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 ♫