Ciro Santilli @cirosantilli 37

If the choice of what to learn depend on a years long dependency graph of other obligations, which currently are the increasingly interlinked:

passing the University entry exam
getting your undergrad degree
getting your PhD

you end up without much choice at all.

The lock-in periods must be much more fluid and shorter term than those, otherwise it makes the almost inevitable pivots to success impossible.

This is something that Ciro Santilli has heard from several people at the end of their undergrad/PhD degrees. Some online mentions:

When I realized the biggest reason to continue my pdh was to be dr helps, that's when decided I should probably leave.

 Read the full article

E. Coli K-12 MG1655 Updated 2025-07-16

 View more

NCBI taxonomy entry: www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?id=511145 This links to:

genome: www.ncbi.nlm.nih.gov/genome/?term=txid511145 From there there are links to either:
- Download the FASTA: "Download sequences in FASTA format for genome, protein"
  For the genome, you get a compressed FASTA file with extension .fna called GCF_000005845.2_ASM584v2_genomic.fna that starts with:
  >NC_000913.3 Escherichia coli str. K-12 substr. MG1655, complete genome AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGCTTCTGAACTG
  Using wc as in wc GCF_000005845.2_ASM584v2_genomic.fna gives 58022 lines, in Vim we see that each line is 80 characters, except for the final one which is 52. So we have 58020 * 80 + 52 = 4641652 =~ 4.6 Mbp
- Interactively browse the sequence on the browser viewer: "Reference genome: Escherichia coli str. K-12 substr. MG1655" which eventually leads to: www.ncbi.nlm.nih.gov/nuccore/556503834?report=graph
  If we zoom into the start, we hover over the very first gene/protein: the famous (just kidding) e. Coli K-12 MG1655 gene thrL, at position 190-255.
  The second one is the much more interesting e. Coli K-12 MG1655 gene thrA.
- Gene list, with a total of 4,629 as of 2021: www.ncbi.nlm.nih.gov/gene/?term=txid511145

KEGG entry: www.genome.jp/pathway/eco01100+M00022

BioCyc promoter database query URL: biocyc.org/group?id=:ALL-PROMOTERS&orgid=ECOLI

 Read the full article

E. Coli replication time Updated 2025-07-16

 View more

20 minutes in optimal conditions, with a crazy multiple start sites mechanism: E. Coli starts DNA replication before the previous one finished.

Otherwise, naively, would take 60-90 minutes just to replicate and segregate the full DNA otherwise. So it starts copying multiple times.

biology.stackexchange.com/questions/30080/how-can-e-coli-proliferate-so-rapidly
stochasticscientist.blogspot.co.uk/2012/02/how-e-coli-grows-so-fast.html
www.ncbi.nlm.nih.gov/pmc/articles/PMC2063475/ Organization of sister origins and replisomes during multifork DNA replication in Escherichia coli by Fossum et al (2007)

 Read the full article

E. Coli Whole Cell Model by Covert Lab Updated 2025-07-16

 View more

github.com/CovertLab/WholeCellEcoliRelease is a whole cell simulation model created by Covert Lab and other collaborators.

The project is written in Python, hurray!

But according to te README, it seems to be the use a code drop model with on-request access to master. Ciro Santilli asked at rationale on GitHub discussion, and they confirmed as expected that it is to:

to prevent their publication ideas from being stolen. Who would steal publication ideas with public proof in an issue tracker without crediting original authors? Academia is broken. Academia should be the most open form of knowledge sharing. But instead we get this silly competition for publication points.
to prevent noise from non-collaborators. But they only get like 2 issues as year on such a meganiche subject... Did you know that you can ignore people, and even block them if they are particularly annoying? Much more likely is that no one will every hear about your project and that it will die with its last graduate student slave.

The project is a followup to the earlier M. genitalium whole cell model by Covert lab which modelled Mycoplasma genitalium. E. Coli has 8x more genes (500 vs 4k), but it the undisputed bacterial model organism and as such has been studied much more thoroughly. It also reproduces faster than Mycoplasma (20 minutes vs a few hours), which is a huge advantages for validation/exploratory experiments.

The project has a partial dependency on the proprietary optimization software CPLEX which is freeware, for students, not sure what it is used for exactly, from the comment in the requirements.txt the dependency is only partial.

This project makes Ciro Santilli think of the E. Coli as an optimization problem. Given such external nutrient/temperature condition, which DNA sequence makes the cell grow the fastest? Balancing metabolites feels like designing a Factorio speedrun.

There is one major thing missing thing in the current model: promoters/transcription factor interactions are not modelled due to lack/low quality of experimental data: github.com/CovertLab/WholeCellEcoliRelease/issues/21. They just have a magic direct "transcription factor to gene" relationship, encoded at reconstruction/ecoli/flat/foldChanges.tsv in terms of type "if this is present, such protein is expressed 10x more". Transcription units are not implemented at all it appears.

Everything in this section refers to version 7e4cc9e57de76752df0f4e32eca95fb653ea64e4, the code drop from November 2020, and was tested on Ubuntu 21.04 with a docker install of docker.pkg.github.com/covertlab/wholecellecolirelease/wcm-full with image id 502c3e604265, unless otherwise noted.

 Read the full article

James Howells Updated 2025-07-16

 View more

www.linkedin.com/in/howelzy/
Might know a thing or two about landfills.
Epic.
www.independent.co.uk/news/uk/home-news/lost-bitcoin-crypto-james-howells-b2406517.html
The bizarre saga started in 2013 when Mr Howells, put the hardware from an old laptop that contained 8,000 bitcoins, the world’s leading cryptocurrency, in a black bag in his hallway.
"I was doing a clear-out in my office and put a lot of items into a bag which I then placed at the front door of my house," he said. "I woke up the next morning and my ex-partner had already taken the bags to the landfill site; she thought she was doing me a favour, it wasn’t her fault."
www.bbc.co.uk/news/uk-wales-67297013

 Read the full article

E. Coli Whole Cell Model by Covert Lab / Output overview Updated 2025-07-16

 View more

Run output is placed under out/:

Some of the output data is stored as .cpickle files. To observe those files, you need the original Python classes, and therefore you have to be inside Docker, from the host it won't work.

We can list all the plots that have been produced under out/ with

find -name '*.png'

Plots are also available in SVG and PDF formats, e.g.:

PNG: ./out/manual/plotOut/low_res_plots/massFractionSummary.png
SVG: ./out/manual/plotOut/svg_plots/massFractionSummary.svg The SVGs write text as polygons, see also: SVG fonts.
PDF: ./out/manual/plotOut/massFractionSummary.pdf

The output directory has a hierarchical structure of type:

./out/manual/wildtype_000000/000000/generation_000000/000000/

where:

wildtype_000000: variant conditions. wildtype is a human readable label, and 000000 is an index amongst the possible wildtype conditions. For example, we can have different simulations with different nutrients, or different DNA sequences. An example of this is shown at run variants.
000000: initial random seed for the initial cell, likely fed to NumPy's np.random.seed
genereation_000000: this will increase with generations if we simulate multiple cells, which is supported by the model
000000: this will presumably contain the cell index within a generation

We also understand that some of the top level directories contain summaries over all cells, e.g. the massFractionSummary.pdf plot exists at several levels of the hierarchy:

./out/manual/plotOut/massFractionSummary.pdf
./out/manual/wildtype_000000/plotOut/massFractionSummary.pdf
./out/manual/wildtype_000000/000000/plotOut/massFractionSummary.pdf
./out/manual/wildtype_000000/000000/generation_000000/000000/plotOut/massFractionSummary.pdf

Each of thoes four levels of plotOut is generated by a different one of the analysis scripts:

./out/manual/plotOut: generated by python runscripts/manual/analysisVariant.py. Contains comparisons of different variant conditions. We confirm this by looking at the results of run variants.
./out/manual/wildtype_000000/plotOut: generated by python runscripts/manual/analysisCohort.py --variant_index 0. TODO not sure how to differentiate between two different labels e.g. wildtype_000000 and somethingElse_000000. If -v is not given, a it just picks the first one alphabetically. TODO not sure how to automatically generate all of those plots without inspecting the directories.
./out/manual/wildtype_000000/000000/plotOut: generated by python runscripts/manual/analysisMultigen.py --variant_index 0 --seed 0
./out/manual/wildtype_000000/000000/generation_000000/000000/plotOut: generated by python runscripts/manual/analysisSingle.py --variant_index 0 --seed 0 --generation 0 --daughter 0. Contains information about a single specific cell.

 Read the full article

E. Coli Whole Cell Model by Covert Lab / Source code overview Updated 2025-07-16

 View more

The key model database is located in the source code at reconstruction/ecoli/flat.

Let's try to understand some interesting looking, with a special focus on our understanding of the tiny E. Coli K-12 MG1655 operon thrLABC part of the metabolism, which we have well understood at Section "E. Coli K-12 MG1655 operon thrLABC".

We'll realize that a lot of data and IDs come from/match BioCyc quite closely.

reconstruction/ecoli/flat/compartments.tsv contains cellular compartment information:
```
"abbrev" "id"
"n" "CCO-BAC-NUCLEOID"
"j" "CCO-CELL-PROJECTION"
"w" "CCO-CW-BAC-NEG"
"c" "CCO-CYTOSOL"
"e" "CCO-EXTRACELLULAR"
"m" "CCO-MEMBRANE"
"o" "CCO-OUTER-MEM"
"p" "CCO-PERI-BAC"
"l" "CCO-PILUS"
"i" "CCO-PM-BAC-NEG"
```
- CCO: "Celular COmpartment"
- BAC-NUCLEOID: nucleoid
- CELL-PROJECTION: cell projection
- CW-BAC-NEG: TODO confirm: cell wall (of a Gram-negative bacteria)
- CYTOSOL: cytosol
- EXTRACELLULAR: outside the cell
- MEMBRANE: cell membrane
- OUTER-MEM: bacterial outer membrane
- PERI-BAC: periplasm
- PILUS: pilus
- PM-BAC-NEG: TODO: plasma membrane, but that is the same as cell membrane no?
reconstruction/ecoli/flat/promoters.tsv contains promoter information. Simple file, sample lines:
```
"position" "direction" "id" "name"
148 "+" "PM00249" "thrLp"
```
corresponds to E. Coli K-12 MG1655 promoter thrLp, which starts as position 148.
reconstruction/ecoli/flat/proteins.tsv contains protein information. Sample line corresponding to e. Coli K-12 MG1655 gene thrA:
```
"aaCount" "name" "seq" "comments" "codingRnaSeq" "mw" "location" "rnaId" "id" "geneId"
[91, 46, 38, 44, 12, 53, 30, 63, 14, 46, 89, 34, 23, 30, 29, 51, 34, 4, 20, 0, 69] "ThrA" "MRVL..." "Location information from Ecocyc dump." "AUGCGAGUGUUG..." [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 89103.51099999998, 0.0, 0.0, 0.0, 0.0] ["c"] "EG10998_RNA" "ASPKINIHOMOSERDEHYDROGI-MONOMER" "EG10998"
```
so we understand that:
- aaCount: amino acid count, how many of each of the 20 proteinogenic amino acid are there
- seq: full sequence, using the single letter abbreviation of the proteinogenic amino acids
- mw; molecular weight? The 11 components appear to be given at reconstruction/ecoli/flat/scripts/unifyBulkFiles.py:
  molecular_weight_keys = [ '23srRNA', '16srRNA', '5srRNA', 'tRNA', 'mRNA', 'miscRNA', 'protein', 'metabolite', 'water', 'DNA', 'RNA' # nonspecific RNA ]
  so they simply classify the weight? Presumably this exists for complexes that have multiple classes?
  - 23srRNA, 16srRNA, 5srRNA are the three structural RNAs present in the ribosome: 23S ribosomal RNA, 16S ribosomal RNA, 5S ribosomal RNA, all others are obvious:
  - tRNA
  - mRNA
  - protein. This is the seventh class, and this enzyme only contains mass in this class as expected.
  - metabolite
  - water
  - DNA
  - RNA: TODO rna vs miscRNA
- location: cell compartment where the protein is present, c defined at reconstruction/ecoli/flat/compartments.tsv as cytoplasm, as expected for something that will make an amino acid
reconstruction/ecoli/flat/rnas.tsv: TODO vs transcriptionUnits.tsv. Sample lines:
```
"halfLife" "name" "seq" "type" "modifiedForms" "monomerId" "comments" "mw" "location" "ntCount" "id" "geneId" "microarray expression"
174.0 "ThrA [RNA]" "AUGCGAGUGUUG..." "mRNA" [] "ASPKINIHOMOSERDEHYDROGI-MONOMER" "" [0.0, 0.0, 0.0, 0.0, 790935.00399999996, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ["c"] [553, 615, 692, 603] "EG10998_RNA" "EG10998" 0.0005264904
```
- halfLife: half-life
- mw: molecular weight, same as in reconstruction/ecoli/flat/proteins.tsv. This molecule only have weight in the mRNA class, as expected, as it just codes for a protein
- location: same as in reconstruction/ecoli/flat/proteins.tsv
- ntCount: nucleotide count for each of the ATGC
- microarray expression: presumably refers to DNA microarray for gene expression profiling, but what measure exactly?

reconstruction/ecoli/flat/sequence.fasta: FASTA DNA sequence, first two lines:

>E. coli K-12 MG1655 U00096.2 (1 to 4639675 = 4639675 bp)
AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGCTTCTG

reconstruction/ecoli/flat/transcriptionUnits.tsv: transcription units. We can observe for example the two different transcription units of the E. Coli K-12 MG1655 operon thrLABC in the lines:
```
"expression_rate" "direction" "right" "terminator_id"  "name"    "promoter_id" "degradation_rate" "id"       "gene_id"                                   "left"
0.0               "f"         310     ["TERM0-1059"]   "thrL"    "PM00249"     0.198905992329492 "TU0-42486" ["EG11277"]                                  148
657.057317358791  "f"         5022    ["TERM_WC-2174"] "thrLABC" "PM00249"     0.231049060186648 "TU00178"   ["EG10998", "EG10999", "EG11000", "EG11277"] 148
```
- promoter_id: matches promoter id in reconstruction/ecoli/flat/promoters.tsv
- gene_id: matches id in reconstruction/ecoli/flat/genes.tsv
- id: matches exactly those used in BioCyc, which is quite nice, might be more or less standardized:
  - biocyc.org/ECOLI/NEW-IMAGE?object=TU0-42486
  - biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00178

reconstruction/ecoli/flat/genes.tsv

"length" "name"                      "seq"             "rnaId"      "coordinate" "direction" "symbol" "type" "id"      "monomerId"
66       "thr operon leader peptide" "ATGAAACGCATT..." "EG11277_RNA" 189         "+"         "thrL"   "mRNA" "EG11277" "EG11277-MONOMER"
2463     "ThrA"                      "ATGCGAGTGTTG"    "EG10998_RNA" 336         "+"         "thrA"   "mRNA" "EG10998" "ASPKINIHOMOSERDEHYDROGI-MONOMER"

reconstruction/ecoli/flat/metabolites.tsv contains metabolite information. Sample lines:
```
"id"                       "mw7.2" "location"
"HOMO-SER"                 119.12  ["n", "j", "w", "c", "e", "m", "o", "p", "l", "i"]
"L-ASPARTATE-SEMIALDEHYDE" 117.104 ["n", "j", "w", "c", "e", "m", "o", "p", "l", "i"]
```
In the case of the enzyme thrA, one of the two reactions it catalyzes is "L-aspartate 4-semialdehyde" into "Homoserine".
Starting from the enzyme page: biocyc.org/gene?orgid=ECOLI&id=EG10998 we reach the reaction page: biocyc.org/ECOLI/NEW-IMAGE?type=REACTION&object=HOMOSERDEHYDROG-RXN which has reaction ID HOMOSERDEHYDROG-RXN, and that page which clarifies the IDs:
- biocyc.org/compound?orgid=ECOLI&id=L-ASPARTATE-SEMIALDEHYDE: "L-aspartate 4-semialdehyde" has ID L-ASPARTATE-SEMIALDEHYDE
- biocyc.org/compound?orgid=ECOLI&id=HOMO-SER: "Homoserine" has ID HOMO-SER
so these are the compounds that we care about.

reconstruction/ecoli/flat/reactions.tsv contains chemical reaction information. Sample lines:

"reaction id" "stoichiometry" "is reversible" "catalyzed by"

"HOMOSERDEHYDROG-RXN-HOMO-SER/NAD//L-ASPARTATE-SEMIALDEHYDE/NADH/PROTON.51."
  {"NADH[c]": -1, "PROTON[c]": -1, "HOMO-SER[c]": 1, "L-ASPARTATE-SEMIALDEHYDE[c]": -1, "NAD[c]": 1}
  false
  ["ASPKINIIHOMOSERDEHYDROGII-CPLX", "ASPKINIHOMOSERDEHYDROGI-CPLX"]

"HOMOSERDEHYDROG-RXN-HOMO-SER/NADP//L-ASPARTATE-SEMIALDEHYDE/NADPH/PROTON.53."
  {"NADPH[c]": -1, "NADP[c]": 1, "PROTON[c]": -1, "L-ASPARTATE-SEMIALDEHYDE[c]": -1, "HOMO-SER[c]": 1
  false
  ["ASPKINIIHOMOSERDEHYDROGII-CPLX", "ASPKINIHOMOSERDEHYDROGI-CPLX"]

catalized by: here we see ASPKINIHOMOSERDEHYDROGI-CPLX, which we can guess is a protein complex made out of ASPKINIHOMOSERDEHYDROGI-MONOMER, which is the ID for the thrA we care about! This is confirmed in complexationReactions.tsv.

reconstruction/ecoli/flat/complexationReactions.tsv contains information about chemical reactions that produce protein complexes:
```
"process" "stoichiometry" "id" "dir"
"complexation"
  [
    {
      "molecule": "ASPKINIHOMOSERDEHYDROGI-CPLX",
      "coeff": 1,
      "type": "proteincomplex",
      "location": "c",
      "form": "mature"
    },
    {
      "molecule": "ASPKINIHOMOSERDEHYDROGI-MONOMER",
      "coeff": -4,
      "type": "proteinmonomer",
      "location": "c",
      "form": "mature"
    }
  ]
"ASPKINIHOMOSERDEHYDROGI-CPLX_RXN"
1
```
The coeff is how many monomers need to get together for form the final complex. This can be seen from the Summary section of ecocyc.org/gene?orgid=ECOLI&id=ASPKINIHOMOSERDEHYDROGI-MONOMER:
Aspartate kinase I / homoserine dehydrogenase I comprises a dimer of ThrA dimers. Although the dimeric form is catalytically active, the binding equilibrium dramatically favors the tetrameric form. The aspartate kinase and homoserine dehydrogenase activities of each ThrA monomer are catalyzed by independent domains connected by a linker region.
Fantastic literature summary! Can't find that in database form there however.

reconstruction/ecoli/flat/proteinComplexes.tsv contains protein complex information:

"name" "comments" "mw" "location" "reactionId" "id"
"aspartate kinase / homoserine dehydrogenase"
""
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 356414.04399999994, 0.0, 0.0, 0.0, 0.0]
["c"]
"ASPKINIHOMOSERDEHYDROGI-CPLX_RXN"
"ASPKINIHOMOSERDEHYDROGI-CPLX"

reconstruction/ecoli/flat/protein_half_lives.tsv contains the half-life of proteins. Very few proteins are listed however for some reason.

reconstruction/ecoli/flat/tfIds.csv: transcription factors information:

"TF"   "geneId"  "oneComponentId"  "twoComponentId" "nonMetaboliteBindingId" "activeId" "notes"
"arcA" "EG10061" "PHOSPHO-ARCA"    "PHOSPHO-ARCA"
"fnr"  "EG10325" "FNR-4FE-4S-CPLX" "FNR-4FE-4S-CPLX"
"dksA" "EG10230"

 Read the full article

Educational charitable organization Updated 2025-07-16

 View more

In this section we list charitable organizations that support education or research:

elifesciences.org/labs by eLife
www.digital-science.com/investment/catalyst-grant/ by Shuttleworth Foundation.
en.wikipedia.org/wiki/PLOS
www.chanzuckerberg.com/ Zuck has already invested in education previously:
- www.forbes.com/sites/kathleenchaykowski/2018/02/14/zuckerberg-invests-in-on-demand-education-site-varsity-tutors-in-50-million-fundraise/#1c9b6b385dab
- uk.businessinsider.com/mark-zuckerberg-schools-education-newark-mayor-ras-baraka-cory-booker-2018-5
openuk.uk/
bccampus.ca/ CC BY, lower undergrad stuff, but better than nothing.
Hmm, some/all of it is a copy of LibreTexts but with URLs shorter than a million characters, e.g.:
- opentextbc.ca/universityphysicsv3openstax/chapter/de-broglies-matter-waves/
- phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/06%3A_Photons_and_Matter_Waves/6.06%3A_De_Broglies_Matter_Waves
Sir Peter Lampl, Education Endowment Foundation and Sutton Trust
Jacobs Foundation, by German-Swiss coffee mogul Klaus Johann Jacobs
joint-research-centre.ec.europa.eu/what-open-education_en
www.non-trivial.org/ "Launch Your Own Impactful Project CHOOSE YOUR CAUSE. GET EXPERT GUIDANCE. FIND A SOLUTION AND MAKE IT HAPPEN."
by United States Government:
- FY 2024 Education Innovation and Research:

 Read the full article

James Somers Updated 2025-07-16

 View more

Huge interest overlap with Ciro Santilli, e.g. he's into

 Read the full article

Education as a system of indoctrination Updated 2025-07-16

 View more

Whenever Ciro Santilli walks in front of a school and sees the tall gates it makes him sad. Maybe 8 year olds need gates. But do we need to protect 15 year olds like that? Students should be going out to see the world, both good and evil not hiding from it! We should instead be guiding them to the world. But instead, we are locking them up in brainwashing centers.

Video "The Purpose of Education by Noam Chomsky (2012)" puts it well, education can be either be:

a brainwashing to make people comply with The Establishment
a way to get people genuinely interested and help them to reach their life goals

He has spoken about that infinitely, e.g. from when he was thin: www.youtube.com/watch?v=JVqMAlgAnlo

Bibliography:

www.youtube.com/watch?v=ts7CEFQM2bE How Education Became Indoctrination: Dr Stephen Hicks (2021) Interview by www.youtube.com/c/KnowlandKnows Interesting channel. "Are you sick of woke-washing in education? Free speech distinguishes education from indoctrination" and "I taught at Eton College before I was fired because 'The Patriarchy Paradox' caused offence.".

 Read the full article

Effect of a change of basis on the matrix of a bilinear form Updated 2025-07-16

 View more

C

is the change of basis matrix, then the matrix representation of a bilinear form

M

that looked like:

B (x, y) = x^{T} M y

(1)

then the matrix in the new basis is:

C^{T} MC

(2)

Sylvester's law of inertia then tells us that the number of positive, negative and 0 eigenvalues of both of those matrices is the same.

Proof: the value of a given bilinear form cannot change due to a change of basis, since the bilinear form is just a function, and does not depend on the choice of basis. The only thing that change is the matrix representation of the form. Therefore, we must have:

x^{T} M y = x_{n e w}^{T} M_{n e w} y_{n e w}

(3)

and in the new basis:

x = C x_{n e w} y = C y_{n e w} x_{n e w}^{T} M_{n e w} y_{n e w} = x^{T} M y = (C x_{n e w})^{T} M (C y_{n e w}) = x_{n e w}^{T} (C^{T} MC) y_{n e w}

(4)

and so since:

\forall x_{n e w}, y_{n e w} x_{n e w}^{T} M_{n e w} y_{n e w} = x_{n e w}^{T} (C^{T} MC) y_{n e w} ⟹ M_{n e w} = C^{T} MC

(5)

proofwiki.org/wiki/Matrix_of_Bilinear_Form_Under_Change_of_Basis

 Read the full article

Eightfold way (physics) Updated 2025-07-16

 View more

Video 1.

Strangeness Minus Three (BBC Horizon 1964)

Source. Basically shows Richard Feynman 15 minutes on a blackboard explaining the experimental basis of the eightfold way really well, while at the same time hyperactively moving all over. The word symmetry gets tossed a few times.

 Read the full article

Einstein notation for partial derivatives Updated 2025-07-16

 View more

The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.

In particular, the divergence and the Laplacian can be succinctly expressed in this notation:

In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as

x_{0}

x_{1}

x_{2}

\partial_{0}

\partial_{1}

and

\partial_{2}

instead of the usual letters

x

y

and

z

 Read the full article

Einstein solid Updated 2025-07-16

 View more

One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.

This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.

 Read the full article

E-learning Updated 2025-07-16

 View more