In my reasonably extensive reading on the subject of the Trinity, the only explanation that even came close to making sense was the (possibly heretical) explanation by C.S. Lewis in his classic book Mere Christianity where he described God and Jesus Christ as separate beings and the Holy Spirit as the link or connection between them. The rest of the conclusions offered for the trinity being one being in three hypostases never made any sense to me. As someone who likes to understand as much as possible, seeing something so totally illogical as the Trinity be the litmus test for orthodoxy is really galling. After all, if something cannot be rationally understood, and is not present in the Bible, how can it be the dividing line between Christian and heretic? Why not make it some clearer doctrine in the Bible like the continuing validity of the Seventh Day Sabbath, or the divinity of Christ?
After all, some of the most insistent arguments I have read and heard made about the Trinity claim that the Trinity is true because it uniquely solves one of the thorniest logical problems that exists in the philosophical branch with which I am most interested, and that is epistemology (the theory of knowledge). This problem is one I have mentioned in other posts  and is the problem of the many and the one. In human thought there are two characteristic heresies that deviate from the truth. On the left hand we have the many and on the right hand we have the one. These two approaches, or what we could call anarchy and tyranny, or relativism and reductionism, or the fox and the hedgehog , represent two characteristic and erroneous ways of thinking that we tend to lapse into as human beings. If we veer to the left, we see anarchy because there are many ways to truth (in such a view) and no underlying unity. There is no legitimate authority, but rather contradictory and impossible to reconcile ideas and truths. If we veer to the right, we end up in the land of tyranny, where there is only one right way to fold towels, only one kind of music that we ought to listen to, only one way to dress or comb your hair, under the tyrannical thumb of some dictator, or where all the Bible refers to one particular time or one particular person or church, or where all godly people belong to one organization. Either way we end up in a ditch.
The problem with the Trinity is that it doesn’t make sense, and therefore cannot be a solution to the logical dilemma of the many and the one. For example, the Trinity posits that the Father, the Son, and the Holy Spirit are co-equal in authority when the Bible clearly states the supremacy of the authority of the Father over the Son (see 1 Corinthians 15:28, 11:3, the latter of which refers to a biblical belief in a chain of authority about which much could be said). Therefore the Trinity supports anarchy, or a lack of a clear chain of authority, in a vain attempt to preserve the unity of God. And in foolish theologians positing that the Trinity is the only way to harmonize the dilemma between the many and the one, a correct option is ignored that preserves the value and purpose of both the many and the one.
Let us therefore briefly examine that doctrine, with due credit given to a more complete discussion provided by others that provides some useful context and additional explanations . For one thing, three is not many, and for another, the oneness of the Trinity does not hold either. So what does? The biblical model of God presents God as a family. Currently that family includes two members: God (the Father, the Ancient of Days) and Jesus Christ (the Word, the Angel of the Lord, the Son of Man: See, for example, Psalm 110:1, Daniel 7:13). However, in the future, that family will include believers who are part of God’s family, of the same form as Christ (see 1 John 3:1-2), no longer marrying and given in marriage (see Matthew 22:30), but being worshiped by those who falsely considered themselves true believers (see Revelation 3:9), such worship being denied even to the angels but only given to God (see Revelation 22:9). Therefore believers in the future will be considered as part of the God family.
This is the true harmonization of the problem of the many and the one. The number of believers in God’s kingdom raised into life incorruptible as part of God’s family will be a great multitude, many billions of people (we hope!). All will have unique personalities, unique combinations of gifts and talents, and yet all will be entirely submissive and obedient to the will of God if they are to enter the Kingdom of God and be citizens in the Jerusalem of God, the new heavens and new earth. Despite the many personalities, many approaches, and many perspectives, they will be subject to one will, namely God the Father’s, just as Jesus Christ is. They will have shown themselves through their conduct subject to one law, namely God’s. And yet they will be many, and different, just as there are many different flowers of the field, and animals of the earth and sky and sea. God loves unity in diversity. That is His way–whereas we only want drab conformity and uniformity or chaos and disorder in our fallen state.
Therefore, we have seen that even though the Trinity is falsely posited as a solution to the logical problem of the many and the one, the family of God and the Body of Christ offer the true solution to the problem. They offer this by offering one law and one authority (namely Jesus Christ as head of the Body and the will of the Father as supreme over all) but many functions, many perspectives, and many members for the diverse human creation that God has created in His own image, each with different and fascinating parts of His own personality and character, all working together for a common goal but using their own unique perspectives, each working on their own part of the massive whole of God’s plan on earth. Therefore, we need not enter into illogical interpretations to solve the problem of the many and the one. All we need is a proper appreciation for both the unity and diversity of what God is doing, and the amazing plan He has for turning human beings into God beings just as little grubby caterpillars turn into beautiful and graceful butterflies in their proper time.