Maths, Category Theory and The Bio-Catalog

What is Category Theory?

Before we get to our key question, what makes #Mathematics an Apologetic?

https://www.hup.harvard.edu/books/9780674009707

 

What is Category Theory? (INTRO):

https://youtu.be/eXBwU9ieLL0

Can you say “morphism”?

You can use #Rings #Halos or #Slanted_Loops to transform a circle into a donut (torus).  Circle → Torus (@ 6:00 mark):

https://youtu.be/eXBwU9ieLL0

 

Category Theory with #Stick_Figures 🕺 

https://youtu.be/FQYOpD7tv30

A #Category consists of a group of objects (e.g. topological spaces), morphisms (maps or arrows) and composition s.t. the Associative Property [(fg)h=f(gh)] and Identity Property (Ia=aI=a) hold.  If you take your #Hyundai_Palisade and drive it thru the #Car_Wash it does not turn it into a Mercedes (which are popular w/ ladies in their 80’s). ☺  The same goes if you driver ur car backwards through the car wash!

Here are some examples of Categories and their morphisms: groups* → homomorphisms, vector spaces → linear transformations, Posets → Orderish Functions and “DJ Smooth Man’s” → smooth maps. ☺→🕺

A #Poset is a Partially Ordered Set.  For example, the Real Numbers along with the relation “less than or equal to” ≤ #LTE

https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/12%3A_Boolean_Algebra/12.01%3A_Posets_Revisited

 

Here are two examples in lattice form …

Categories have common structures, hence #Category_Theory

Inventor (Discoverer ♫) credits go to Eilenberg & Mac Lane (1945) and their paper “General Theory of Natural Equivalences.”  The key idea was natural transformation.  “Functor” comes  from Carnap and “category” from the philosophy of Aristotle, Kant, and C.S. Peirce (see below), but redefining it mathematically.

https://plato.stanford.edu/entries/category-theory/

Speaking of Aristotle, what about his #Biology ?

Let’s switch gears to #Natural_Transformations Categories of Life, The Biological Catalog and #TrueTruth

This is Aristotle's Biology - limited variation within Essential Types of Life (ETL's) - horses, hydras and humans, for example.

Here is my paper on Academia:

https://www.academia.edu/40897603/Biological_Essentialism_A_Minority_Report_Jay_Hall_

I've written a whole book on the topic that came out two years before Devitt's work (Oxford Univ. Press):

www.barnesandnoble.com/w/biological-essentialism-jay-hall/1140135320

If your Father was a turtle and your Mother was a turtle, then you are a turtle.  In addition, all your children will be turtles.  The entire group is of the same Natural Kind (ETL).  Some scholars are #Brave enough to stand up against #Big_Science and oppose evolution.  Nathan Jeanson (Ph.D. Cell Biology – Harvard) for example:

https://answersingenesis.org/store/product/replacing-darwin/

Mathematician David Berlinski also opposes the standard narrative on origins.  An example closer to Darwin's time is Charles Sanders Peirce (d. 1914), who was a pioneer of symbolic logic, set theory, probability theory, semantics, and semiotics.  He rejected #Darwinism and contrasted the “Gospel of Greed” (Survival of the Fittest) with the “Gospel of Love”:  

 

The movement of love is circular, at one and the same impulse projecting creations into independency and drawing them into harmony.  This seems complicated when stated so; but it is fully summed up in the simple formula we call the Golden Rule. … [It is not] Act for the greatest good of the greatest number.  Love is not directed to abstractions but to persons; not to persons we do not know, nor to numbers of people, but to our own dear ones, our family and neighbors.  "Our neighbor," we remember, is one whom we live near, not locally perhaps but in life and feeling.

https://www.academia.edu/21766227/On_Peirces_Theory_of_Evolutionary_Love

 

FYI: Physics vs. MetaPhysics …

https://www.magiscenter.com/blog/difference-between-metaphysics-physics-limits

 

*But Math never applies to the #Real_World ?? …

Lie Groups & Quarks: 

https://www.ckoerber.com/media/professional/Koerber-SU3-Physics.pdf

 

my site: https://totalyouth.us/

 

Note: The last chapter of my book Biological Essentialism makes the case that bio-essentialism naturally leads to the #Young_Earth view.

www.barnesandnoble.com/w/biological-essentialism-jay-hall/1140135320

 

** kudos – graphic sources:

https://chatgpt.com/c/6a79534b-8554-83ea-96bb-8a35bf054ff7

https://avatars.mds.yandex.net/i?id=41e11153a2142a69e6b9f1333f83540fd3984a2f-5285349-images-thumbs&n=13

https://www.shutterstock.com/shutterstock/photos/793083208/display_1500/stock-photo-detail-view-on-car-wash-car-wash-foam-water-automatic-car-wash-in-action-793083208.jpg

https://people.math.osu.edu/cogdell.1/6112-Eilenberg&MacLane-www.pdf

https://calcworkshop.com/relations/lattices/

https://tse3.mm.bing.net/th/id/OIP.rCNQ9NLeKyZH_J6FHCVtXQHaFn?r=0&rs=1&pid=ImgDetMain&o=7&rm=3

https://en.wikipedia.org/wiki/Category_theory

 

#Category #Categories #Category_Theory #Maths #Math #MathZ #Mathematics #Tour_ofthe_Calculus #Hyundai #Palisade #Car_Wash ♫ #TrueTruth #Schaeffer #Total_Youth “for Total truth, support earth’s Youth” #TotalYouth_US #USA #Free_Math ! #Get_Reals ## #FISH 🐟 #natural_kinds #Putnam_n_Kripke #Gospel #JN316 ╬ #Heaven ↑ Sinner→Saint #Physics #Metaphysics #Aristotle #Philo #Philosophy #think #nachdenken #CS_Peirce #SymboliX ELSE (A→B)∧(¬A→C) #evolution #Darwin #Darwinism #Genesis #species #Biological_Essentialism #Bio_Ess #jay_l_hall #identity 0*0 = #Her0 ☺ #MATHIS #fun (& furniture) #F_U_R_N_I_T_U_R_E ☺☺ #Golden_Rule #God #Jesus #Bible #BB6640 ╬ #Day6 🕺 #lattice ♦ #morphism #objects #ObjekT #ini RU feelin’ #IRAY ?? “Wow ima Tree!” #Geometry #TOP #MAN #Top_Man #Mark_Steiner #Apologetic #Apologetics #ApologetiX ♪ #Mighty_Morphin_Power_Rangers #MMPR #Angel_Grove #Zordon #NodroZ #Rita_Repulsa #ZED #Z #zz #Mt26_36to46 c + @ = #CAT #Got_CATs ?? #Berlinski #Eric_Metaxas #Socrates #So_CrateZ #essentialism M/F #cuántos_baños #Crevo #Creationista #GEN1to11 #GIII #Fuzzy_Wuzzy hair→nohair bear→bear (not alligator!) #DEVO ↓ #Eilenberg #MacLane #Year1945 #WWII #Operation_Mincemeat #Sicily → #Sardinia = #EQ #Young_Earth_Science #YES #Geology #geochronology #radiometric ♫

Biological Essentialism and Young Planets, Act Blue, Redistricting in Virginia and How Social Media Pushes Porn Addiction

-- Biological Essentialism & Young Planets –

What is Biological Essentialism?  Cats are cats, bats are bats and apes and people do not have a common ancestor.  Horses, hydras and humans are examples of Essential Types of Life (ETL's).  Bio-essentialism is basically Aristotle's Biology: 

www.barnesandnoble.com/w/biological-essentialism-jay-hall/1140135320

Bio-essentialism would hold that trilobites and giraffes lived at the same time.  So, the majority of the rock record testifies to a single global cataclysm.  If catastrophism is the right approach to interpreting the rock record and there never was an "Age of Dinos" since all Essential Types of Life (ETL's) began at the start, then our lovely planet must be much much younger than mainstream science allows.  Let's all "Make Earth Young Again" (#MEYA)!

 

In the March 2021 issue of Microscopy Today, we learn of the discovery of nerve fragments from a Triceratops collected from the Hell Creek Formation in Montana.   How could these delicate nerve fibers remain intact after 66M years?  Maybe our home planet is young after all.  From dinosaurs, let's turn to pandas who live a dog's life.  They're loners, have high infant death rates, reach maturity slowly and the females are only receptive during a narrow time window.  John Gittleman, in a paper "Are the Pandas Successful Specialists or Evolutionary Failures?," dropped the kraken on the pandas' woes:

 

Both panda species [giant and red] are also susceptible to fatal infection by canine distemper virus and various bacteria and ecto-parasites.  These problems may be due to low levels of dietary protein and other nutrients potentially limiting function of the immune system or to small founder populations resulting in deleterious inbreeding effects. ...The red and giant pandas are therefore being hit from two sides.  On the one hand, life-history traits of small and slow-growing neonates are producing vulnerable young.  On the other hand, the two panda species face unusually strong sources of mortality - both intrinsic and extrinsic.

 

From the Young Earth standpoint, this is no conundrum.  For more information, see chapter 12 of my book, “Implications of Biological Essentialism.”

www.barnesandnoble.com/w/biological-essentialism-jay-hall/1140135320

If the Earth is young, what about the other planets?  Neptune has considerable internal heat, radiating more than twice the energy it receives from the sun.  If the Solar System is young, this is no problem.  The magnetic field of Neptune is about as strong as that of Uranus.  Magnetic fields decay with time, so Neptune says, “I’m young!”  Neptune’s magnetic field is not aligned with the rotation axis and does not pass through the center – an enigma for #Mainstream_Science

https://www.icr.org/article/solar-system-neptune

 

See chapter 13 of my book Is a Young Earth Possible? for arguments for young planets: “Straight Out of the Solar System.”

https://www.amazon.com/Young-Earth-Possible-Science-Youthful/dp/1088860788/

 

✩Now to the News✩

**ActBlue Acts #BAD !

The activist group ActBlue has been pleading the Fifth Amendment a lot lately.

The House’s Administration, Judiciary, and Oversight and Government Committees put out a report: “Fraud on ActBlue, Part II: Illicit Foreign Donations and a Cover-Up Spur Mass Resignations and Firings on ActBlue’s Legal and Compliance Team.”

In addition, Texas Attorney General Ken Paxton filed a lawsuit against ActBlue for “misleading consumers about its unlawful donation processes that allow fraudulent and foreign donations to undermine the integrity of our nation’s elections.”

https://thefederalist.com/2026/04/20/new-house-report-details-actblues-illicit-foreign-donations-and-a-cover-up/

 

**VA Redistricting Fiasco

A Virginia court has declared the state's redistricting vote unconstitutional recently.

Certain requirements for referendums were not followed.  Several cases are challenging various aspects of the referendum. The Tazewell Circuit Court blocked  certification of the election and denied a motion to stay pending appeal.

https://www.foxnews.com/politics/virginia-court-declares-states-redistricting-vote-unconstitutional-legal-win-republicans

 

We read the following in Audacity of Hope:

 

These days, almost every congressional district is drawn by the ruling party with computer-driven precision to ensure that a clear majority of Democrats or Republicans reside within its borders. Indeed, it’s not a stretch to say that most voters no longer choose their representatives; instead, representatives choose their voters.

https://studfile.net/preview/11962524/page:7/

 

Now for some Maths!

 

A compact shape is where the points on the boundary are as close as possible to the center.  A circle is the most compact and regular polygons are highly compact.

https://support.esri.com/en-us/gis-dictionary/compact-shape

 

A regular hexagon (all sides & angles =) is convex.  A star is not – you can take two points within the shape and connect them with a line and that line is not entirely within the star.  Hodge, Marshall & Patterson in their paper in The College Mathematics Journal from 2010 state, “Convexity-based measures of shape compactness provide an effective way to identify irregularities in congressional district boundaries. A low convexity coefficient may suggest that a district has been gerrymandered …”

https://www.researchgate.net/publication/233685365_Gerrymandering_and_Convexity

Consider Illinois’ 4rth Congressional District, it has a wild shape.  There is a thin bridge connecting the Melrose Park region to the Cicero region because of the requirement that districts be contiguous (e.g. there’s 48 contiguous States).

https://news.wttw.com/2016/02/16/illinois-4th-congressional-district-candidates?mini=2020-02

The convexity coefficient indicates the likelihood that a district contains the line segment joining any pair of randomly selected points.  The convexity coefficient for the Fourth District of Illinois is 0.237 which is not good.[1]  Take a look at the Oklahoma Congressional Districts.  Nothing too crazy as for their shapes.  I would put the whole of Oklahoma county into District 5, but other than that I would give Oklahoma a good mark for the divisions.

https://www.mapshop.com/oklahoma-congressional-districts-wall-map/

 

By the way, Nobel Prize-winning economist Kenneth Arrow (d. 2017) demonstrated that there is no perfect voting system:

https://www.ams.org/publicoutreach/feature-column/fcarc-voting-arrow

 

** Social Media #SocMed & The Porn Pandemic

Social media’s addictive features have recently been on trial in California and Florida.  Will the #Tek_GiantZ change their ways and repent?  Are you suffering from anxiety, depression, dysmorphia fears and addictions?  Will you now sue the owners of #Tick_Tack #UToob and other major moguls?  Are you caught in a vicious cycle of #Doom and self-harm?  Certain internal documents show that companies designed platforms to be addictive.

https://www.theepochtimes.com/article/after-landmark-verdict-next-trial-over-social-media-harms-focuses-on-teen-boys-addiction-6007026?welcomeuser=1

 

According to the Lawsuit Information Center, “The presence of predators on social media and the sharing of explicit content can lead to cases of child sexual abuse.”

https://www.lawsuit-information-center.com/social-media-addiction-lawsuits.html#harm

 

Will there now be a flood of attorneys suing social media for porn addiction?

 

Be sure to check out our interview with Dr. Dan Biddle of Genesis Apologetics:

https://thenewscasters.com/podcast/true-truth-weekly-episode-5/

 

Feel free to connect with me on LinkedIn: Jay Hall M.S.

https://www.linkedin.com/in/jay-hall-m-s-b64526a

 

We'd love to hear your feedback - pro or con, just go to TotalYouth.us

https://totalyouth.us/contact-us

You can find links to our books and other Social Media there.

 

Note:

1) “Gerrymandering and Convexity” by Jonathan K. Hodge, Emily A. Marshall & Geoff Patterson, The College Mathematics Journal 41(4):312-324, SEP 2010, p. 314.

https://www.researchgate.net/publication/233685365_Gerrymandering_and_Convexity

 

Our new podcast:

https://thenewscasters.com/true-truth-weekly/

I'm in Oklahoma City - if you can suggest anyone for a possible interview, just give me a holler. 

 

My site: https://totalyouth.us/

 

** kudos – graphic sources:

https://chatgpt.com/c/69ebe140-5e9c-83ea-aea0-134772a6529b

https://www.mapshop.com/oklahoma-congressional-districts-wall-map/

https://www.cnet.com/tech/services-and-software/microsoft-brings-bing-ai-to-more-browsers/

 

#Young_Earth_Experience! #YEE # Young_Earth_Science #YES  #Young_Earth_Theory_Intelligence #YETI  #Xtan ╬ #Christian #Christianity #Xty

#Noah #Global_Flood #Deluge #Creationista #Revival #God #Jesus #Bible #Gospel #porn #addiction #depression #SocMed #Voting #Kenneth_Arrow #redistricting #FAIR #ActBlue #Blu #Sad #down ↓ #OKC #Thunder #Oklahoma #States #like_n_subscribe ! #Biddle #Hodge #Marshall #Patterson #Math #Maths #MathZ #iπ_DU ? #Mercury #Venus #Earth #Mars #Jupiter #Saturn #Uranus #Neptune #Pluto #Goofy #Guuglii (new search engine?) #TrueTruth #weekly #weakly ? #Weak_Lee ☺ #Lawsuit_Information_Center #LIC #CIL #LI #books #bux $$ #MAPS #BB6640 ╬ #Illinois #IL #ILL #Chicago #ShyTown ✩

Westminster Wasp - Anti-ZERO

 

 >> Anti-ZERO <<

This orb of #Whackz oll waze gets older, but never wiser

#BigTime just gives me the swoonz

Maths depression geekz mii down, like #ZERO people

I've nulled-out, just like TV's #Zoom

 

I knew that 4567 goes for prime pri¢es

We must all stryve for #ZERO vices

Not perfect, but Christ is

Tale as old as thyme

Woke #UP dreaming from the dreaming

#ZERO_Day I'll watch as you're weaving

Cause zero limits can be #MEME ing [lim, x→0, sin(x)/x]

4 infinite time [cf. Gabriel's Horn, see below]

 

It's me, π

Mathy problem, it's e [≈2.72]

At #Tea_Time, everybody wants T

I'll stare directly at the Σum, but never @ the terror

It must be a tease deriving #Rootz for the #Anti_ZERO

 

Sometimes, I feel like every1 is a #prime 4 #Hades

And I'm the monster on the #kill

#Too_BIG to hang out, crunching fractals 4 the #CityPlannerz

Punched through #DeHart & I'm 2 blame ...

 

Lana Del Rey knows #Gospel versus altruism

Like some kinda Math-Whiz Con-Man ‼

Tale as old as #Y6K

I keep dreaming of Wine & #Skiddlez

One day I'll solve the dire elliptic #Riddlez

#MyThesaurus will lose all its meanings

4 the last #Rhyme

 

I've always found harmonic functions kinda funny ☺

Near Death Convergence never will

Der Riddler's wife, Lorena, hides Gödel's #DarkLogic and screams out

She's "laughing" loud at us from Hell

  -- ICE-J (5-8-23 AD ╬)

 

How many ancient king lists (~Sumerian King List) go back millions of years? ... #ZERO !

How many errors or contradictions are there in the Bible? ... #ZERO ‼

How many times has #AOC spoken the truth in public announcements in 2023?  My estimate: T(AOC)≈0

What is the opposite of 0?  Why ∞ of course!

 

He gives more grace. Therefore He says:

“God resists the proud,

But gives grace to the humble.”

Therefore submit to God. Resist the devil and he will flee from you.

  -- James 4:6,7

"The heart is deceitful above all things, and desperately sick; who can understand it?" (Jer. 17:9)

"I have seen everything that is done under the sun, and behold, all is vanity and a striving after wind. ... For in much wisdom is much vexation, and he who increases knowledge increases sorrow." (Eccl. 1:14,18)

"The hopes of the godly result in happiness, but the expectations of the wicked come to nothing." (Pr. 10:28, NLT).

 

By this gospel you are saved, if you hold firmly to the word I preached to you. Otherwise, you have believed in vain.  For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures.

  -- 1 Cor. 15:2-4

 

"Frankly Scarlett, this dear job of #LIFE is not all a bed of #BeerAndSkittles ..."

  -- Jay L. Hall M.S. (defender of Young Earth Science) 

 

YES Virginia, there really was a Zero Mostel (d. 1977):

https://www.imdb.com/name/nm0609216/

He played Tevye in “Fiddler on the Roof” on Broadway:

https://www.nytimes.com/1977/09/09/archives/zero-mostel-dies-of-heart-failure-at-62-zero-mostel-is-dead-at-62.html

However, Chaim Topol, who passed away in March, acted out the role for the film:

https://www.pbs.org/newshour/arts/israeli-actor-chaim-topol-known-for-role-of-tevye-in-fidler-on-the-roof-dies-at-87

So ... does that make #Topol the real #Anti_ZERO ??

 

#Anti_Hero - Taylor Swift:

https://youtu.be/b1kbLwvqugk

 

If you're a Ph.D. Art Historian & can explain this to me, I'd love to hear it ...

Just click the "CONTACT" button @ the top:

https://totalyouth.us/

 

When is "Tea Time"?  More importantly, when is t(0)?

I claim it was just thousands of years ago >>

Is a Young Earth Possible?  ★★★★½

  https://www.amazon.com/dp/1088860788

YES - Young Earth Science  ★★★★

   https://www.amazon.com/YES-WorldView-Fallacies-Collapse-Darwinism/dp/0692320075

 

First show ever of #Zoom ♪ ♫

https://youtu.be/kWovTxC-KPY

 

Thx to Eric Cartagena for the #AOC graphic:

https://www.linkedin.com/posts/josearizaga_activity-7060473134277156864-2uoF?utm_source=share&utm_medium=member_desktop

 

Thx to Fermat's Library for this cool #Maths fact - 4567 is the only prime with four consecutive increasing digits:

https://www.linkedin.com/posts/fermatslibrary_this-is-the-only-prime-with-four-consecutive-activity-7060954047289196544-H5vQ?utm_source=share&utm_medium=member_desktop

 

Gabriel's Horn - Maths Paradox:

https://www.reddit.com/r/math/comments/8m1rof/seemingly_obvious_things_that_are_actually_false/

 

Riddler's wife "Lorena" >>

https://www.reddit.com/r/DCcomics/comments/ygpcl2/riddlers_wife_lorena_who_is_she_catwoman_lonely/

 

Shot Thru the ♥ & #ur2 Blame ...

https://youtu.be/iWIF8_DqW44

I know I'm #LivinOnPrayer ╬ <><

https://youtu.be/FgLKVYaEcW8

#BonJovi #OohWah #OohWah #WayOf½

Shout to the Lord - Apologetix:

https://youtu.be/FZlTkGA_kkY

#ROM5_1to5 #BadDaze

 

#LDR LP's of 2025 ...

https://www.newyorker.com/humor/daily-shouts/future-lana-del-rey-albums

 

my site: https://totalyouth.us/

 

#Fermat_LI #Maths #Mathz #JN3_16 #LanaDelRey #Alone #Aloner #Alonest  #Anti_ZERO #TooSwiftLee #TaylorSwift #LanaDelRey #BonJovi #HalfWayThere

#YES #YoungEarth #YoungEarthScience #YETI #YoungEarthTheoryIntelligence #Apologetix #chemtrailz #Year2025 #HarmonicFunction #HarmonicSeries #JudasKiss #betrayal #WestminsterWasp #WestminsterWaspWED