A Scientific, Philosophical, and Theological Summary of Middah and Algorithms:
The Judeo-Christian Development of Mathematics

By
Dallas F. Bell, Jr

Mathematics[1] is the natural language of intellects to describe and analyze amounts.  Its development comes from interactions of humans with the innate problem-solving ability capable of formulating complex ideas from observations and logic.  Observed objects represent values for which numbers are given to specific amounts.  The ten digits on the human hand equal the base 10 or decimal system for numbers[2] and are perfectly designed for communicating amounts from birth.  The innate human language of mathematics[3] is commonly witnessed by infants holding up a finger(s) to represent the amount of something they desire or to indicate their age.  This instinct is so strong that parents are often advised to take steps to curtail finger counting of their children in order to stimulate cognitive advances in mathematics. 

Numerical amounts can be expanded by adding, decreased by subtracting, divided, and multiplied.  The rate of increase or decrease can be measured to find the original quantity, differential and integral calculus.[4]  Measures are needed to communicate weight, distance, size, pressure, temperature (weather and metallurgy), and energy, etc.  This requires tools for measurement standards, such as rulers, scales, counters (beyond finger-symbolism),[5] compasses, plumb lines, and thermometers,[6] etc.  With those tools, land can be surveyed,[7] complex architecture achieved, accurate distances can be traveled, astronomy matured, and new tools created, such as clocks[8] and calendars.[9]  Carl Friedrich Gauss called number theory the queen of mathematics.[10]  Wisdom is the righteous application of knowledge, which includes witty inventions[11] as seen in geometric and matrix woven cloth.[12]

The degrees of angles create geometry to analyze proofs,[13] analyze convex and concave optics,[14] and create trigonometry to determine the function of shapes, sine and cosines, and tangent and cotangents, etc.[15]  Graph mathematics can then simulate the planes for plotting interpolation and analysis of variables.  Proven rules and immutable laws of mathematics are established and those principles, used to create logarithms[16] and atomic theory of chemistry[17] etc., can be used to avoid the false philosophy of chaos and scientifically build more immutable laws, such as congruence,[18] harmonics,[19] hydrodynamics,[20] colors,[21] light,[22] magnetism, and electricity[23] etc.  Then principles of physics,[24] gravity,[25] probabilities,[26] and warfare etc. can develop and more tools made, e.g. pulleys,[27] levers,[28] screws,[29] cogwheels,[30] vacuums,[31] and pumps etc., with more principles, such as water displacement of floating objects,[32] fluid dynamics[33] etc.

Opposites are the natural contrast of things.  If there is a number 1 and 2 then it is reasonable to think about a -1 and -2.  Natural numbers are separated from fractions of whole numbers called integers.  Integers can be positive numbers (1, 2,…) and negative numbers (…, -2, -1).  Axioms of induction can process integers.  An axiom of mathematical induction could be if N is a set of all positive integers (N = {1, 2, …}) and S is any subset of N, then if S possesses the two properties where 1 is an element of S and for every arbitrary positive integer k, (k + 1) is an element of S whenever k is an element of S, then S = N.   

Equations are scientifically developed for equality where there are equal and not equal outcomes for which equal means philosophically true and theologically good, and not equal means philosophically untrue and theologically evil.  Then temporal and eternal justice is rationally, logically,[34] and poetically[35] extrapolated.  This spatial concept merges with the rational extension of numbers for the reality of infinity.              

The mathematics of infinity is encased within eternity.  Galileo stated that the universe is a grand book written in the language of mathematics.  MIT’s professor of physics, Max Tegmark, said the universe is made up of math and math can explain all existence, including the human brain.  The Divine language of mathematics is seen in the vanguard of Hebrew letters[36] given to Adam and Eve around 6,000 years ago with letters having numerical values.[37]  Additionally, God said He said let there be light (Gen. 1:3; II Cor. 4:6) and it was.  He framed the world with His word (Heb. 11:3).  Finite intellects think in parts that can be added, subtracted, multiplied, and divided.  This fractional cognitive process is needed for understanding relationships by motion, speed, size, distance, and weight.  They are catalogued as time and space.

Time is a portion of eternity where finite beings exist and potentially can make sense of their existence.  Beginning with God creating light (Gen. 1), Judeo-Christian Scriptures give examples of math.  The linear series of individuals in genealogies, especially from Adam to Noah and his three sons (Gen. 5).  Noah built the ark with Golden Ratios around 2335 B.C. (Gen. 6:14-22), used the discrete series of numbers to account for the separate animals, and demonstrated a hydrodynamic[38] understanding of water displacement for floating objects.  Abraham’s servants used weights and measures 1856 B.C. (Gen. 24:22).  According to God’s law (Lev. 27:30-33), Abraham demonstrated the decimal system by tithing around 1911 B.C. (Gen. 14:18, 28:22, Hebrew ma’aser, a tenth, tithe; Heb. 7:1-10, Greek apodekatoo, to tithe).   Solomon also used scales which required adding, subtracting, multiplication, division, and fractions by 965 B.C. (Prov. 11:1, 16:11).  He compared the way of a bird in the air and the way of a ship in the sea—fluid dynamics or the motion of projectiles in the air and the theory of waves (Prov. 30:19).  He built God’s temple using material to reflect an understanding of the nonmaterial infinite realm.[39]  Hezekiah built a conduit (II Kings 20:20), and recorded the sun going backward on a sundial ten degrees around 698 B.C. (II Kings 20:9-11; Is. 38:8).  The Scriptures record the sun, moon, and star constellations are guided by ordinances (Job 9:9, 38:31-33[40]; Jere. 31:35-36), such as Arcturus (the Great Bear), Arion, Pleiades (seven stars), Mazzaroth (the twelve constellations or pattern of stars also called the zodiac).  The sun and moon are for seasons (Ps. 104:19).  The seven days of a week were revealed around 3941 B.C. (Gen. 1-2).  The months of the year are annotated (I Chr. 27:1-15).[41]  Moments[42] and hours[43] divide the day.

Around 1275 B.C., complex woven embroidered cloth and fine linen were used in the tabernacle (Ex. 35:35).  Jewish metrology covers long measures,[44] land measures,[45] weights,[46] and liquid measures.[47]  A measuring line was used around 521 to 518 B.C. (Zech. 2:1-2) and the sides of cities were measured after 1235 B.C. (Num. 35:5).  A plumb line was used in 755 B.C. (Amos 7:7-8).  Hot (Is. 49:10) and cold (Job 37:9; Acts 28:2) weather (climatology and meteorology observed in Job 37:9-11 and Luke 12:54-57) temperatures are contrasted (Job 24:19) and God controls them (I Sam. 12:16-19).  The importance of knowing exact temperatures is necessary for metallurgy (Jere. 6:29) and other disciplines, such as chemistry.[48]  Set theory is seen by the recording that when one of God’s laws, formalized around 1275 B.C. (Ex. 20-24; Lev. 1-27), is broken the whole set of God’s laws is broken.  For example in the Old Testament, breaking God’s set of laws include sexual perversion (I Kings 15:12), murder (II Kings 21:16), idols (II Kings 21:21), and other gods (II Kings 23:24), and this principle is reinforced in the New Testament (Matt. 5:19-28; James 2:10-11).  Those sets have truth values that compose a truth table, which are not subject to incomplete causal data seen in fuzzy sets and fuzzy logic (measuring one’s finite self by the mutable standard of finite others, II Cor. 10:12-13).  Ultimate pressure (Ps. 38:2) and energy are beyond natural law and maintains the material realm (Job 26:12, 38:4-11; Heb. 1:3).

An axiom of deduction, if this then that, is Divinely demonstrated (Gen. 2:17) when God accurately said if you eat of the forbidden tree you shall die, not make a felix culpa.[49]  False induction was satanically offered soon after (Gen. 3:1-5) that you will not die if you eat of the forbidden tree.  God’s word has always had a truth value of T and Satan’s words has always had a truth value of F.  The whole Bible is an unique and indispensable set of instructions, an algorithm,[50] for human decision-making[51] with historical examples of the individual and societal outcomes of compliance and noncompliance.[52]  It begins with the Genesis creation of this temporal existence (the Abraham covenant of God to mankind) and extends to the end of this temporal existence in Revelation (the prophesied Messianic covenant of God to mankind[53]), with a look at the eternal algorithm in heaven for the redeemed and hell for people that reject redemption.  That necessary data provides the coping mechanism for inevitable circumstances caused by evil from freewill.  Matrix mathematics was used to indicate the game theory decision process in columns and rows of options to obey and not obey God’s commands and perceived outcomes by Adam and Eve in the Garden of Eden.  They wrongly chose the probability that they would not receive a negative outcome as God said would occur and did occur.  Later, Cain developed a weapon of warfare to kill Abel (Gen 4:8) and warfare strategies were developed (Gen. 14:2).  Musical instruments[54] and songs[55] were also developed.

This ability can be compared to other beliefs, such as the time of the development of mathematics in China.[56]  The 2002 book by Hymen Gabai, titled Judaism, Mathematics, and the Hebrew Calendar, expands on the Jewish development of mathematics.  Moritz Steinschneider published a work in 1864 on the Mishnat ha-Middot,[57] considered the oldest non-scriptural Hebrew record of mathematics which looked at the elements of geometry.  It is agreed that mathematics is not universally useful for everything and does have general areas of less application, such as with humor, irony, etc.

The truth of Scriptures is evident in many ancient cultures, such as Gen. 1-11 in Chinese pictographs.[58]  Scriptures explain the past in Genesis 1 written by Moses prior to his death around 1235 B.C., and John 1 written by John between 90 and 95 A.D.  They say in the beginning was only God.  He was Father, Son, and Holy Spirit.  They have always exchanged love, not by a human choice and decision-making series of acts but as their uniform and eternal nature.  They created space and objects apart from themselves.  Among the objects created where ones with life.  That life included beings with intellect which requires freewill to choose this or not choose this within fixed behavioral boundaries.  Their freewill now required God’s justice, grace, and mercy along with His extended love and redemption for eternal rewards in heaven or hell.  The Scriptures also explain the prophesied future in the book of Daniel (after 594 B.C.) etc. and John’s other writing in Revelation (around 95 A.D. on the island of Patmos).[59]

This universe has particles that move in space and cause time.  That movement had a first cause.  The first Causer, the Alpha and Omega, the beginning and the end,[60] was outside of space and time.  This Being created with purpose and was absent the limited characteristics of finite intellects.  He is not the absence of anything, but is the intellect from which all is created.  We know God exists and must exist by science/observation of natural laws, beauty, and efficiency of creation.  He is also evident from philosophy/logic,[61] poetry,[62] and mathematics seen by justice, love, mercy, grace in His purposeful intellect.  Theology/revelation in Scriptures have fulfilled prophesy, such as the Messiah (Jesus) and the return of Jews to their land realized in 1948, and confirm and are confirmed by science and philosophy.  Finite epistemology vertices of truth merge with theology being the queen (science, observation, theory, replication-law; philosophy, logic, poetry, mathematics-law; theology, revelation, experience, morality-law).  Galileo, Pascal, Newton, Faraday, and Maxwell, etc. are known for demonstrating aspects of all pillars of law.

To say an effort is either hard or soft science is to make a vastly uninformed statement.  Science is a method that relies on logic language of philosophy which needs the revealed morality of theology.  If a person has good revealed morality from their theology, they may potentially have efficient philosophical logic and potentially have efficient or true science.  On the other hand, if the science uses logic from inefficient morality it’s potential to be efficient or true is greatly degraded.  A good scientist is a good theologian.  By this we see that science can show or say nothing.  It is the scientist that purposefully orchestrates un-purposeful data.  Carbon atom deposits and atoms of metal ore do not become valued until a human jeweler processes them into jewelry.

Untrue or bad theology that created untrue or bad philosophy which led to untrue or bad science was recorded by the Catholics murder of the mathematician Hypatia (daughter of Theon of Alexandria) after 415 A.D.[63]  Against the protests of the Greeks, Muslims burned the libraries in Egypt after 641 A.D. due to the comment of the caliph Omar, “…If the books contain what is agreeable with the book of god, the book of god is sufficient without them, and if they contain what is contrary to the book of god, there is no need for them, so give orders for their destruction.”  That destruction took six months to consume the collected written knowledge of the time in Egypt.[64]  The world confined to the small intellect of a few religious leaders with untrue theology and revealed morality was called the dark ages for retarding the Divine human endeavors of science, philosophy, and theology.  Eventually, the reality of truth overcame the evil of untruth and ended that period.

In these last days, humans are increasing in learning but are not able to come to the knowledge of truth (II Tim. 3:7).  Knowledge of truth is repentance (I Tim. 2:4.).  It is becoming as in the days of Noah before the punitive flood (Gen. 6:1-8).  This era also requires Divine punitive action (Matt. 24:27-51; Luke 17:22-36).  They are lovers of themselves, covetous, boasters, proud, blasphemers, disobedient to parents, unthankful, unholy, without natural affection, trucebreakers, false accusers, incontinent, fierce, despisers of people that do good, traitors, heady, high-minded, lovers of pleasure more than lovers of God, having a form of godliness but denying the power of God, and they creep into houses and lead captive silly women laden with sins away with many lusts (II Tim. 3:1-8; Prov. 30:11-14).  As stated before, the truth will eventually be victorious as it has always been.  In 1912, Charles Dawson said he had discovered a half man and half ape in Piltdown, East Sussex.  It was found to have consisted of the altered mandible and some teeth of an orangutan deliberately combined with the cranium of a fully developed human and exposed as hoax in 1953.  In 2009, scientists at the Climate Research Unit of the U.K.’s University of East Anglia were caught manipulating and destroying data.  In 2010, Marc D. Hauser, Harvard psychologist, was found responsible for eight counts of scientific misconduct by the university.      

Theologically, God exists in essence of His being without beginning or end, m’olam l’olam, from forever to forever.  He is complete and whole without change.  He is size-less, colorless, shapeless, and motionless.  Finite beings use senses to input the intellect for understanding required for decision-making and the subsequent purposed behavior.  We can see God with the innate mind from senses that confirm His existence and self-revelation.  Moses saw God’s glory (1275 B.C., Ex. 33:18-23).  Jacob saw a form of God (1763 B.C., Gen. 32:30).  No man has actually seen God the Father (John 1:18, 6:46).  To see Jesus is to see the Father (John 14:9).  Jesus is in the Father and the Father is in Him (John 14:10).

Finite beings think in fractions of an infinite whole.[65]  That limitation is not possible with the infinite God.  Infinite persistence[66] sets of knowledge have always existed in God’s omniscient intellect, such as infinite numbers.  Since He is omniscient His knowledge is unchanging in that He neither gains or loses knowledge, and can not be surprised.  He gives wisdom when His believers ask,[67] and this does not decrease God’s set of data.  The infinite whole of God’s knowledge is one infinite set, and may potentially contain dimensions.  God’s glory lights heaven (Is. 24:23, 66:19; Rev. 21:23).  God is love and His love, justice, mercy, and grace do not occupy space as He does not occupy space.  The Son, Jesus, was incarnated 2,000 years ago and His earthly and resurrected body occupied space.  It could be seen and touched by human senses.  His face shall be seen (Rev. 22:4).

God’s intangible infinite perfect existence shows why the fear of Him is the beginning of wisdom,[68] why humans need to accept His infinite love and live by faith,[69] and the churlishness and pure depravity of blasphemy.  It also explains the futility of finite created human disobedience of God and trying to move closer to Him across an infinite gulf with redemptive works to atone for violating His laws, which denies His power, grace, and position.  God redeems for His own mercies’ sake, His righteousness’ sake, and for His name’s sake.[70]  Everyone has violated God’s set of laws.  Some incorrectly believe that God will forgive and redeem everyone that by freewill violated His laws due to their having done their best with what they were created with by Him.  This would mean everyone would be redeemed, even Satan, and we know this is not nor could not be true.  Contrary to Blaise Pascal confirmation that they were fixed points, it also would incorrectly mean God’s laws are not fixed points to be obeyed.  We know this is not true because God would not punish and exercise His justice causing the need for mercy and prevenient grace[71] to be irrelevant.

The redemptive gospel (G) of God is a balanced equation of opposite valences or power.  God’s disposition toward sin (D) + His action (A) + the consequences of the human decision (C) = G, so D,A,C = G. G = “for God so loved the world” is + D, “that He gave His only begotten Son” is – A, “that whoever believes in Him shall not perish but have everlasting life” is + C (John 3:16), so the inverse or opposite valences are God has just wrath toward the world’s sin is – D (Rom. 2:5-9), His Son’s death and resurrection atones for sin is + A (Rom. 5:8-9), those that do not believe in Him will justly perish and spend eternity in hell is – C (Rev. 14:10), so (+D, -A, +C plus –D, +A, -C = G).  The unredeemed that have a knowledge of what is righteous (D, A) and choose to reject it (– C) requires a greater eternal damnation than the unredeemed that had less knowledge and rejected righteousness (the set of D, A can be > or < than another set of D, A) (Matt. 23:14).  Each of the unredeemed is still justly eternally damned (- C), but it is righteous to have worse degrees of eternal damnation for those unredeemed whose will to sin against the holy God was greater (a set of - C can be > or  < than another set of - C).  The repentance for sin, required for redemption (Mark 1:4; Acts 2:38), can not be forgiven by finite priests, but by the infinite Father God (Matt. 23:8-10, 27:3-10; Acts 8:22; II Tim. 2:25).       

Thus, we need redemption and a Redeemer which only the perfect God of love could provide.  Jesus fulfilled the scriptural text for this prophesied Messiah.  If a finite human believes on Him, he will be redeemed by the eternal power of God (John 3:16).  All prayer must be in Jesus’ name (John 14:13).  There is one God and one mediator between God and man the man Christ Jesus (I Tim. 2:5).  No one can say Jesus is Lord except by the Holy Spirit (I Cor. 12:3).  Jesus is complete God the Son and is complete man.  This is an existential imperative.  All birth certificates, business contracts, and school diplomas are based on the time of His existence on earth.  The Divine existence of Jesus has all the power and ability of His nature of God the Son, e.g. Jesus’ divine nature can be with all believers at once, and yet His human body retains its human abilities.  Jesus’ finite human body did have information communicated to it by God, but it did not have His infinite Divine attributes communicated to it in order to miraculously[72] overcome all the limitations of human nature or else His temptations and atoning sufferings on the cross would not be real and redemptive (Heb. 2:18).  God can not be tempted with evil nor tempt others with evil (James 1:13).

God is complete and equally God the Father, Son (Jesus), and Holy Spirit without being fractions of the whole God (Gen.1:26).  Redeemed believers of Christ Jesus are joint heirs with Him (Rom. 8:17).  This means every believer gets all the benefits equally and without fractions of a whole finite set or else the value of being a joint heir would grow smaller and smaller as the number of believers grows to a point of being worthless, as would occur with temporal property inherited from a deceased human relative.  The faithful in the Old Testament did not receive the promise, but God has provided a better thing for His New Testament faithful without which the prior faithful will not be made perfect or complete without the latter faithful.[73]  By one man’s sin from violating God’s law (Adam), death entered creation and all men must be judged for their sins.  By one man’s redemption (Jesus), eternal life is possible by the atoning for all men (Rom. 5).  It seems paradoxical that to obey God’s law is freedom and to do what we want is to be enslaved by sin.  To spiritually live is to die to self-will and to die to self-will is to spiritually live (Rom. 6:6-23).  The physically dead do not have any portion in our world under the sun (Eccl. 9:5-6).  To talk to them desiring for them to effect a change in our world is called necromancy.  Catholics, Taoists etc. have this intercessory[74] doctrine of witchcraft as they teach and practice praying to the physically dead for which the just penalty is physical and spiritual death.[75]    

As many people know, a paradox is a statement which seems to contradict what we know to be true due to a lack of data or the inability to comprehend known data.  We have thus far examined ideas considered paradoxes by many people, such as the triune nature of God, His self-existence outside of time and space, His creating ex nihilo, His omniscience when anthropomorphically communicating with man in Scriptures for finite man’s time/space understanding,[76] His being omnipresent and creating apart from Himself, His omniscience and omnipotence requires atonement which is not possible for finite beings accomplished by themselves, and the possibility of being joint heirs with the redeeming Christ. 

An equation for a paradox could be as follows, incomplete relevant finite data – complete potentially relevant infinite data = relevant data that prevents a paradox.  It may be said, incomplete relevant finite data + relevant unknown data = potentially complete data that prevents a paradox.  Then complete data = no paradox given the data can be comprehended by a finite intellect.  Many people think the following is a paradox.  If God is immutable how can He seem to change and become angry at the disobedient (Num. 11:33) or be pleased by the faithful (Heb. 11:6).  It can be rationally reasoned that the complete data would include God having always known that He would justly apply His response to disobedience and obedience at the perfect time and no change actually occurred.  The sins of the redeemed will blotted out (Neh. 4:5; Ps. 51:1; Acts 3:19) and will not be remembered by God (Heb. 8:12, 10:17) on judgment day.[77]  He still retains all knowledge, but His grace places the unrighteous behavior into the category of perfect eternal forgiveness, which can never change and lose infinite redemption (I Peter 1:2-5).  

Zeno’s stadium paradox was refuted by Aristotle (Physics 239b33) because Zeno seemed to be confused about relative velocities or Aristotle was confused about Zeno’s proposal that space and time can only be divided by a definite amount.  Maimonides made a similar paradox regarding motion called the millstone, which required an understanding of the continuum.  The Banach-Tarski paradox proved that it is possible to convert one sphere into two using cuts and rotations.  This transformation involves objects that can not exist in our universe.  That is an example of pure mathematics which studies abstract concepts.  Applied mathematics uses mathematical methods that may be applied to practical problems in our universe, e.g. computer science, economics, etc.  These categories change as with number theory[78] in pure mathematics being used today in cryptography, which is an applied mathematics.  The pure mathematician, G. H. Hardy, debated this distinction in his book A Mathematician’s Apology.[79]   

There are beliefs of many dimensions in our universe or endless Buddhist type creations that are called paradoxes.  All movement in our universe had to have a first cause and a finite start point and so must be finite.  Then, those initial beliefs are not possible true by science, philosophy and theology, and can not be paradoxical.  The cults of Scientology, Mormonism, New Age etc. have varying beliefs that they can become God (theosis) or are gods[80] when it is axiomatic that they could not have pre-existed themselves being created by themselves outside of time and space.  The heart of a fool frets against God (Prov. 19:3).  The unredeemed world can not see God the Father or receive the Spirit of truth.  Neither can they know God, but believers know God because His Spirit is in them (John 14:17) and they have the mind of Christ (I Cor. 3:16).  This is the only way of understanding infinite mathematics eternally.  It has been said that what comes into our minds when we think about God is the most important thing about us.[81]  Everyone should know that there will always be a remnant of God’s redeemed to glorify Him and do His will.[82]          

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