = 𝑥, and f and g are differentiableand 𝑔 ∘ 𝑓 isalsodifferentiableviathe chainrule,

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𝐷𝑔( 𝑊) 𝐷𝑓( 𝑉) = 𝐼 𝑛
In orderfor f to have an inverse,itisnecessarythatthe Jacobianmatrix Df have rank n, so insome
casesf is nota diffeomorphism. Iisa scalar fieldwhichmakesupf.nis the variable whichmakesup
f,and belongstoa scalar field.
https://en.wikipedia.org/wiki/Differentiable_manifold
The rank of g at x isthe rank of thislineartransformation,butif the rankis0, thenW doesnothave
a vector fieldonit,ithas a scalar onit.
http://mathworld.wolfram.com/TensorRank.html
Comparisonwithanswer:
𝑥 𝑗 is 𝑥 𝑖, as rulesof summationdonotallow anyone suffix toappearmore than twice ina single
term.
The rank of g at x can be undefined(0).
Exercise I.3.3. 2016/09/01-2016/09/19.
The pullbackf* on V of a covariant tensorfieldon W is a covariant tensor field.For instance,for a
covariant vector ωand a mapping f givenin local charts by the functions 𝒚 𝜶 = 𝒇 𝜶(𝒙 𝒊), with yα
coordinateson W and xi
coordinateson V, the pullbackis definedby
( 𝒇∗ 𝝎)𝒊( 𝒙) =
𝝏𝒚 𝜶
𝝏𝒙 𝒊 𝝎 𝜶( 𝒚( 𝒙)).
Extendthe definitionandproperty to covariant tensors.
http://mathpages.com/rr/s5-02/5-02.htm
http://www.brighthubengineering.com/machine-design/120073-difference-between-tensors-and-
vectors/
A tensorissomethingwhichyoumultiplyavectorbyto change its directionandmagnitude.
An example of acovarianttensorisTx.
T 𝑥 = [
𝜕𝑦
𝜕𝑥1 ,
𝜕𝑦
𝜕𝑥2 ,… ,
𝜕𝑦
𝜕𝑥 𝑛
]
https://en.wikipedia.org/wiki/Pullback_(differential_geometry)
https://en.wikipedia.org/wiki/Tensor
A pullbackisa special formof a linearmap,whichisfromthe space of 1-formson V to the space of
1-formson W.
A linearmapisrepresentedbyamatrix (2-dimensional array) inabasis (x or f(x)),andsoisa 2nd
-
ordertensor. A 2-dimensional arrayisanymatrix the same size or biggerthan:
𝐀 = [ 𝑎11]
A space is a set. A mapis a function.
https://en.wikipedia.org/wiki/One-form

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The linearmapis eitherthe space of 1-formson V or the space of 1-formsonW.
α isone instance of y. f* isa special instance of f.
For a mappingf with Xi coordinatesonV,the pullbackisdefinedby:
Pullbackof covarianttensorfields:
( 𝑓∗ 𝑉) 𝑥( 𝑋1,… , 𝑋𝑠) = 𝑉𝑓( 𝑥)(𝑑𝑓𝑥( 𝑋1), …, 𝑑𝑓𝑥( 𝑋𝑠))
Exercise I.3.4. 2016/09/20-2016/10/09. (To be continued in 01/2017.)
Checkthat the quantities(3.6) (respectively3.7) transformas the componentsof a 2-contravariant
tensor(respectivelya2-covarianttensor) underachange of coordinates.
(ℒ 𝑋 𝑇) 𝑗𝑘 = 𝑋 𝑖 𝜕𝑇 𝑗𝑘
𝜕 𝑥 𝑖
− 𝑇 𝑖𝑘 𝜕𝑋 𝑗
𝜕𝑥 𝑖
− 𝑇 𝑗𝑖 𝜕𝑋 𝑘
𝜕𝑥 𝑖
. 3.6
(ℒ 𝑋 𝑇) 𝑗𝑘 = 𝑋 𝑖 𝜕𝑇𝑗𝑘
𝜕𝑥 𝑖
+ 𝑇𝑖𝑘
𝜕𝑋 𝑖
𝜕𝑥 𝑗
+ 𝑇𝑗𝑖
𝜕𝑋 𝑖
𝜕𝑥 𝑘
.3.7
How 3.6 transformsto3.7.
http://homepages.engineering.auckland.ac.nz/~pkel015/SolidMechanicsBooks/Part_III/Chapter_1_
Vectors_Tensors/Vectors_Tensors_13_Coordinate_Transformation_Tensors.pdf
Tensortransformationformula.
𝑇𝑖𝑗 = 𝑄𝑖𝑞 𝑄𝑗𝑞 𝑇′ 𝑝𝑞, 𝑇′𝑖𝑗 = 𝑄 𝑞𝑖 𝑄𝑞𝑗 𝑇𝑝𝑞
Differentwaysof writingtensors.
Tensorsuperscriptsubscriptnotation. Upperindicesrepresentcomponentsof contravariantvectors,
lowerindicesrepresentcomponentsof covariantvectors.
Tensorapostrophe meansthe transpose of amatrix.
ℒ is a laplace transformorlagrangiantransform.
Quickbridge Direct Work. 2016/11/04-2017/02/04.
Try solvinggeneral relativityequationsfora wormhole.
A sheetof bentpapercouldbe completelyfolded,bringingtogethertwopartsof space and time.
Create a mini blackhole thatemitsgravitons.
Concentrationsof energyemitgravitons.Sowhenyoujump,youare decreasinggraviton
transmissionbetweenyourself andthe earth.
Do magnetsemitgravitons.
Unifiedforce theory.
Separate forcesat workwhenjumping,deducegravitons.Use thistopredictforce requiredforthe
Quickbridge.
Space travel happensall aroundus.
Travellingfasterthanthe speedof light.

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If you getthe currentquestioninthe problemcrunchercorrect,move onto solvingEinstein's
equations.
Use currentintuitive explanationinbooktoworkout how much spacetime curveswithacertain
mass.
G11 = 8*pi*G*T11-cosmologicalconstant*g11. G is Newton'sgravitational constant.g11is a metric
tensorwhichisunitlessandrepresentsspacetime structure,thisisthe solutionof the equations.
G11 is the Einsteintensor,withunitsof 1/m^2and representsspacetime curvature. T11isthe
stress-energytensorwithunitsof J/m^3andrepresentsenergywithinspacetime.
G11 = R11 – ½*Rg11. Where R11 isthe Ricci curvature tensorandR isthe scalar curvature.
Do equationspredictdeformationof spacetime shownindiagram.
The tensorsare symmetric4x4tensors,soas a resultof thisthere are 16 equations.
dx appearsin the metrictensor.
Use Sagemathtoplugin the numbers.
The metrictensorconsistsof four dimensions.
Graph solutionsof the EinsteinFieldEquations,soyoucansee whetheritfitswiththe Quickbridge
design,graphthe flowof time aswell.
There are 10 EinsteinFieldEquations,thisisacceptedfact.
You can reduce the numberof equationsbyinsertingvalues.
Use fusionreactorat highertemperatures toprovide the necessaryenergy.
Doeslightbendaroundmasses.Whendoeslightcurve.Detectbendinlight,tosee bendin
spacetime. Detectchangesintravel of soundwaves.
http://physics.stackexchange.com/questions/109731/how-to-measure-the-curvature-of-the-space-
time
Avoiddeformationof spacetime closetoquickbridge:applyanequal andopposite force from
anothermass.
Write ownequationsforquickbridge andsolvethem.
Material that absorbsgravitonsandturns themintoheat.
Vertical printingwithmaterial insertedbetweenprinterheadandpaper.
Control gravitonswithunifiedforce theorye.g.magneticfield.
Use fansto counteractforce producedby gravitonse.g.dysonairconditioning.
Stress-energytensorcomponents: https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
Formsof the Schwarzschildsolution: http://physics.gmu.edu/~joe/PHYS428/Topic10.pdf
𝑑𝐬2 = (1 −
𝑎
𝑟
) 𝑐2 𝑑𝑡2 − (1 −
𝑎
𝑟
)
−1
𝑑𝑟2 − 𝑟2(𝑑𝜃2 + sin2 𝜃𝑑𝜙2)

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c isthe speedof light,ais the Schwarzschildradius,risthe radial coordinate (where the observeris,
inmetres),tis a universal time coordinate (measuredbyastationaryclocklocatedinfinitelyfar
away,in seconds),thetaisthe colatitude coordinate (angle fromnorth,inradians),phi isthe
longitude coordinate(inradians),ds^2isthe Schwarzschildmetric.
−𝑑𝑠2 = 𝑑𝑠2
𝑎 =
2𝐺𝑀
𝑐2
G isthe gravitational constant,Mis the mass of the object.
Componentsof the Schwarzschild metric,ds^2.
𝑑𝑠2 = 𝑔11 𝑑𝑟2 + 𝑔22 𝑑𝜃2 + 𝑔33 𝑑𝜙2 + 𝑔44 𝑑𝑡2
Where g isthe metrictensor.
What doesdx meanin general relativity: http://web.mit.edu/edbert/GR/gr1.pdf
dt^2 meansthe difference vectorbetweentwopointssquared.
𝑑𝑠2 = [
𝑑𝑟2 0 0 0
0 𝑑𝜃2 0 0
0 0 𝑑𝜙2 0
0 0 0 𝑑𝑡2
]
Schwarzschildmetricinmatrix form: http://mathpages.com/rr/s5-05/5-05.htm
𝑑𝑠2 =
[
(1 −
𝑎
𝑟
) 𝑐2 0 0 0
0 −(1 −
𝑎
𝑟
)
−1
0 0
0 0 −𝑟2 0
0 0 0 −𝑟2sin2 𝜃]
Aim:Fill the matrix with numbers.
a = (2*6.67408*10-11
*1010
)/2997924582
.
“a” isthe Schwarzschildradius. 299792458 isc, the speedof light. 6.67408*10-11
isG, the
gravitational constant.See above equation.
ds^211 inthe above matrix isthe difference intime. The othercomponentsare changesinthree
dimensionsof space. Findsto getthe distance betweentwopoints. Eachcomponentdescribesa
change,whichcan be integratedtogetthe distance and soobtainthe otherpoint.
Curvaturesasexpressedbythe Riemanntensor.
Interpretationof the Schwarzschildmetric:
http://gfm.cii.fc.ul.pt/events/lecture_series/general_relativity/gfm-general_relativity-lecture4.pdf
Use curvilinearcoordinatestoobtainageneral expressionof the line element.
Schwarzschildmetricforbeginners: http://casa.colorado.edu/~ajsh/schwp.html
𝑑𝑠2
11 = (1 −
𝑎
𝑟
) 𝑐2 𝑑𝑡2

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𝑡2 = ∫ (1 −
𝑎
𝑟
) 𝑐2 𝑑𝑡
𝑡2
𝑡1
𝑡 = ±(∫ (1 −
𝑎
𝑟
) 𝑐2 𝑑𝑡
𝑡2
𝑡1
)
1/2
Way to testslightspacetime curvature,sothatthe shape of the designof the Quickbridge canbe
done at a weaklevel toa safe extent.
Detectchange in positionandvelocityof soundwave afterithastravelledthroughspacetime.
Avoidaffectingspacetime closetoquickbridge:use extradimensions.
GraphingSchwarzschildsolution.
Is itpossible tocreate or destroyspace.
MaximallyextendedSchwarzschildspacetime.
Aim:howto use cancellationof gravitytoshieldobserversfromthe quickbridge. Use distance asa
shield,turnonquickbridge whenspacecraftissuitablypositioned. Aim:energycandeform
spacetime,socanit be usedas a shield.Aim:canenergycurve spacetime inone direction.Energy
absorber. Doesenergydeformspacetime afterithasbeenabsorbed?No,butitneedstobe
unabsorbedtocancel out quickbridge spacetimedeformation.Energycanbe unidirectional.Butthe
gravitonsemittedcanbe inany direction.Dogravitational wavescarryenergy?Absorptionof
gravitational wavespaper.Gravitational wavedetectorsuse some mechanismindetectorstoabsorb
gravitational waves.Butthe LIGOwebsite saysgravitational wavespassthroughthe earth
unabsorbed.Wavesof opposite amplitude cancancel eachother out.
Aim:whatabsorbsgravitational waves.Gravitational wavescanbe emitted,outof phase withthe
gravitational wave thatyouwishtocancel.Directthe cancellingwave tangentiallyatthe
quickbridge,the quickbridge openingbeinground.Energycanbe usedas the source of the
cancellingwaves.
Metric tensorbefore quickbridge isturnedon,metrictensorafteritisturnedon.Metrictensor
describesentryandexitpointsof quickbridge.Dogravitational wavescancel:stackexchange says
theydo.Space translator:move objectsfromone place toanother,usinggravitational waves.Sun
has 10km gravitational wave.Beamof lightfromone endof the room to another.Detectingchanges
ingravityat altitude:lavalamp,where lavalumpisthe same size andimpedance high.Gravitational
wavescause changesinfrequencyandamplitude of lightwaves. The quickbridgecanbe built,but
how.
Use a recentpaperas a standardfor mywork: arXiv:1701.07709v2 [astro-ph.HE] 1 Feb2017.
2017/02/04.
Work backwardswithdistance fromEarth to Mars and fill inthe metrictensormatrix.
Symbolically,the metrictensorcanbe betweenanytwopoints.
How gravitational wavesaffectthe evaporationof mercuryorany othercolouredgas.Shine alight
at watervapour.Write an equationrelatingtime toboil andinitial temperature.Once the kettle has
boiled,see howmuchof the watervapourcondensesatdifferentheights.See how abarometeris
made.Measure the amountof condensationbyweighingthe paperwithcondensationon it.

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Put a dropof wateron eachof the two piecesof paper,weighthe paperatintervalsandsee which
one driesfirst.
Boil a kettle using1litre of waterat heightandon the floor,time how longittakesforthe kettle to
switchitself off.
Use a top pan balance tomeasure a heavyweightonthe table andon the floor.
Use a snowglobe,orlongglittertube,agitate itusinga fixedamountof energy,e.g.roll itdowna
slope,andsee howlongittakesto settle onthe table andon the floor.Use coloureddustinthe
watertube.
Use a pendulum,upstairsanddownstairs.
For the quickbridge toattract Mars, the distance betweenthe earthandMars shouldbe smaller,
accordingto the metrictensor.
Ethical implications.
Disruptthe sun anduse it as an energy source forthe quickbridge.
Mars will still be close toEarthusingthe Einstein-Rosenbridge,somovingMarsisthe same thing.
Detectgravitational waves:measure decrease inenergyasgravitytakesover.Atdifferentheights:
disheswithwater,covered byclingfilmwithahole;write anequationlinkingtemperature,
evaporationrate andair pressure.Airpressure isdirectlylinkedtogravitational force.Use an
equationforconvectioncurrentstodeterminethe temperature atdifferentheightsinaroom.Put
the two containersrightnexttoa radiator,so that theyare both at the same temperature.Puta
thermometernexttothe outside of the container.Save potnoodlepots.
2017/02/04.
Aim:write anequationforthe quickbridge.Coordinate systemdistorted+cancellingwaves=
Quickbridge spacetime deformation. Usingthe metrictensorfromthe Einsteinfieldequations:
𝑔 𝑢𝑣 + 𝑐 𝑢𝑣 = 𝑞 𝑢𝑣.
𝑐 𝑢𝑣 = −𝑒 𝑢𝑣.
𝑔 𝑢𝑣 = 𝑞 𝑢𝑣 + 𝑒 𝑢𝑣.
Aim:findoutthe distance betweenthe entryandexitpointsbeforeandafterthe quickbridge is
switchedon.
𝑑𝑠2 = 𝑑𝑥 𝑖 𝑑𝑥𝑖 = 𝑔𝑖𝑗 𝑑𝑞𝑖 𝑑𝑞 𝑗
Where gij is the metrictensor,dq is an infinitesimal displacementinthe metricspace,ds^2is the line
element.
𝑑𝑠2 = (ℎ1 𝑑𝑞1)2 + (ℎ2 𝑑𝑞2)2 + (ℎ3 𝑑𝑞3)2
𝑞1, 𝑞2,𝑞3 is x,y, z. dqis the difference indistance of x,y,z.
ℎ 𝑖 = √ 𝑔𝑖𝑖
Scale factors:
ℎ1 = √ 𝑔11, ℎ2 = √ 𝑔22, ℎ3 = √ 𝑔33.

12
𝑔𝑖𝑗 = ( )
𝑞𝑖 = ( )
Numerical check:Distance toMars: 54.6 millionkilometres.Distanceof the edge of a doorframe.
http://www.physicspages.com/2013/03/21/tensor-product-numerical-example/
Firstvector:positionof the earth:
𝐴 𝑖 = (
1
1
1
1
)
Secondvector:positionof Mars:
𝐵 𝑗 = (55.6 × 109 1 1 1)
Metric tensor:
𝐴 𝑖 𝐵𝑗 = (
55.6 × 109 1 1 1
55.6 × 109 1 1 1
55.6 × 109 1 1 1
55.6 × 109 1 1 1
)
Aim:calculate the energyrequiredtoproduce the deformationforthe quickbridge.
Numerical example of the use of the stress-energytensor.
http://www.conservapedia.com/Quantitative_Introduction_to_General_Relativity
2017/02/04.
Needsmore spacetime curvature thanthe suniscurrentlyproviding.Extractenergyfromthe
supermassiveblackhole atthe centre of the galaxy,as itrotates,as it attracts.
What isthe force experiencedclosetoa blackhole?Tensileforce experiencedatthe centre of the
rod = (standardgravitational parameter (times) lengthof rod (times) massof rod) /(4 (times)
(radiustocentre of gravity)^3) . Schwarzschildradiusof the supermassiveblackhole atthe centre of
the galaxyis13.3 millionkilometres.Supermassiveblack holeshave amassof hundredsof
thousandstobillionsof solarmasses.Standardgravitational parameterof supermassiveblackhole =
gravitational constant (times) 10million (times) massof the sun= 6.67408 (times) 10^(-11)
(times) 10^7 (times) 1.989 (times)10^30 = 1.327474512 (times) 10^27.
Force experiencedatcentre of rod = (1.327474512*10^27*1*1)/(4*1^3) = 3.3186863*10^26
Newtons.
How dowe harnessthisforce?Use anotherrenewablesource of energytoexertanopposite force.
How dowe harnessthe force arounda rotatingblack hole?Use a gravitational turbine.
Can infiniteamountsof energybe generatedbyasequence of fusionandfissionthatrepeatsitself?

13
2017/02/07.
Energyabsorberabsorbsgravitons.Watermay absorbgravitons.Energyspewedfromamaterial
whichcurvesspacetime the oppositeway.
Use curvaturessectiononschwarzschildsolutionWikipediapage tocalculate energyrequired,using
E=mc^2.
Schwarzschildcoordinatesare polarcoordinates.
Quickbridge equation:Twodiagonally symmetricstress-energytensors,whichare relatedtoeach
other,one tensorinone setof equations,relationinanotherequation.
Relationof masses:8 dimensional tensordescribingthe relationinpriorflatspacetime;or4
dimensional tensorwiththe positionof one massasthe origin.
Solve equationwithone mass.Superimposethe resultingstress-energytensorontopof the stress-
energytensorof the othermass.
The original coordinatesare integratedtofindthe new lengthbetweenthem.
Maybe spacetime stretchingisdifferentfrombeingcompressedbutwithspacetime mostly
unaffected.
Quickbridge wouldneedtocompressspace,butnotcompressthe persontravelling.The spacetime
inthe Quickbridge shouldcompresstogetherandunitsdisappearwhile the person'sspacetime
remainsthe same.See whetherequationspredictspacetime unitscandisappear.
Graphingthe schwarzschildsolutionwouldenable ustosee whetherthe calculationsare correct,
and if our understandingof the use of the schwarzschild metriciscorrect.
The distantmass/energyforthe Quickbridge cancome froma fusionreactor.
Negative massformsthe tube of the Quickbridge,positive massatthe destinationend.
Negative energymaycreate negative mass.
Schwarzschildwormhole AndrewHamilton.
Can gravitational force be cancelled:the pointopposite the massona circumference experiences
negative force;onthe side of the mass,use anothermassto cancel the attractionoutside the tube;
use two rotatingmassestocreate negative forces aroundacircumference,one inthe centre and
one outside the circle;use one massoutside the circle,sothe middle ishollow.
Shieldingrequiredaroundcirclingmass.Energysinktoproduce shielding.Energydeforms
spacetime,sospacetime canbe modifiedbyenergysinks.Peoplemustwearenergysinkstopass
through.
EnergyrequiredbyQuickbridge:compare thistothe energyinthe sun.
Riemanntensor:fourcornersof a square,withx,y, z and time topositionit;maybe thisisnotthe
exactdescription.
Maths to describe spacetime curvature.
Coordinate systemdistorted+cancellingwaves=Quickbridgespacetime deformation.

14
Unit square isspacetime withoutcurvature,equationcandescribe curvature of multiple squaresif
the squarescan be coalesced.
Pointdeformationof asquare:centre of cube (0, 0, 0, 0), attractingpoint(x,y,z, t),magnitude of
attractingforce (m),attractingforce isforce requiredtomove the centre of the cube bya multipleof
itsunitlength.
Riemanntensorisa cube with8 corners(vectors) andtime (16 valuesintotal).
Findevidence of theoryinnature orenvironment.
LIGO publications.
Gravitydoesnot getusedup.
Aim:howto cancel out gravity.Use multiple pointmassesaroundthe circumference.
Gravitational wave measurement:whenapendulumstopsswinging.
Inverttensormathematics.
Finda space for your gravitational force experimentwithpotsof waterevaporating.
Experimentwhere small massaffectsevaporationagainstgravity:greatlydifferentamountsof water
evaporatingunderclingfilmwithone hole,regularlymeasure onscales,evaporationrate due to
mass of waterand temperature.
Can papersbe publishedonpersonal websites?Dependsonthe journal policy;thisisespeciallyokay
if the journal isopenaccess.
Artificial source of gravitational waves.Studythe innereartofindoutthe nature of these
gravitational waves.Currentliterature saysthatelectromagneticwavesproduce gravitational waves.
What are the featuresof thisartificial source of gravitational waves:small mass,small amountof
energy.Isthere anywhere innature where thisphenomenonisfound?No.Hypothesizesomething
whichmay produce gravitational waves.Gravitoncircuit,like electriccircuit.Itwouldhave a source
of gravitational energy.
What forcesappearto act againstgravity?A balloonmayemitgravitational waveswhichcancel out
the gravitational wavesemittedbythe earth.Thismustbe the case as the earth,independentof the
balloon,still emitsgravitational waves.
Artificial source of gravitational waves:objectwhichincreasesanddecreasesinmass.If the balloon
increasedinmass,itwouldfall towardsthe earth.Forthe balloontorise and increase inmass,it
mustcontinue toemitgravitational wavesalmostoutof phase withthose of the earth.
A hypothetical machine whichcouldinterfere withthese gravitationalwavessotheyare outof
phase or inphase.Hypothesize awayinwhichitwoulddothis.It can slow downthe gravitational
waves,sotheychange phase.Like waterwhichholdsfishupagainstgravity.Google:whatslows
downgravitational waves?Mattercanfocusgravitational waves,like ingravitational lensing,
however,ithasto be matterof highdensity.
Anothersource of gravitational wavesfaroutinthe solarsystem.Althoughif the gravitationalwaves
towardsthe earth were eliminated,Marswouldautomaticallytravel outwards.

15
2017/02/21.
What mass wouldbe requiredtocurve spacetime sothatthe distance toMars ischangedfrom
54.6*10^9m to 0.1m?
(1-2*m/r)^(1/2) dr from r=0 to r=54.6*10^9 (distance toMars).
((1-2*m)^(1/2))/(r^(1/2)) dr
= ((1-2*m)^(1/2))r^(-1/2) dr
= ((1-2*m)^(1/2))/(1/2)*r^(1/2)
= ((1-2*m)^(1/2))*2*r^(1/2)
0.1 = ((1-2*m)^(1/2))*2*(54.6*10^9)
m = 0.5kg
Checkthat the correct values have beenused.
Detection of gravitons 2017/01/06.
Theytravel ina straightline,andare able topenetrate objects.More massive objectsemitmore
gravitons.The sumtotal of gravitonsemittedcanbe foundbymeasuringthe total massattracted.
On small objects,lookatbacteriaattracted.Effectof gravitonsonbrownianmotion.Aim:write a
formula.Total mass(orbitingoron surface) attractedinone direction,multiplication,openbracket,
distance tocentre of objectstudied,minusdistance tooutsideof object,close bracket.Tensorfor
3D shape of the object.Aim:whatif there were noobjectsinvicinity.Place aconsiderablysmaller
objectinvicinity,lookatitsacceleration,distance tocentre of objectstudiedwherethisacceleration
happens. Massmultipliedbyacceleration.Aim:how doesthisbuildonprevioustheories.Givesa
methodof measuringgravitonemissioninone direction,previoustheoriesare notdirection-specific,
thoughEinsteinfieldequationsare,experimentexampleappliesto small objects.Total effective
gravitons.Small moleculesdetectedbyradiationemittedaftervibration.Force boardwhichdetects
force exertedonitby small objects,doitabove small object,thendoitabove emptyspace.Force
board shouldbe sosensitivethatitdetectsa single graviton,nanospring(amolecule like aspring).
Quickbridge Direct Work. 2017/02/22.
Quickbridge.04/02/2017.
Sub-goal:Howdoesfusiongenerateenergy,whatisthe startingpointandwhatis the endpoint?
Buildingthe quickbridge athome.Refractionof lightbyalargerglasscup withwaterinit, compared
to a smallerglasscupwithwaterin it.The greaterthe massof the glasscup, the strongerthe light.
What are the possible accidentsthatmay happenwiththe quickbridge?Improperpositioningof
movedobjects,explosions.
There shouldbe a portionof the quickbridge behindMarsso the gravitational wavesemittedtravel
no further.
There isan attractional force betweenaballoonandotherobjectsinspace whichoutweighsthe
attractionto Earth.

16
If an objectislightenough,itemitscancellinggravitational waves,soitfloatsup.Itsown
momentumoverridesthe force attractingitto Earth. The balloon'smomentumcomesfromthe
spinningof the earth,like weatherpatterns.
How to use the metrictensor?Lengthof a parameterizedcurve vector:x^(r)=x^(r)((u)),where x^(r)
isa verticallywrittenvectoranduis the parameter.Thiswouldbe the original distancefromEarthto
Mars.
http://leto.net/x/2008/12/5-min-math-metric-tensor.html
Infinitesimal displacementelement:dx^(r)=p^(r)((u))du.Basicallyp^(r) isanothervectorwhichis
slightlylargerorsmallerthanx^(r).We needthe infinitesimal displacementelementbecause we are
tryingto measure the lengthof the curve,bitbybit.The lengthof thisdisplacementelementis:ds=
(sqrt)(g_(mn)p^(m)p^(n))du.The lengthof the curve fromu=u_(1) to u=u_(2) isL =
(integral)((top)(u_(2))(bottom)(u_(1)) ds).ThensubstituteindsintoL. The metrictensoris
requiredtodefine distance alongacurve whenworkinginanon-cartesiancoordinate system, e.g.
spherical.A two-dimensional parameterizedcurve vectorgivesathree-dimensional curve.
How to make gravitational wavescancel?The interveningmachine needstoslow downthe
gravitational wave by180 degrees.Use a more sensitive interferometertodetectwhetherthe
wavesare in phase or not.
Hypothesize amethodof artificiallycreatinggravitons?Supercoolingwater.Intolowertemperatures
than before,e.g.3.14 Kelvin.Supercooledwateremitscancellinggravitational waves,soyoucan use
thisinthe opposite directionof travel.
In a fusion reactor,hydrogencomestogethertoformhelium.How doesafusionreactorproduce
energy,whichbondsare involved?
Put numbersinmetrictensor.x^(r)=x^(r)((u)).We justhave adistance,andthisisgivenbythe
vector(u).
Cancellinggravitational wavesemitted=1 / ((exponential)(temperatureof supercooledwater)) .
The stress-energytensorshouldbe easytopopulate withnumbers,asonlythe energyof the
originatingsource isrequired.
What numbersshouldwe putintothe stress-energytensor?T_(11)=Joulesperm^3,all other
componentsare 0. If the mass-energyiscontainedin1m^3,we onlyneedtonow worryabout the
mass andenergy.16 simultaneousequationsare reducedto1.
How dowe findoutthe energyrequiredtoget toMars? Write 2 simultaneousequations,one with
no energyandcurrentdistance toMars, the otherwithenergyandshorteneddistance toMars.
What numbersshouldgointothe Ricci curvature tensor?It issymmetric.Calculate ricci curvature
tensor.Definitionof the ricci curvature tensor.Google:Ricci curvature tensorR11. Itis calculated
fromthe Riemanntensor.Google:Ricci tensorflatspace.R11= 0 inflatspace.The Ricci tensorputs
the metrictensorincontext,the metrictensordescribestwopointsandthe Ricci tensordescribes
the way inwhichspacetime iscurvedalreadyforthese twopoints.Google:Riemanntensorfor

17
space around the sun.Use the line elementforthe Schwarzschildmetrictocalculate the Riemann
tensor.Do the reston the computer.
Energyfrom fissioniswhenthe strongforce ina nucleusisreleasedbysplittingof atoms.The energy
fromfusioncomesfroma slightdecrease inmasswhentwonuclei are fused;the missingmassis
releasedasenergy.Asbothprocessesinvolvea decrease inmass,fusionandfissioncannotbe used
ina cycle to produce infinite amountsof energy.
How dowe artificiallycreate gravitons?Putanatom nexttopositivelychargedplates,andelectrons,
so the atom isfooledby thinkingitispartof more mass.Artificiallymimiccommunicationthat
comeswithquantumentanglement.Higgsbosonmayinteractwithprotonsandneutronstogive
themmass.
We can't artificiallycreate gravitons,asgravitycomesonlywithmass.
Use a blackhole to attract Mars to nearEarth.
Focusgravitational wavestoone pointanduse that to attract Mars.
Line elementforthe Schwarzschildmetric:c^(2)dT^(2) =(1-r_(s)/r)...Where cisthe speedof light,T
isthe propertime,r_(s) isthe schwarzschildradius,risthe radial coordinate.
Google:qmplusexercisesclass3.Calculate metrictensor.Calculate metrictensorforschwarzschild
solution.
Ricci tensorfor the schwarzschildsolution:R_(11)...Thisisnotwhat we want,as the schwarzschild
solutiondoesnotinclude energy.
Google:numerical calculationof the ricci tensor.Google:Calculate spacetimecurvature fromthe
Schwarzschildsolution.Howismassof the quickbridge relatedtothe curvedspace?Time,phi and
thetaare constant.Distance incurvedspacetime =(integral)(top:originaldistance)(bottom:
0)((dr)/(sqrt)(1-2×mass/r)).Distanceincurvedspacetimeis0.1 metres.The original distance is
54.6×10^9 metres.Integral of (1-2×mass/r)^(-1/2).Integrate(1-2*m/r)^(-1/2) drfromr=0 to
r=54.6*10^9. Use a graphto illustrate how mvariestogive distance incurvedspacetime.
2017/02/26.
Try the calculationagain. What isthe mass requiredtodeformspacetimesothatthe distance to
Mars becomes0.1m? The radial coordinate isthe circumferenceof acircle centeredonthe star
dividedby2*pi inmetres. Google:distance Schwarzschildmetric.
𝑟𝑠 =
2𝐺𝑀
𝑐2
Where r_(s) is the Schwarzschildradius,Gisnewton’sgravitational constant,Mismass,and c isthe
speedof light.
𝑑𝑠2 = (1 −
𝑟𝑠
𝑟
)−1 𝑑𝑟2
Where ds isan invariantspacetime interval,ameasure of a distance betweentwopointsin
spacetime,risthe circumferential radius.

18
𝑠 = ∫ (1 −
𝑟𝑠
𝑟
)−1 𝑑𝑟
𝑟
0
𝑠 = ∫ (
𝑟
𝑟
−
𝑟𝑠
𝑟
)−1 𝑑𝑟
𝑟
0
𝑠 = ∫ (
𝑟 − 𝑟𝑠
𝑟
)−1 𝑑𝑟
𝑟
0
𝑠 = ∫
𝑟
𝑟 − 𝑟𝑠
𝑑𝑟
𝑟
0
𝑠 = ∫ 1 −
𝑟
𝑟𝑠
𝑑𝑟
𝑟
0
𝑠 = [ 𝑟 −
𝑟2
2𝑟𝑠
]
0
𝑟
0.1 = 54.6 × 109 −
(54.6 × 109)2
2
×
𝑐2
2𝐺𝑀
0.1=54.6*10^9-((54.6*10^9)^2)/2*(3.00*10^8)^2/(2*6.674*10^-11*M)
M = 1.8*10^37 kg.
Thismass isgreaterthan the mass of the earth.Sothe energyforthe Quickbridge cannotcome from
fusionorfissiontoprovide energytodistortspacetime.Itistime toinvestigatethe Higgsboson.
https://uk.mathworks.com/help/coder/examples/introducing-einstein-s-theories-of-relativity.html
2017/03/05.
Try the calculationagain.
𝑟𝑠 =
2𝐺𝑀
𝑐2
Where r_(s) is the Schwarzschildradius,Gisnewton’sgravitational constant,Mismass,and c isthe
speedof light.
𝑟𝑠 =
2 × 6.674 × 1011 𝑀
3.00 × 108 .
Wolframalpha:(2*6.674*10^11*M)/(3*10^8)
𝑟𝑠 = 4449𝑀.
𝑑𝑠2 = (1 −
𝑟𝑠
𝑟
)−1 𝑑𝑟2
Where ds isan invariantspacetime interval,ameasure of a distance betweentwopointsin
spacetime,risthe circumferential radius.
Schwarzschildsolutionproperdistance.

19
𝑑𝑠 = (1 −
𝑟𝑠
𝑟
)−
1
2 𝑑𝑟
∫ 𝑑𝑠 = ∫
𝑑𝑟
√1 −
𝑟𝑠
𝑟
𝑟
0
𝑠 = ∫ (1 −
𝑟𝑠
𝑟
)−
1
2 𝑑𝑟
𝑟
0
𝑠 = ∫ (
𝑟 − 𝑟𝑠
𝑟
)
−
1
2
𝑑𝑟
𝑟
0
𝑠 = ∫ (
𝑟
𝑟 − 𝑟𝑠
)
1
2
𝑑𝑟
𝑟
0
Wolframalpha:
integral1/sqrt(1- s/r) dr = r sqrt(1- s/r) + 1/2 s log(2r (sqrt(1- s/r) + 1) - s) + constant
Where logis the natural logarithm.
x isM.
54.6*10^9*sqrt(1 – (4449x)/(54.6*10^9)) + (½)*4449x*log(2*54.6*10^9*(sqrt(1
– (4449x)/(54.6*10^9)) + 1) – 4449x)=0.1
5.46×10^10 sqrt(1 - 8.14835×10^-8 x) + 4449/2 x log(1.092×10^11 (sqrt(1 -
8.14835×10^-8 x) + 1) - 4449 x) = 0.1
Wolframalpharanout of a computation time.
Try Sagemath. x and y are M.
x = var('x')
solve([5.46×10^10*sqrt(1 - 8.14835×10^-8*x) + 4449/2*x*log(1.092×10^11
(sqrt(1 - 8.14835×10^-8*x) + 1) – 4449*x)==0.1], x)
Tryingagain inSagemath,withthe correctsyntax:
y = var('y')
solve([5.46*10^10*sqrt(1 - 8.14835*10^(-8)*y) +
4449/2*y*ln(1.092*10^(11)*(sqrt(1 - 8.14835*10^(-8)*y) + 1)-4449*y)==0.1],
y)
[y == -1/22245*(546000000000*sqrt(-2813/34522326606*y + 1) - 1)/log(-
4449*y + 109200000000*sqrt(-2813/34522326606*y + 1) + 109200000000)]
Try graphingthe resultwitha range of r values inSagemath.
M = var('M')
plot(5.46*10^10*sqrt(1 - 8.14835*10^(-8)*M) +
4449/2*M*ln(1.092*10^(11)*(sqrt(1 - 8.14835*10^(-8)*M) + 1)-4449*M),(M,-
10^6,10))

20
𝑀 ≈ −106 𝑘𝑔.
It ispossible fornegativemassestoarise from the Schwarzschildsolution.
Perhapschange the interval values.
http://physics.stackexchange.com/questions/130810/what-is-the-schwarzschild-metric-with-proper-
radial-distance
Newcalculation,whereR-2Mmeasuresthe properradial distance outwardfromthe horizon.
𝑅 − 2𝑀 = √ 𝑟( 𝑟 − 2𝑀) + 2𝑀ln[√
𝑟
2𝑀
− 1 + √
𝑟
2𝑀
].
M_1 = var('M_1')
plot(sqrt(5.46*10^10*(5.46*10^10-2*M_1))+2*M_1*ln(sqrt(5.46*10^10/(2*M_1)-
1)+sqrt(5.46*10^10/(2*M_1))),(M_1,-10^2,10))
Whenmass is -10^21kg, the properdistance is 438628.000000000 - 3.14159265358979e21*I.
Whenmass is -10^2kg, the properdistance is5.45999980188723*10^10 - 314.159265358979*I.
Whenmass is10kg, the properdistance is5.46*10^10.
Whenmass is10^2kg, the properdistance is5.46000019811277*10^10.
Whenmass is10^3kg, the properdistance is5.46000175086916*10^10.
𝑀 ≈ −1021 𝑘𝑔.
Google:whatisthe properradial distance withregardstothe schwarzschildsolution.
Calculate the properdistance forthe sun.
𝑅 − 2𝑀 = √ 𝑟( 𝑟 − 𝑟𝑠) + 𝑟𝑠ln[√
𝑟
𝑟𝑠
− 1 + √
𝑟
𝑟𝑠
].
𝑟𝑠 = 3000

21
𝑟 = 149.6 × 106
sqrt(149.6*10^6*(149.6*10^6-3000))+3000*ln(sqrt(149.6*10^6/(3000)-
1)+sqrt(149.6*10^6/(3000)))
1.49616805081065*10^8
The properdistance isactuallylongerthanthe radial coordinate. Sothe smallervalue (of the initial
distance anddistance incurvedspacetime) shouldbe r,whichisthe distance incurvedspacetime.
Calculate the properdistance fora Schwarzschildradiusof rs=10^37m and r=0.1.
s=10^37
r=0.1
sqrt(r*(r-s))+s*ln(sqrt(r/s-1)+sqrt(r/s))
1.57079632679490e37*I
s=-10^27
r=0.1
sqrt(r*(r-s))+s*ln(sqrt(r/s-1)+sqrt(r/s))
7.99277837364062*10^9 - 1.57079632679490*10^27*I
𝑟 𝑠 = −1027
m.
𝑟𝑠 = 4449𝑀.
𝑀 ≈ −2.25 × 1023kg.
For s=10^37 and r=0.1, r=<2GM, so the properdistance iscontainedbythe blackhole.Thisgivesan
interiorSchwarzschildsolution.Thismeansthatthe blackhole itself will containthe distance from
Earth to Mars.
2017/03/08.
Equationforthe decayof the Higgsboson.
What doesthe Higgsbosondo? The Higgs bosonclustersaroundparticlesastheymove throughthe
Higgsfield.The more massa particle has,the more Higgs bosonsitwill attract.
http://edition.cnn.com/2011/12/13/world/europe/higgs-boson-q-and-a/
Whendoesa Higgs bosondecay?Almostimmediatelyaftertheyare produced. One possible mode
of decayproducestwophotons.
http://particleadventure.org/the-higgs-boson-decays-into-other-particles.html
What createsthe Higgs boson?Whenthe Higgsfieldbecomesexcited.
https://en.wikipedia.org/wiki/Higgs_boson

22
Google:equationforhiggsdecaytotwo photons.(TODO)
http://www.hep.lu.se/atlas/thesis/egede/thesis-node17.html
Γ𝐻→𝛾𝛾
What doesH right arrowgamma gamma mean.
It meansthe Higgsbosondecayingintotwophotons.
2017/03/24.
Write a newequationfora local fieldinablack hole,createdbyHiggsbosons,whichcanavoid
spaghettificationwithinthe blackhole.
force exertedbyasingle higgsboson.
To create a Higgsboson,justdo whattheydo at CERN,smash particlestogether.
2017/04/14.
What area of maths do youneedtoknow to become familiarwithtensors?Differential geometry.
Metric tensor:fourdimensionsacross,fourdimensionsdown.Findadimension,seehow itis
affectedbythe value inthe metrictensor,outinthe same dimension(asthe metrictensoris
symmetric).
How doyou buildthe Quickbridge?Hypothesize the wayitworks,andsee if that matchesupto
experimental data,revise the theory.Once the theoryiscomplete,itcanbe built.
Cooledsuperconductorandmagnetemitcancellinggravitational waves;increase the sizeof the
superconductor,move itbehindMarsanduse it to guide the planet.
How doesgravitational attractionarise?The nucleiof atomsinclose proximitycommunicate with
each other.If theyare fooledintothinkingtheyare partof a larger mass,artificial gravitational
attractionoccurs. Two atomstogetherhave greatergravitational attractionthanif theywere
summed.Itstandsto reasonthat gravityismediatedmainlybythe nucleus,asthisisthe main
providerof mass.It maybe possible tosendgravitational wavestoa nucleusandfool itintothinking
that itis part of a largerwhole,thuscreatingartificialgravity,however,thisdoesnotfitwith
observations.The nucleiof atomsmaycommunicate withayetundescribedparticle,togive rise to
gravitational attraction.
Can informationtravel throughthe Einstein-Rosenbridge.
How dowe solve spaghettification?A blackhole maybe splitapartby an oasisof non-distorted
space,if artificial manipulationof gravityexisted.
Originof the graviton:How particlescommunicate witheach other.
Write an equationforthe evaporationof water.T,S_(e),V,S,D, M_(w),M_(E). dM_(w) =
(T*S_(e)*M_(w)*S*M_(E))/(D^2).Where Tistemperature,S_(e) issurface areaexposedto
evaporation,Sissurface areaof water,D is distance tocentre of earth,M_(w) ismass of water,
M_(E) is massof the earth.

23
Is itpossible toartificiallyproduce the Higgsboson?Yesitis.
How wouldyouuse the Higgsbosonto give more massto one particle?Create a strongerHiggsfield.
How muchenergyisrequiredtoproduce the Higgsboson?A small amount.
Typesof calculations:typesof mathematical proof.
Findan existingequationanddosomethingtoitto prove a point.
Thinkof how to prove somethingmathematicallyinwords,andwhatyouare tryingto demonstrate.
Aim:demonstrate absorptionof gravitationalwavesmathematically.
Gravitational wavesare absorbedwhenmeetingdestructive interference.Cangravitational waves
be unidirectional?Dependsonthe shape of the source.Doa matrix to represent360 degrees
aroundthe Quickbridge.Thinkof the shape of the graph solution.Quickbridgeencasedinside a
hollowshell,withone holepointingtoMars.
Readabstracts frompapers.
Readthe gravitational wavesWikipediaarticle andlookupunknownvariablesandmathsoperators.
Detectionof gravitational waves:Higgsbosondetectoratdifferentheights,giving3Dview of a field.
Observe Higgsbosonsastheyappearnaturally.
Google:howto detectthe Higgsboson.
Google:Sagemathschwarzschildsolutionexample.
Propertiesof the Higgsboson.
What doesdx on itsown mean.
How isdx^2 differentfromdx.
Integrationof dx^2.
What doesds^2 mean.
Schwarzschildsolutiondistance.
Properdistance Schwarzschildsolution.
The Higgs fieldhas4 components.
Gravitational wave detector:blocksof whitelight.
Creatingnewmaths:mathsneedstobe backwardscompatible.Make existingmathspractical.
Google forexperimental datatocontribute towardstheory.Dissectexistingmathsmanipulations,
e.g.multiplication.
Equationfora solutiontothe Einsteinfieldequationsthatallowsthe distance fromEarthtoMars to
be shortened.
Nakedsingularitymetric.
Local spacetime withinablackhole can be changed,soit issafe to live inside one.

24
ApplyHiggsbosonequationstothe Einstein fieldequations.
Finda part of the Higgstheorysimilartothe Einsteinfieldequations.
Su(2) and spacetime curvature tensor.
Askquestionsasyouworkthingsout as part of your majoradvance on your phone.
Whichpart of Higgstheorywas usedinthispaper?Look at the equationslabelledsu(2).
What issu(2)?
Try to write equations:see if atensorinthe Einsteinfieldequationscanbe substitutedforamatrix
inHiggs theory.
2017/06/02.
Whichmatrix in Higgstheorylookssuitable tocombine withatensorinthe Einsteinfieldequations?
Higgsfield.Tryto workout a mechanismforcurvingspacetime usingthe Higgsboson.
Checkyour maths:prove itis correct.
Gravitational wave sensormade usinginterferometryatthe atomiclevel.
Purpose of combining Higgsbosonequationstothe Einsteinfieldequations:see if Higgsbosonscan
be producedto control spacetime curvature.
To travel fromone place to anotherat the speedof light.Disassemble atstartingpoint,assemble at
endingpoint.Copyknowledgefromperson'sheadatstartingpoint,assembledrone orhologramat
endingpoint.The fastestpossiblespeedacarbon atomcan travel hasto be lowerthanthe speedof
light.Energyisneededtomove inspace,butenergyisnotrequiredtomove intime.The earthis
movingquickly(orbitingthe sun),butwe don'tfeel it.
The Quickbridge maybe possible,asmassive spacetime disturbancesoccurwhenblackholesare in
action.However,thisdoesnotpreserve the integrityof mattersurroundingit.Mathematical
equationtodescribe aregionof space,whichisseparatedinhalvesbyenergy,butwhichcome
togetherwhenthe energyisstopped.The creationof space fromenergy,asthiswaswhathappened
inthe bigbang.
How can gravitational wavesbe emittedinjustone direction?Emitcancellinggravitationalwavesin
otherdirections.Cangravitational wavesbe absorbed?Yes.
Use R for calculations.
There isfundingforthe Quickbridge,butyourworkmustbe of publishedstandard.
Aim:thinkof a bettergravitational wave experiment,one thatissure toproduce results,pretend
youhave all the materialsyouneed.
Look at publicationsfromyourlocal universitytosee whatequipmenttheyhave.
Is itpossible tointegrate dr^2on the righthand side of the schwarzschildsolutionwhenthe
coefficientincludesr,andtherefore the coefficientisnota constant?

25
Invent/create new mathstodescribe the Quickbridge.Write downindetailyourconceptionof this
newmaths.Thinkof how yourmaths can be solved.
Detectphotonswhichthe Higgsbosondecaysinto.
Photondetector.
What determineswhichtype of decaythe Higgsbosontakes.
Finda way of doingprojectswhichtouchesonrelevantbasics.
Solvingthe Einsteinfield equationsforapointmass,e.g.nakedsingularity.
If E=mc^2, calculate the energyrequiredtocreate anearth, or the interveningspace andmatter
betweenone endof the Quickbridgeandthe other.
Energycan create space:thinkaboutthe bigbang and the expandinguniverse.Beforethe bigbang,
there waslotsof energy,andsocreatedmatter andspace. If energycancreate matter,itcan also
create space.
2017/07/15.
Make notesonthe Higgsmechanisminthe Noteslist.
https://en.wikipedia.org/wiki/Higgs_mechanism
What quantityof Higgsbosonswouldbe requiredtogenerate enoughmasstocurve spacetime
enoughtomake a Quickbridge?We wouldneedtofindthe strengthof the Higgsfield,which
interactswithotherparticlestogive particlesmass.Wouldanyparticle acquire anyquantityof mass
if there were enoughHiggsbosons?
https://physics.aps.org/articles/v6/111
Findsomeone withtheoreticalphysicsexposure tocollaborate with.
End of time. 2017/02/04-2017/04/06.
Look at StephenHawking'swork.
If there is a bigcrunch, time will end.
End of time.
How to prolongthe time we have?Stopourpart of the universe expanding.Turnplanets andstars
back intonebulae. Thisappliesif the universe isdestinedtoinfinitelyexpand.
There may be a time particle,whichcontrolshow time passesforeachmass.Nothinglike thisexists
inthe literature asof 2017/04/06.
Use the Einsteinfieldequationstosee underwhatconditionstime flowsbackwards.
https://en.wikipedia.org/wiki/Retrocausality

26
Papersearch:how spacetime isaffectedbymassphysics.
2017/06/02.
It isa little riskytogoback intime.
At the endof an infinitelyexpandinguniverse,time will notend.
Space must continue if time continues.
If the universe isaclosedsystem,there shouldbe awayto regainlostenergy.
Time runsslowerat the beginningof the universe, asitexpandsfromasingularity.
Increasedspacetime curvature meansshorterdistancesandlongertimes.
The aim of the endof time projectisto finda wayfor time and space to continue,shouldtherebe a
bigcrunch.
End of time.2017/02/28.
There are nopublishedpapersonthe endof time,althoughthere isabook.
End of time.
Time shouldhave ashape,as it isa dimension.
Ways to unlinktime fromspace,asusuallytheyhappentogether.
Expandingendof the universe:aswe getfurtherandfurtherawayfrom masses,time willrunfaster
and faster. Infinitelyfarawayfrommasses,time will runinfinitelyfast. Therefore the source of more
time isclose to masses. Findaway of measuringtime preciselyclosetomasses.
Creation of a new universe. 2017/02/22.
Creationof a universe.04/02/2017.
Rewindanexpandinggalaxyandexpanditagain,likeamini-universeinside ours.
Whenyoucollapse anexpandinggalaxy,doeseverythingjustfall intothe supermassive blackhole?
That's right.Perhapsthere needstobe some formof artificial interventionforablackhole to release
matter.Turn it intoa white hole.
Can youwrite an equationwhere the blackhole turnsintoawhite hole?A white holeisthe reverse
of a blackhole.Energywithinblackhole +intervention=massfroma white hole.Whatisa model of
howa blackhole works?A blackhole mayhave a temperature,sowhenthisisraised,itemits
matter.Raise interventionvariable e.g.temperature,andthe energywithinablackhole isconverted
to mass froma white hole.If the interventionvariableisbelow acertainamount,nomassis
emitted.Whatmathsisusedto calculate thresholds?Segmentedregression.Thresholdvalue for
whena blackhole becomesawhite hole =1 - (currenttemperature of blackhole) /(temperature
requiredtobecome awhite hole).If the thresholdvalue is0or negative,awhite hole isformed.Can
an equationbe wrote where blackhole forces(orspacetimecurvature) become white holeforces
afterthe change of temperature?Stopexploringthisavenue because asthe blackhole absorbs
matter,it getshotter.Whatis anothermodel forhow the blackhole works?Searchthe literature.

27
The black hole hasmass,but the singularityisof infinite density.The discrepancyinthis maybe due
to displacementof absorbedmattertoanotheruniverse.
Creationof a newuniverse.04/02/2017.
Is there anexplanationof howablackhole may stoptransferringmatterintoa new universe,in
accordance withourobservedbigbang?Noexistingexplanation.The instantastar fallsintothe
blackhole andthe massof the blackhole doesn'tchange,iswhena new universe ismade.Or
perhapsthe blackhole storesupmass inthe singularityandreleasesitinone go to another
universe.Asthe black hole'ssingularityisinfinitelydense,there isplentyof material tomake
anotheruniverse with.
Black holes decrease entropy. 2017/04/05.
Thisis logical,giventhatmatteriscondensedinablackhole.
Google:doesentropydecrease inablackhole.
https://www.quora.com/Do-Black-Holes-decrease-entropy
Black holescanexplode,givingrise tonew matter.
http://www.thephysicsmill.com/2015/06/14/speculative-sunday-can-a-black-hole-explode/
Writingnewmaths:combine existingmaths,e.g.Einsteinequationsandquantumtheory.
Can blackholesbe made to explode?
By applyingalarge shearforce.
If a cycle of entropydecrease andexplosionoccurs,thenwe have alarge amountof matterto work
with.
Stackpirt
2017/04/05.
How doesa neural networkwork?
The networkistrainedusinga seriesof inputsandoutputs.Aslongasthe neuronsinthe hidden
layerhelpproduce the rightoutput,the exactpaththat the informationtakesisflexible.
http://www.explainthatstuff.com/introduction-to-neural-networks.html
How to inputwordsintoa neural network?
Turn it intobinary.
http://datascience.stackexchange.com/questions/869/neural-network-parse-string-data
Use anotherneural networktoprocessthe wordsintopositive andnegative news.
Stackpirt.2017/02/17.
How to write a winningstocktradingalgorithm.
Sfear
2017/10/31.

28
Thisbusinessshouldhelpothers.Itshouldbringnormalitytoahigherlevel.Itshouldrevolutionise
peoples’lives.Itisnotreallya political movement,evenif itinfluencespolitics.Itistodo with
technology.Perhapsitissomethingwhichmakespeoplework. Itisa gadgetwhichisportable.It
containsan artificial intelligence,whichstoresamillionunfinishedprojects.Doesthisvarietyhelp?It
splitsupa projectintoa millionunfinishedprojects.The varietydoeshelp,butitshouldbe tested.
Hm. Let’stry splittingupmycompanyproject.
1. What’sthe floorplanlike?
Tree notes,whichyoudo wheninspirationstrikes.Optiontoconvertitintoa textfile.Whatif it
takesawayyour brain?Wouldhelpyouworkingonyourproject,though.Givesyoua memorytest.
Marble witha rubbercoat.Keywordsattached(optional) to helpyoufindeachnode inthe tree.
Traverse the tree by rolling.Zoomintothe tree.Linktextfilerepresentationtothe printer,and
Onedrive.Longevityof informationisif itislinkedtoexistingtechnology.The pendantonlyactivates
neara wall.Highcontrastprojection.Putthe device close toyourear,whenoutdoors.Use
headphones.Like automaticcall menuoptions,whenusingthe voice functionality.
2. What’sthe keyfunctionalityof yourproduct?
3. What rubberisthe coatingmade of?
Wheneveryone overcomesprocrastination,yourprojectwill be finished.
1. Answer.Floorplan:Engineeringspace.Testspace.
Thisprojectstoresprojectinformation.
Sfear,sphere.Fearof tablets,hospital,andjail.Rollingaction:core suspendedinliquid.Glasssurface
for pressure toproduce a click.Camerarotatesto face the wall.

30
University Maths Puzzles
Analyse howthe answersare done,thoroughly.
Folding rectangular sheet problem. 2016/08/02-2016/08/03.
http://www.qbyte.org/puzzles/puzzle01.html
http://www.qbyte.org/puzzles/p001s.html
If a rectangularsheetisfoldedsothattwodiagonallyopposite cornerscome together,andthe
crease formed isthe same as the length,whatisthe ratioof the longerside of the sheettothe
shorterside?
Rectangularsheetonitsside.A diagonal crease goingfromthe topedge to the bottomedge,like a
backwardslash . Knownlengths:l = crease.Crease right angledtriangle shorterrightangledside =
w. l^2=w^2+(crease rightangledtriangle longerside)^2.(1).A longdiagonal goingfromthe topleft
handcorner to the bottomright handcorner.(Long diagonal)^2= l^2+w^2. (2). The longdiagonal

31
and the crease bisecteachotherat right angles.(l/2)^2+((longdiagonal)/2)^2=l^2.(3).Make long
diagonal the subjectof (2):longdiagonal = sqrt(l^2+w^2).(4).Insert(4) into(3):(l/2)^2 +
((sqrt(l^2+w^2))/2)^2=l^2.1^2/4 + (l^2+w^2)/4 = l^2. l^2+l^2+w^2=4l^2. 2l^2+w^2=4l^2. w^2=2l^2.
1=(2l^2)/(w^2).sqrt(1/2)=l/w.
Correction(3):(l/2)^2+((longdiagonal)/2)^2=(hypotenuseof rightangledtriangle formedbycrease
and longdiagonal)^2.(6) A newrightangledtriangle formedbydroppinganaltitude fromthe right
angledtriangle withthe hypotenuseasthe crease.Thistriangle issimilartothe parentrightangled
triangle.Infact,there are two rightangledtrianglesformedbydroppingthisaltitude.The bigger
rightangledtriangle fromdroppingthe altitude.Crease rightangle triangle hypotenuse:l.Crease
rightangledtriangle longerside:w.Largerof the rightangle triangle fromdroppingthe altitude,
hypotenuse:w.Largerof the rightangledtriangle fromdroppingthe altitude,longerside:a.
l/w=w/a.(5).Smallerof the rightangledtrianglesfromdroppingthe altitude,hypotenuse:unknown
side of the crease right angledtriangle.Smallerof the rightangledtrianglesfromdroppingthe
altitude,longerside:b.l/w=(unknownside of the crease rightangledtriangle)/b.
Correction(1):l^2=w^2+(crease right angledtriangle otherside)^2.(9)
(9) and(6) are similarrightangledtriangles.Hypotenuses:longersides=l^2/w^2 = (hypotenuse of
rightangledtriangle formedbycrease andlongdiagonal)^2/(l/2)^2. (7) l/w=(hypotenuseof right
angledtriangle formedbycrease andlongdiagonal)/(1/2).l/w=2*hypotenuse of rightangled
triangle formedbycrease andlongdiagonal.Hypotenuse of rightangledtriangleformedbycrease
and longdiagonal = l/(2w).(8) Insert8 into6: (l/2)^2+((longdiagonal)/2)^2=(l/2w)^2.(10) Insert4
into10: (l/2)^2+((sqrt(l^2+w^2))/2)^2=(l/2w)^2.l^2/4+(sqrt(l^2+w^2))^2/4=l^2/(4w^2).
l^2/4+(l^2+w^2)/4=l^2/(4w^2). l^2+l^2+w^2=l^2/w^2. 2l^2+w^2=l^2/w^2. (11) w =
sqrt((sqrt(1(1+1)))-1) =sqrt( (sqrt(2))-1) =1.55 . (2l^2)/w^2+1=l^2/w^4. l/w=ratio.l=1,w=1.55,
1/1.55=0.65.
2l^2*w^2 + w^4=l^2. w^4 + 2l^2*w^2 – l^2=0. x=w^2. x^2+2l^2*x-l^2.
𝑤2 =
−2𝑙2 ± √4𝑙4 − 4(−𝑙2)
2
= −𝑙2 ±
√4𝑙4 + 4𝑙2
2
= −𝑙2 ±
√4𝑙2(𝑙2 + 1)
2
= −𝑙2 ±
2𝑙√(𝑙2 + 1)
2
𝑤2 = −𝑙2 ± 𝑙√(𝑙2 + 1)
Comparisonwith answer:
b=(a/b)*sqrt(a^2+b^2).b^2=(a^2/b^2)(a^2+b^2). b^2=a^4/b^2+a^2. b^4=a^4+a^2*b^2.
Triangular area. 2016/08/11.
http://www.qbyte.org/puzzles/puzzle01.html
AEXD area= ∆ABC – (a+b+c).
𝐴𝐸𝑋𝐷 𝑎𝑟𝑒𝑎 =
1
2
𝐵𝐶 ∗ 𝐵𝐴 ∗ sin 𝐵 − (𝑎 + 𝑏 + 𝑐)
∆𝑎 + ∆𝑏 =
1
2
𝐵𝐶 ∗ 𝐵𝐸 ∗ sin 𝐵
𝐴𝐸𝑋𝐷 𝑎𝑟𝑒𝑎 =
𝑎 + 𝑏
𝐵𝐸
∗ 𝐵𝐴 − (𝑎 + 𝑏 + 𝑐)

32
𝑎 =
1
2
𝐵𝐸 ∗ 𝐵𝑋 ∗ 𝑠𝑖𝑛𝐸𝐵𝐶
Divide intosquares.Use calculus.
Volume of an elliptic cone with the tip removed. 2017/01/26.
𝑉 = 𝜋𝑎𝑏𝑙.
Where V is the volume of anellipticcylinder,aisthe shortestradiusof the ellipse,bisthe longest
radiusof the ellipse,l isthe lengthof the cylinder.
The volume of an ellipticcone withthe tipremovedisthe volume of the smallerellipticcylinder,
plushalf of the difference betweenthe smallerellipticcylinderandthe largerellipticcylinder.
𝑉2 = (∫ 𝜋𝑎2 𝑏2 𝑑𝑧− ∫ 𝜋𝑎𝑏 𝑑𝑧
𝑙
0
𝑙2
0
) ÷ 2 + ∫ 𝜋𝑎𝑏 𝑑𝑧
𝑙
0
.
Nick’s maths puzzles. 2017/08/26.
Puzzle 2(?).Whatproportionof the whole triangle doesa+b+ctake up.
Factor out areasof a, b, andc withinthe expressionforthe whole triangle.AEXDisthe whole
triangle minusa+b+c.A isthe top corner of the triangle,Bisthe leftcorner,C isthe rightcorner,D is
the middle leftpoint,Eisthe middle rightpoint.Sowhole triangle containsa+b+c+AEXD,itshould
be possible toseparate outa+b+c from the whole triangle.
Miscellaneous
Finding volume of an irregular solid
Separate intoplanesof a determinedthickness,findthe equationof the line of the irregularedge.
Splitthe irregularline upanduse parabolas.Twoareasnextto eachother of tinythickness:findthe
average of the irregularline,orthe average of the area of the twoareas. Curve fitting.Averageof
irregularline:setyas the subjectandadd the righthand sidestogether.Doprogrammingwithan
irregularsolidasan example.Equationof irregularline:use tangents,average tangentstoan
irregularline.Irregularsolid'scentre shouldbe the origin,andareascalculatedasif theywere inthe
upperrightquadrant.Aim:whatif there were holesinthe solid:needtorepositionaxessotheyare
centeredinthe middle of the hole.
Using radiation to move molecules in the body
Sendradiationof a particularfrequencytoexcite moleculesof aspecificstructure,findoutwhere
the target moleculesare.Applicationinhealing.Tomove the molecule,make watervibrations
behindthe molecule,dampenvibrationsinfront.Or make the molecule vibrate more inone
directionthanitdoesthe opposite direction.Nanotechnologytomake amolecularengine.
Connect software to hardware
Look at raspberrypi projects.The software outputstopinsonthe computerboard.The pinsare
connectedtothe hardware.
Use texteditorfornewversionsof the problemcruncher.
Small simulation of a planet’s weather systems. 2017/05/19.
Goal: predictionof weather,terraforming.

33
Heat upa small sponge sphere toevaporate the water,cool the glass anddimple itsothe
condensationfallsbackonthe sphere.
Use water’sviscositytomake itstickto the sphere’sunderside.
To make it rain:submerge the undersideof the sphere inwater.Itrainson the upperhalf of the
sphere. Oruse capillary tubestoguide the rain,soit fallsupside down,afteritissqueezedoutof the
sponge sky.Or maybe use windtomake the rain fall upside down.
Google:howto make itrain upside down.
To make a tornado:use microwavestoheatupspecificpartsof the waterand air,to manipulate it.
https://www.universetoday.com/75695/how-do-tornadoes-form/
Self-evolving system. 2017/07/25.
A closedcontainerwithmovingatoms.
Ground rules:the closed containermustnotbreak.There isradiationcomingfromatoms.The total
energycontainedstaysthe same. Rulesforhow atomsinteractwitheachother.
What if thisclosedcontainercontainedatomsthatincreasedincomplexity,inresponse toother
atoms?
New computer. 2017/06/10.
Computerthatis run byair molecule machinery.
Precise trackswithprecise movement.
Precise trackscouldbe createdby printing.
The central processingunitcan thenbe continuouslyupgraded,withthe electronicsassociatedwith
the central processingunitbeingrathersimple.
Tracks are black,resistorsare blue,transistorsare green,capacitorsare red.
Each pointis illuminatedbytwolamps,one horizontal andone vertical.
How fastis thiscomputer?
Photoncircuit,usesphotons,sofasterthanelectroniccircuits. Lampisthe batteryequivalent.
Neural networksappliedtohardware.
Learning maths using the Sagemath manual. 2017/03/03.
Work made possible asSagemathisopensource.
Make sure code examplesare original.
Explainenoughmathssoitis understoodhow touse the functions.
Give equationsthatthe Sagemathfunctionsrepresent.
Give examplesof variables,e.g.[0,2, 1], that come inand out of the functions.
Erfo
Get holdof Chinese watercressthatfloatson waterandsee if itgrows inGreat Britain.

34
Urine containsplentyof potassium.Thisisusedinfertiliser.Putfaecesandurine onsoil tohelpthe
plantsgrow.
Take water fromthe riverand boil it.
Erfopaper. 2017/02/03-2017/02/04.
Firstproduct: infinitelyrecyclable paper.
Aim:has anyone else done this? A searchforinfinitelyrecyclable paperyieldsasearchresultwhich
sayspaper can be recycled7 timesbefore itsfibresgettooshort.
Aim:whatare the desirable propertiesof erfopaper?Lightweight(canbe made intothinsheets,
holdstogetherasa thinsheet), writable(slightlyrough,pale,attractsink),nontoxic,recyclable
infinitely(made of e.g.chains, whichdonotbreakdowninthe recyclingprocess),cheap.
What chemicalshave these properties?Nontoxic:polymer. Writable:plasticwitharoughened
surface. Biodegradableplastic,whichdegradesintocarbondioxideandwater bythe actionof
microorganismse.g.starch-basedbioplastic. Workoutthe entire productionprocesssothatno fossil
fuelsare used,sothat biodegradable plasticiscarbonneutral.
https://en.wikipedia.org/wiki/Biodegradable_plastic
Aim:ispaperalreadybiodegradable?No,because of the inorganiccomponentof paper.Sofar,there
are biodegradable papercups,andbiodegradable Gascogne kraftpaper,butbecause papermaygo
to a landfill site,the papernevertrulybiodegrades. Stone-basedpapersare nottrulysustainable
because theyrequire the extractionof limestone,aformof digging.
http://www.paperonweb.com/A1048.htm
http://eq.tumblr.com/post/7044176102/is-paper-biodegradable
What isrequiredtomake a sustainable biodegradable paper?Environmentallyfriendlyprocesses
mustbe usedinthe makingand degradingprocess.
What advantage doesaninfinitelyrecyclable paperhave overabiodegradablepaper?We cansee
directlythatpaper,whenrecycled,becomespaperagain.Whereaswithbiodegradable paper,we
knowthat itbecomescarbondioxide andwater,butcannotsee wheniteventuallyfindsitswayback
intoa plant. Alsothe biodegradingprocesstakestime,whereasif the paperisrecycled,the cyclesof
use can be faster.
What makespaperwritable? Use nanotechnologytoproduce small poresonthe surface of
erfopaper. Letthe polymerbe pressed againstmetal withporesonit,e.g.metal membrane. The
porousmetal ismade by dissolvinghydrogeninmoltensteel.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3035924/
http://www.metalmembranes.com/
What isa directional pore? A pore whichallowssubstance throughitinone direction.
Is PVC100% infinitelyrecyclable?Yes,viafeedstockrecycling.
http://www.recovinyl.com/pvc-recyclable-material-ideal-reprocessing
http://www.sustainability-ed.org.uk/pages/pvc3-3.htm

35
2017/02/04.
Erfosurface:see if crayola will payforadvertisingtheirbrandinconjunctionwiththisproduct.
Use an infinitelyrecyclable plastic.Currentlyheatingplasticcausesittodegrade,meaningeventually
aftera certainamountof heatcycles,itbecomesunusable.
Carbios.
Extract plasticfromlandfill waste andrecycle it.
Aim:finda goodway to sell enzymaticdegradationof PET.
Newmaterial thatrequiresonlyheatingtorecycle:polymerbondsdon'tbreakwithheating,
strengthof intramolecularbondsfargreaterthanintermolecularbonds.Lookupbondstrength.
Organicpolymerlist.PolyVinylChloride feedstockrecyclingcanresultinnew PVC.
Pad: eachpage sticksout fromunderneathitscover,toallow forpage turning.
Make one,make more if youreceive orders.
Make itat lowcost soit iscompetitive.
Source,design,manufacture erfosurface.
Experimentwithplasticpockets:smudgingwithanotherpocket,writingmultiplelines.
Aim:preventlinesonerfosurface fromsmudging.Adddoublesidedstickerstoglue the covertothe
white PVCsheet.Addpockettothe coverso the white PVCsheetisslottedinthere.Sellone white
PVCsheetat a time.PutPVCsheetsina hardPVC coverwhichopenslike abookandclicksshut.
Hardnessof PVCdependsonthe lengthof chain.
Make a thickpad.
Needstobe takenapart to separate PVCof differentcolours.
Type of printerinkwhichcanbe usedtoprint onwhite PVC.
Nanotechnologytoholdcoversinplace onwhite PVC.
2017/02/04.
Infinitelyrecyclablematerials.
Thinkof the molecularstructure of existingmaterials.
Thinkof what propertiesyouwantthe paperto have.Thinkof whatwouldbe inthe molecular
structure of erfopapertogive itthese properties.
Processdesign.
Have a goodbusinessmodel,soerfopaperbecomespopular.
Polymerwhich doesnotsticktoporoussteel plates.
White opaque polymer.
Fixedamountof polymerwhichisladledontoporoussteel,thenspreadouttocoverthe entire
poroussteel plate.Heatthe polymerinapot.

36
Scrub off pencil andsoluble inkfromerfopaperusingasponge andwater.
Thinkof how the manufacturingprocesscanbe automated.
The polymermustclearlygetthe pore imprintfromthe steel.Itshouldbe heatedtohighenough
temperature.
Write detailedplanwhenchoice of polymerismade.
How will the paperworkinprinters.
The ink mustnot be rubbedoff easily.Itshouldbe partiallyabsorbedbyerfopaper.Use coverfor
paper.
Permanentcopiesof textcanbe scanned.
Erfopaperpad.
Crowdfundingorself-fundingtogetthe pad made,thenventure capitalistfundingtomove into
manufacturing.
Making the pad:stiff plasticbackingandwhite sheetsstitchedtogether.Bindingmachine.
Use washable inkfromafountainpen.
Pad coverdesign:PVClockwhichishingedtocover,twosidesof the lockpushtogetherandlock
tightly,frontcoverhasone side of the lock,back cover hasother side.
How to engineertwosidesof lock?Plasticpopbuttons.Triangulartongue supportedby2stripsof
plasticconnectingtwosidesof the tongue together,whichmeansitacts like twoclothespegsand
can flatten.The tongue slotsintothe otherside of the lock.
Visitplacestoborrowequipmentnecessarytomake erfosurface,fordemonstrationproduct.Work
out howto automate productionbefore firstorderisplaced.
See if youcan get by at home by"making"the product:permanentmarker,plasticresealablebag,
white paperinthe bag.
Mum doesn'tlike thisidea.
Erforecycler. 2017/02/04-2017/05/16.
How to change one type of atom to another:nuclearfusionandnuclearfission.
Is there anyneedtoinvestigate this?Nuclearfissionisalreadycheapenough.Nuclearfusionis
currentlybeinginvestigatedbyawhole varietyof people.
The energyrequiredbyfusion,andfission,forrecyclingcanbe createdby a processwhichproduce s
pure elements.
Ordinaryplasticdoeseventuallygetbrokendownbythe environment.
2017/06/02.
Energyis requiredduringfusionandfission,sothatnew typesof atomsare synthesised,quite
differenttofusionandfissiontocreate energy.

37
What waste wouldresultfromthe erforecycler?A reliance onpowerfromfusionmeansthe creation
of a lotof heliumwaste.Usingsolarpowerinthe erforecyclermeansthatthe waste fromfusionis
keptinthe sun,ratherthan on earth.
Bacteriawhichcan breakdown bioplastic.
Reduce radioactive waste fromfission,bybreakingnucleione byone,inamuch more controlled
process,suchthat the nuclei producedare notradioactive.
Bioplasticrecycling.
Sustainable goods
2017/04/06.
How isfarmingsustainable.
The nutrientcycle.
2017/06/22.
Calculate the complexityof livingthings,comparedtothe manufacturedproduct,andpredicthow
fasttheybreak down.
Erfo.
For everypiece of woodburned,atree shouldincrease bythe same biomass.
Is there a bacteriumthateatsplastic.
Is there a bacteriumthateatstextiles.
Fate of plasticsastheyare brokendown.
Can plasticsbe turnedintosoil.
Do bonesdecay,andare theyinany waysimilartoplastics.
Renewable energy from a black hole. 2017/04/08.
Harnessenergy froma radiatingblackhole.
App for the visually impaired. 2017/02/06.
A software whichcandescribe apicture to a blindpersoninwords.

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