As men, we have limitations, in terms, of our natural abilities and reasoning. Yet, as New Testament scripture states...
"[Mat 19:26 KJV] 26 But Jesus beheld [them], and said unto them, With men this is impossible; but with God all things are possible."
The boundaries and fallibility of man's machinations, in terms of scientific and mathematical reasoning, become ever more apparent as one advances in degree at the university level. This author has a post-baccalaureate in computer science and software engineering. Plus, he is an amateur mathematician who engages in pursuing "classical" problems as a recreational diversion.
Yet, man's knowledge in the advanced mathematical arts is mere foolishness in the sight of God. As the apostle Paul wrote...
[1Co 3:19-21a KJV] 19 For the wisdom of this world is foolishness with God. For it is written, He taketh the wise in their own craftiness. 20 And again, The Lord knoweth the thoughts of the wise, that they are vain. 21 Therefore let no man glory in men....
And, how we can glory in men! Certain names are considered unquestionable in the fields of this world's wisdom and knowledge. Currently, while reading through a "classic" textbook on conceptual physics which explained the historical development of the scientific discipline, it was revealed that Aristotle reasoned the following. "An object that was three times larger than a smaller object would fall three times as quickly." This "belief" was basically unchallenged for over a couple of millennia. Why? Who would dare question an oracle, such as the "well-respected" Aristotle. He could never be in error. Well, eventually, Sir Isaac Newton questioned this "belief" and "discovered" that objects fall at the same rate of acceleration caused by gravity. And, for over a couple centuries, Newton's reasoning is now the "unquestionable reality" of physics. In truth, many such names exist in history. These include Einstein, Bohr, Kepler, Copernicus, Socrates, Euclid, al-Khwarizmi, Erdos, and others.
Yet, as men of the Christian faith, we must agree that only one man who has walked this Earth has lived a life without flaw or blemish and spoke "Unquestionable Truths". This was Jesus of Nazareth, the Christ. Our Hebrew and Islamic brothers, the other faiths groups drawn from the Book, might disagree. Yet, they would agree that El-Olam, the Everlasting God, is Omniscient, Omnipotent, and Omnipresent. He is our El-Shaddai making timely provisions.
Yet, as stated by the apostle Peter,
[Act 10:34-36 KJV] 34 Then Peter opened [his] mouth, and said, Of a truth I perceive that God is no respecter of persons: 35 But in every nation he that feareth him, and worketh righteousness, is accepted with him. 36 The word which [God] sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:)
So, the Lord places very little value our claims of great "worldly" accomplishment. In fact, we do ourselves a "spiritual" disservice if we become an idol for others. The Lord detest the "high places" that do not glorify Him.
[2Ch 31:1 KJV] 1 Now when all this was finished, all Israel that were present went out to the cities of Judah, and brake the images in pieces, and cut down the groves, and threw down the high places and the altars out of all Judah and Benjamin, in Ephraim also and Manasseh, until they had utterly destroyed them all. Then all the children of Israel returned, every man to his possession, into their own cities.
So, a quick foreshadowing of the conclusion is this, seek the Lord's Wisdom, first, and this world's knowledge with the proper perspective, second. Our knowledge has a purpose, but know fully that it has its limits and flaws. Yet, it is like us "natural" and "imperfect".
[1Co 2:9-16 KJV] 9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him. 10 But God hath revealed [them] unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God. 11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God. 12 Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God. 13 Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual. 14 But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know [them], because they are spiritually discerned. 15 But he that is spiritual judgeth all things, yet he himself is judged of no man. 16 For who hath known the mind of the Lord, that he may instruct him? But we have the mind of Christ.
An example of the limits of man's knowledge and the failings of what we so readily lean upon which is so untrustworthy follows.
Muhammad ibn Musa al-Khwarizmi was a Persian mathematician credited with the origination of elementary algebraic reasoning. He is the reason that we "balance" equations. Al-Khwarizmi's personal machination algebra is the basis of the modern mathematical reasoning that is the cornerstone of many other mathematical sub-fields and many scientific disciplines, including the physics that supports bridges and building structures, the chemistry that yields "life-saving" medications, and biology that governs political decisions concerning the environment. Yet, as we will see al-Khwarizmi will never be confused with Sesame Street's Count von Count who never lost track of a single object that he was tallying.
About the time most of us viewed Sesame Street, Easy Rider on the Electric Company, and Zoom, we also learnt concepts like one plus three was four. We saw diagrams which showed one orange, a plus sign, and three other oranges. We would count all of the oranges and deduce that four oranges was our sum. Simple enough. What if we had a box with nine books in it and were told that we should divide them in thirds? We would place them one at a time in three different bins in a "round-robin" fashion. This is the act of division, grouping, or partitioning. We started out with four oranges, and, when all was said and done, four oranges remained. Or, we started with nine books and, upon completing our operation, nine books were evenly distributed between three bins without any remaining. This is the nature of the basic operations of addition, subtraction, multiplication, and division most children learnt in elementary school. They are "object preserving". During these operations, objects are neither created nor destroyed. This should be a quite comforting notion, since algebra is the basis of Newtonian physics which teaches that energy is neither created or destroyed; it is a universal constant that is conserved and never lost.
Yet, let us look at the nature of the modern state of the reasoning which al-Khwarizmi shared with the world, based upon the notion of counting objects, also known as mathematical implements. Consider the following:
Working as a professional mathematics tutor at a junior college has taught that students “hear” explanations or “see” the implements within a problem differently. For instance, the “normal” mathematics student will “see” the expression (15 * x)/3 + 5 = y, when x = 7, and determine that y must equal 40 based upon the defined order of operations in the "mathematical" statement.
( 15 * 7 ) = 105
( 105 / 3 ) = 35
( 35 + 5 ) = 40
And, some students with a “rare” gifting who falsely are deemed “poor” mathematicians will “hear” the instructor’s explanation that (15*7) or 105 objects exist on the right side of the equation and these mathemagically become 40 on the left. Well, how does that 105 objects on the right and 40 on the left balance under “equality”? That is quite a feat of prestidigitation.
In fact, they truly do not. The division is an act of “partitioning” or “grouping” which makes 3 bundles of 105 without any objects remaining. These are each of size 35. And, the addition augments one or more of those groups with 5 more implements. The definition of addition in algebra does not specify whether one or more of those bundles receives five additional objects. One might assume that this is done in parallel for all of the bundles. Yet, such is not by definition.
In the eyes of students who are viewing the problem from the fundamental perspective of counting “object”, like oranges or books, this affects the total number of objects represented by the final value of y. So, in the view of some, y should be 120 in 3 groups of 40 or 110 with a bundle of 40 implements plus a pair of groupings with 35 implements.
Regardless of how one views this, over a hundred objects on the right become fewer that fifty on the left. This is called an “equality” or a “balanced” equation when it is more of a “reduction” or “whittling”. Students who see the problem “differently” from a nonstandard vantage-point are not “deficient”; they simply have an “uncommon” insight which unfortunately baffles them in light of standard teachings. While learning algebra in middle or high school, they are those ones who still grasp the fundamental teaching of counting mathematical implements, like apples and oranges or books and pencils, learnt while in the earliest years of grade school.
Upon first noticing this line of reasoning and its seeming “validity” from the standpoint of mathematical objects, memories of the other “quantitative” sciences arose where the equations manipulated often represent amounts of bosons, photons, atoms, moles, kilograms, liters, meters, moles, and so on. This makes one wonder; Could scientist be losing track of physical objects in some of our derivations with a fundamental flaw in abstract reasoning? Could this “standard” and "commonly" accepted miscounting of implements be the reason that classical physics was not fit for certain situations. Time has not permitted further investigation, since it is just the pursuit of a great understanding of "foolishness".
Does losing track of the implements, if one is measuring an electromagnetic phenomena that depends upon a number of charge particles such a current or its cousin magnetic field, have any real significance. Could the reasoning surrounding these physical properties of matter be simplified if one accounts for each implement originally present? Is engineering innovation possible if we simply "see" and "hear" what the rare few who are deemed "poor" mathematicians? Simply, because one "sees" or :hears" what others do not in a situation, does not mean that such person is "stupid" or "suffering" from a mental defect, such a hallucinogenic form of schizophrenia.
[Mat 13:14 KJV] 14 And in them is fulfilled the prophecy of Esaias, which saith, By hearing ye shall hear, and shall not understand; and seeing ye shall see, and shall not perceive:
In that the original spirit of counting objects and balancing scales using al-Khwarizmi's methods was for keeping tallying in marketplaces and ancient production centers, it important that modern mathematics maintains the same fidelity concerning the conservation of "implements". Whether this miscounting existed from its inception or not is unknown. It might have been that deadly sin of avarice which inspired a counting technique which whittled away at hins of oil or ephahs and omers of grain so one might swindle his clients.
What is known? Man's disingenuous motivations and lust for lucre might affect his interpretations of factual counts and records. What we do know is that...
[Pro 20:14 KJV] 14 [It is] naught, [it is] naught, saith the buyer: but when he is gone his way, then he boasteth.
[Pro 28:21 KJV] 21 To have respect of persons [is] not good: for for a piece of bread [that] man will transgress.
[Pro 20:10, 23 KJV] 10 Divers weights, [and] divers measures, both of them [are] alike abomination to the LORD. ... 23 Divers weights [are] an abomination unto the LORD; and a false balance [is] not good.
[Jhn 2:13-17 KJV] 13 And the Jews' passover was at hand, and Jesus went up to Jerusalem, 14 And found in the temple those that sold oxen and sheep and doves, and the changers of money sitting: 15 And when he had made a scourge of small cords, he drove them all out of the temple, and the sheep, and the oxen; and poured out the changers' money, and overthrew the tables; 16 And said unto them that sold doves, Take these things hence; make not my Father's house an house of merchandise. 17 And his disciples remembered that it was written, The zeal of thine house hath eaten me up.
[Pro 15:2, 14 KJV] 2 The tongue of the wise useth knowledge aright: but the mouth of fools poureth out foolishness. ... 14 The heart of him that hath understanding seeketh knowledge: but the mouth of fools feedeth on foolishness.
Yet, if we want True Wisdom. We only must ask.
[Jas 1:1-9 KJV] 1 James, a servant of God and of the Lord Jesus Christ, to the twelve tribes which are scattered abroad, greeting. 2 My brethren, count it all joy when ye fall into divers temptations; 3 Knowing [this], that the trying of your faith worketh patience. 4 But let patience have [her] perfect work, that ye may be perfect and entire, wanting nothing. 5 If any of you lack wisdom, let him ask of God, that giveth to all [men] liberally, and upbraideth not; and it shall be given him. 6 But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed. 7 For let not that man think that he shall receive any thing of the Lord. 8 A double minded man [is] unstable in all his ways. 9 Let the brother of low degree rejoice in that he is exalted:
[Pro 4:7-15 NIV] 7 The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. 8 Cherish her, and she will exalt you; embrace her, and she will honor you. 9 She will give you a garland to grace your head and present you with a glorious crown." 10 Listen, my son, accept what I say, and the years of your life will be many. 11 I instruct you in the way of wisdom and lead you along straight paths. 12 When you walk, your steps will not be hampered; when you run, you will not stumble. 13 Hold on to instruction, do not let it go; guard it well, for it is your life. 14 Do not set foot on the path of the wicked or walk in the way of evildoers. 15 Avoid it, do not travel on it; turn from it and go on your way.
[2Ti 2:15-16 KJV] 15 Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth. 16 But shun profane [and] vain babblings: for they will increase unto more ungodliness.
[2Ti 2:5-7 KJV] 5 And if a man also strive for masteries, [yet] is he not crowned, except he strive lawfully. 6 The husbandman that laboureth must be first partaker of the fruits. 7 Consider what I say; and the Lord give thee understanding in all things.
[Mat 5:17-20 NKJV] 17 "Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill. 18 "For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled. 19 "Whoever therefore breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches [them], he shall be called great in the kingdom of heaven. 20 "For I say to you, that unless your righteousness exceeds [the righteousness] of the scribes and Pharisees, you will by no means enter the kingdom of heaven.
So, True Wisdom becomes apparent when one heeds and hears the Teachings in the Law.