​“Feasts significance”

A) OVERVIEW OF FEASTS: NATIONAL, GOD-APPOINTED EVENTS OF SPECIAL SIGNIFICANCE (LEV 23:1-2)

Lev 23 begins with God speaking to Moses, and telling him to speak to the people. Note the instruction words in the command -- speak, say, proclaim. God specifically commanded Moses to be His mouthpiece. This is the pattern in every new section of Leviticus. Again and again, we need to ask ourselves "Why does God choose words?". Later on, after Moses' death and the people of Israel move on, they keep going back to the words of Moses that God commanded him to speak. We live in a world where everyone is trying to tell us something, sometimes to the point that we feel so saturated. But these writings are not just another person's words. These are the words of God. What, then does it mean to proclaim the words of God? It is not just to speak, but to speak as Jesus did. Jesus spoke with authority. When God chooses a person to speak, He chooses that person to proclaim His words. This makes the subsequent instructions so important.

There are 2 phrases that God used to describe His instructions -- "holy convocation" and "appointed feasts". To convocate is to assemble, therefore to obey this instruction, one had to gather. The holy convocation was the holy event for the gathering of His people. God was also telling Moses to tell the people, that there were special gatherings where the whole nation was to gather at the time God had determined. They gather not because it's convenient, or because they wanted to get something out of it. They gathered because God says so.

This passage reminds us that God does not just use words lightly. God's words shape behavior. God is God. This is the principle and idea behind the book of Leviticus. The Bible never talks about God with a small g ("god"). As a Christian, we believe that this higher authority speaks, and has a view on many topics including Himself. He demands that HIs words be proclaimed and obeyed for our good.

God lays out 7 feasts in Chapter 23: 

Sabbath (Lev 23:3) -- They were not to do work, but it was to be a Sabbath to the LORD. They were to be devoted to the Lord, and to pay attention to sacred matters.

The Passover (Lev 23:4-8) -- An annual event commemorating the day when God judged Egypt, but He passed over Israel. They were not more righteous or special, but because the blood of the Lamb was spilled on their behalf. Jews who had to remember this annual event would remember this and their special identity.

Feast of Firstfruits (Lev 23:9-14) -- This was for worship, signifying the giving of God the best of their harvest.

Feast of Weeks (Lev 23:15-22) -- Takes places 50 days after the Feast of Firstfruits

Feast of Trumpets (Lev 23:23-25) -- It was a day of rest, marked by a blast of trumpets.

Day of Atonement, Yom Kippur (Lev 23:26-32) -- An annual event marked by the slaughter of lambs. It's, in a sense, a national experience of killing and animal, and with the smell of blood in the air, they were to remember how they were all sinners.

Feast of Booths (Lev 23:33-44) -- To remind the people of their migrant nature and how they were pilgrims for 40 years

We'll go over these in greater detail in the subsequent weeks, but as we read these verses, we need to think about the significance of these feasts for the community. It doesn't just take place in special places, but it takes place privately and corporately, and takes place wherever God's people are.

These feasts also tell a story. The themes of these feasts are: rest, atonement, dedication, gratitude, gathering, atonement, pilgrim. God was telling them their story again and again, reminding them that they were sinful people that were brought out of Egypt. He provided for them in the forgiveness of sins, and also their daily provisions, and will also one day bring them to their final rest. They depend on Him fully and this place is not their home, they were only passing through. This is the story of the Christian life too. In the same way that God sent Moses to tell their story, these words also tell our story. And the worst thing they could do is to forget their story. We too are also prone to forgetting these messages, themes and who we are. 

😎 FEAST OF FIRSTFRUITS: REFLECTING GRATITUDE AND GOD-CENTERED DEDICATION FOR THE COMING HARVEST (LEV 23:9-14)

Let’s home in on the Feast of the Firstfruits. They were to celebrate this when they enter the land, on the day after the Sabbath (i.e. the first day of the week). Notice that this command was given to them while they were in the wilderness, and could not celebrate it until they entered the land. Yet, they were informed about this and were expected to tell their children this command. Hearing this, the Israelites must have felt frustration mingled with hope. They knew what lay before them, but yet they had not obtained it yet. They were reminded of their present reality, but were promised a world to come. This Feast is a promise from God that He will bring them to where He wants them to be.

To celebrate this Feast, they were to give a sheaf of the firstfruits to the priest (Lev 23:10b). They had to harvest, and select a portion to bring it to the priest. The priest was to wave it on the day after the Sabbath (Lev 23:11). He didn't just wave it for fun and anywhere he pleased, but He waved it before the LORD. This was only possible because they have seen the presence of the LORD (i.e. glory cloud). The worshipper was also to offer a male lamb a year old without blemish was also offered as a burnt offering as a sign of their dedication (Lev 23:12). The food and drink offering is also given as a sign of their fellowship with God (Lev 23:13-14). 

What is the principle behind the Feast of Firstfruits? The people of God were to know that they owe their best to God. Nothing they have did not come from Him. It was definitely risky for them to offer the first of their harvest to God. Who knew if there would be more harvest? But in doing so, they were to learn faith and trust in the God who has proven His faithfulness over and over again. For us too, this reminds us that we don't just give God the best, we are also to give God first. This is His due and our priority. This Feast was also to mark their dedication and fellowship with the God who provides. 

As the Bible unfolds, this idea of of firstfruits expands and takes on additional meanings. In Num 18:2-13, the firstfruits had another function. The people offered them them to God, but God then gives it to the priests. This order is important -- the people offered to God, who used it to provide for His servants and the people were not to just give it to the priests directly. Thus, the people of Israel also indirectly keeps the priesthood going. It meets the practical need of priests. However, at some point in Israel's history, God's people had lapsed and in 2 Chron 31:4-6, we read of King Hezekiah organizing the people to obey this command again. They were out of fellowship with God when they did not celebrate the feast. Why is this important? Prov 3:9-10 tells us how life works best and inside the wisdom literature, the offering of firstfruits is tied to honoring God. This was the bigger principle behind this offering. 

In the New Testament, Jesus is described as the firstfruits of "those who have fallen asleep"(1 Cor 15:20). We are to consider the resurrection of Christ here. Resurrection is different from resuscitation. Resurrection is to be raised from the dead to never die again. Only one person has been resurrected, and that is Jesus. These verses in 1 Cor promise that later fruit in the pattern of Jesus' resurrection, will arise. The New Testament is taking the idea of firstfruits not just to describe physical harvest, but also spiritual harvest. We will also be guaranteed a physical resurrection. This Feast was ultimately to point us to our resurrection promise.

The Feast of Firstfruits is not just an archaic celebration instituted by God for His people in a certain time. The principle and idea behind this feast also has present implications for us. What do we do with the resources God has given us? Do we tithe? How do you use your time, gifts, relationships, influence, emotional capital? Have you given God the firstfruits in these areas? We give God the best of what we have because we know that all good gifts come from God. And we are not giving anything that we own. We are mere stewards, and we are giving back to Him what is originally His. We live on borrowed time, all of us. None of us can tell God that we are going to do things for Him tomorrow, or at a certain point in time. The Feast of Firstfruits also point us to the hope that is to come -- of our physical resurrection when Christ comes again to make all thing new. How has your identity as a follower of Jesus Christ stamped your life and behaviour completely? How deeply has this identity taken hold of you so it shapes your very life?

Pulpit Commentary
Verse 16. - He brought me into the inner court. The last and the worst form of desecration follows. It was the "inner court" (Joel 2:17) which, after the exile, was entered only by the priests. During the monarchy, however, it seems to have been accessible to kings and other persons of importance, as in the case of Solomon (1 Kings 8:22, 64; 1 Kings 9:25) in the revolution against Athaliah (2 Kings 11:4-15), and Hezekiah (2 Kings 19:14), and Josiah (2 Kings 23:2). Ezekiel does not say that the men whom he saw were priests, though the number twenty-five suggests that they were taking the place of the high priest and the heads of the twenty-four courses of the priesthood (1 Chronicles 24:4-19), and so symbolized the whole order of the priesthood as the seventy elders represented the laity. In 2 Chronicles 36:14 the chief of the priests is spoken of as having been prominent in "polluting the house of the Lord." They were seen turning their backs to the temple of Jehovah, i.e. the sanctuary. The very act was symbolical of their apostasy (2 Chronicles 29:6; Isaiah 1:4; Jeremiah 7:24). And they did this in order that they might look to the east and worship the rising sun. That, and not the temple (Daniel 6:10), was the Kiblah of their adoration. The sun worship here appears to have had a Persian character, as being offered to the sun itself, and not to Baal, as a solar god. Of such a worship we have traces in Deuteronomy 4:19; Deuteronomy 17:3; Job 31:26; 2 Kings 23:5, 11. 

Parallels...

Hebrew
So He brought
וַיָּבֵ֣א (way·yā·ḇê)
Conjunctive waw | Verb - Hifil - Consecutive imperfect - third person masculine singular
Strong's 935: To come in, come, go in, go

me to
אֶל־ (’el-)
Preposition
Strong's 413: Near, with, among, to

the inner
הַפְּנִימִית֒ (hap·pə·nî·mîṯ)
Article | Adjective - feminine singular
Strong's 6442: Interior

court
חֲצַ֣ר (ḥă·ṣar)
Noun - common singular construct
Strong's 2691: A yard, a hamlet

of the house
בֵּית־ (bêṯ-)
Noun - masculine singular construct
Strong's 1004: A house

of the LORD,
יְהוָה֮ (Yah·weh)
Noun - proper - masculine singular
Strong's 3068: LORD -- the proper name of the God of Israel

and there
וְהִנֵּה־ (wə·hin·nêh-)
Conjunctive waw | Interjection
Strong's 2009: Lo! behold!

at the entrance
פֶ֜תַח (p̄e·ṯaḥ)
Noun - masculine singular construct
Strong's 6607: An opening, door, entrance way

to the temple
הֵיכַ֣ל (hê·ḵal)
Noun - masculine singular construct
Strong's 1964: A large public building, palace, temple

of the LORD,
יְהוָ֗ה (Yah·weh)
Noun - proper - masculine singular
Strong's 3068: LORD -- the proper name of the God of Israel

between
בֵּ֤ין (bên)
Preposition
Strong's 996: An interval, space between

the portico
הָֽאוּלָם֙ (hā·’ū·lām)
Article | Noun - masculine singular
Strong's 197: A vestibule

and the altar,
הַמִּזְבֵּ֔חַ (ham·miz·bê·aḥ)
Article | Noun - masculine singular
Strong's 4196: An altar

were about twenty-five
כְּעֶשְׂרִ֥ים (kə·‘eś·rîm)
Preposition-k | Number - common plural
Strong's 6242: Twenty, twentieth

men
אִ֑ישׁ (’îš)
Noun - masculine singular
Strong's 376: A man as an individual, a male person

with their backs
אֲחֹ֨רֵיהֶ֜ם (’ă·ḥō·rê·hem)
Noun - masculine plural construct | third person masculine plural
Strong's 268: The hinder part, behind, backward, the West

to
אֶל־ (’el-)
Preposition
Strong's 413: Near, with, among, to

the temple
הֵיכַ֤ל (hê·ḵal)
Noun - masculine singular construct
Strong's 1964: A large public building, palace, temple

of the LORD
יְהוָה֙ (Yah·weh)
Noun - proper - masculine singular
Strong's 3068: LORD -- the proper name of the God of Israel

and their faces
וּפְנֵיהֶ֣ם (ū·p̄ə·nê·hem)
Conjunctive waw | Noun - masculine plural construct | third person masculine plural
Strong's 6440: The face

toward the east;
קֵ֔דְמָה (qê·ḏə·māh)
Adverb | third person feminine singular
Strong's 6924: The front, of place, time

and they
וְהֵ֛מָּה (wə·hêm·māh)
Conjunctive waw | Pronoun - third person masculine plural
Strong's 1992: They

were bowing to the east
קֵ֖דְמָה (qê·ḏə·māh)
Adverb | third person feminine singular
Strong's 6924: The front, of place, time

in worship
מִשְׁתַּחֲוִיתֶ֥ם (miš·ta·ḥă·wî·ṯem)
Verb - Hitpael - Participle - masculine plural
Strong's 7812: To depress, prostrate

☀️of the sun.
לַשָּֽׁמֶשׁ׃ (laš·šā·meš)
Preposition-l, Article | Noun - common singular
Strong's 8121: The sun, the east, a ray, a notched battlement

✨Every event on God’s calendar is very important to all BELIEVERS in YESHUA. Despite the fact that most Christians have consigned the biblical festivals to a “long-forgotten history” of the Jewish people, these festivals are just AS VITAL to Christian identity TODAY as they were in Bible days! The festivals which YESHUA and the APOSTLES celebrated as they “joined their Jewish families and communities in worship” of the GOD OF ISRAEL still have PROFOUND significance for the Messianic Jewish COMMUNITY and for ALL Christians today.

Pictures of the Messiah🐑

The greatest value of the festivals for Believers in Yeshua is that they REVEAL TRUTHS about the Messiah, just as PAUL, the Jewish rabbi and Christian apostle, pointed out in Colossians 2:16–17: “These [Sabbath and festivals] are a shadow of things to come, the REALITY of which is the Messiah.” All of the seven festivals outlined in Leviticus 23 are prophetic pictures of the Messiah.

There could not be a more PERFECT picture Painted of the “PERSON and WORK of YESHUA HaMashiach” than the three spring festivals. Yeshua was -recognized- as the Lamb of God who would remove the sin of the world by no less a PROPHET than John the BAPTIZER ( John 1:29), so it should have surprised no one when Yeshua was crucified on the very day of Passover. The SAVIOR was also the PERSONIFICATION of matzah (unleavened bread) in that he never succumbed to the leaven of sin (1 PETER 2:22). In fact, he was the BREAD of LIFE who came down from heaven to GIVE everlasting life to ALL who would -believe- upon Him ( John 6:33, 41, 50). Finally, Yeshua was also the FIRSTFRUITS💎 of the resurrection (1 Corinthians 15:23) who was resurrected on the very day of the Festival of Firstfruits🍎 following His crucifixion.

What are the “firstfruits”!of the “wheat” crop?! 

Just as surely as God fulfilled the spring festivals by FILLING them with the GRACE of MESSIAH, so THE FALL🍎 festivals will also be “FULFILLED by YESHUA” at the END of the AGE. Without a doubt, God “WILL SEND Yeshua Messiah” who for the present “must remain in heaven” until the time comes “for God to RESTORE everything as He promised🌈 long ago through His HOLY PROPHETS” (Acts 3:20–21). When the Messiah comes, moreover, He will FULFILL all the events in THE FALL festivals that God has promised throughout Holy Scripture.

Rosh Hashanah: Trumpeting🎺 the “End of the Age
The High Holy Days of the Fall Festivals begin with the celebration of Rosh Hashanah, which is described in Scripture as Yom Teruah, “the day of blowing [of shofars]” (Leviticus 23:24). 🎺The penetrating sound of the shofar (ram’s horn) harkens back to the day when Abraham, at God’s bidding, offered Isaac in the Akedah (“binding”) on the altar on Mount Moriah only to discover that GOD had PROVIDED the sacrifice, a ram caught by his horns in a thicket (Genesis 22:8, 13). The shofar blasts that are sounded on Rosh Hashanah to initiate the “Ten Days of AWE are “designed to call God’s people to introspection” and to repentance.”

Rosh Hashanah is FILLED with PROPHETIC INSIGHT, -foretelling the future- TIME when, as the end of the AGE approaches, God has ordained a great day of AWaKENING! The divine shofar will be blown on Yom Teruah (Rosh Hashanah), and this clarion call will be designed to “summon Israel, the Church, and the world to “repentance and restoration.” Joel 2:1 speaks of this Yom Teruah: “Blow the shofar in Zion...let all the inhabitants of the land tremble: for the day of the Lord is coming; surely IT IS NEAR.” The importance of this event cannot be overemphasized, for Scripture declares that it will be GOD HIMSELF who will blow the shofar to SIGNAL the end of the age (Zechariah 9:14), just as tradition maintains that God Himself blew the shofar in the beginning of time in order to initiate the creation of the universe on Rosh Hashanah (Talmud: Rosh Hashanah 27a). The last shofar sound will issue forth this proclamation: “The kingdom of the world has become the kingdom of our Lord and of his Messiah, and he will REIGN forever and ever”(Revelation 11:15).

Yom Kippur: A Final Day of Atonement
In biblical times, Yom Kippur was the culmination of the Ten Days of AWE that began on Rosh Hashanah. It was the one day on the divine calendar when God annually summoned His people to repentance and RENEWAL. This was a day of fasting and “soul-searching” in which the people of Israel examined themselves “to see that they were in the faith,” a practice that carried over into the nascent Messianic community of the first century (1 Corinthians 11:28). Again, what Israel did for centuries was DESIGNED by God to be prophetic of what -would occur- at the “end of the age.”

Subsequent to the prophetic Rosh Hashanah blowing of the shofar in Zion to awaken all people, Yom Kippur SPEAKS of another profound End-Time event when “all Israel will be saved,” when “the DELIVERER will come out from ZION and will remove ungodliness from Jacob” (Romans 11:26). This will be a time of restoration during which Israel is destined to RECOGNIZE the Messiah and to be RECONCILED to Him (Zechariah 12:10). It will be the ultimate fulfillment of Israel’s final Day of Atonement when God Himself will open a “fountain for sin to the HOUSE of DAVID” (Zechariah 13:1), PROCLAIM all of those who obey the sound of His shofar to be RIGHTEOUS (Isaiah 60:21), and INSCRIBE their names in the Lamb’s Book of Life 🌳 (Revelation 21:27).❤️

Sukkot: The Messiah -IS COMING-

The Festival of Sukkot is the final Torah festival on God’s calendar. This festival celebrated the end of all the harvests, but it also required the Israelites to “remember their journey” from Egypt to Canaan by living for seven days in sukkot (booths or huts). Sukkot was described as “The Season of Our Joy” (Zeman Simchatenu) and was the greatest time of celebration on the calendar. In fact, the first- century celebration of Sukkot in Jerusalem was beyond spectacular. While recalling the transitory nature of human existence, this festival also featured TIME to SEARCH the heavens for SIGNS of the Messiah’s coming.

In Scripture, Sukkot is called both “Tabernacles” (Leviticus 23:34) and “Ingathering” (Exodus 23:16). Interestingly, when it is called “Ingathering,” it is said to occur “at the end of the year” or “at the turn of the year.” This correlates perfectly with Yeshua’s declaration that “the harvest is the end of the age” (Matthew 13:39). The second coming of Yeshua, therefore, corresponds to Tabernacles, the prophetic time when the Messiah will “send his ANGELS with a “great shofar” and they will GATHER together His ELECT from the four winds, from one end of the sky to the other” (Matthew 24:31). In that Sukkot speaks of of the age, both Jews and Gentiles—all the righteous of the earth— will be gathered together in Jerusalem to CELEBRATE the last great festival (Tabernacles).“ingathering,” it also predicts that at the end of the age, both Jews and Gentiles—all the righteous of the earth— will be gathered together in Jerusalem to celebrate the LAST great festival (Tabernacles).

This Sukkot will celebrate the inauguration of the UNIVERSAL KINGDOM of the Messiah in God’s capital city, Jerusalem. This was the event of which Paul spoke, the time when in an administration “suitable to the fullness of the times,” God Himself will “bring all things in heaven and on earth together under One head, even Messiah” (Ephesians 1:10). At that time, the righteous will rule with Yeshua HaMashiach (Revelation 20:6), and together they will “possess the everlasting kingdom of God forever and ever” (Daniel 7:18).

For many centuries, millions of Jews around the world have prayed for the coming of the Messiah. Likewise, for two millennia Christians from every nation of the Earth have awaited the return of the Messiah. In the fullness of time, the expectations of both Jews and Christians will finally come to fruition🍎. God’s Word of promise is CERTAIN: “Until heaven and earth pass away, not one yud or crown will pass from the Torah until all is fulfilled” (Matthew 5:18). What Yeshua HaMashiach began 2,000 years ago when He fulfilled the spring festivals will be completed when He returns to fulfill the fall festivals.


🕊⏱🌈👏🏻CELEBRATE!👏🏻🌈⏱🕊

Messianic Believers—and, indeed, all Christians— still have the same opportunities that the earliest apostles had to remember the most important events in salvation history when they celebrate Pesach and Shavuot. Likewise, they can hear the sound of the shofar on Rosh Hashanah, challenging them to pray on Yom Kippur for repentance and for the redemption of Israel and of the whole world. They can also join together in celebrating Sukkot, anticipating the RETURN of Yeshua HaMashiach in what will be the climactic event of ALL human HISTORY— the time when God will again tabernacle with HUMANITY (Revelation 21:3) and all the people of the Earth will live in HARMONY as God spreads over them His universal sukkah shalom (Luke 2:14; 19:38).


​Measurement of the Temple: cornerstone; 

Ezekiel 41:1
Verse Concepts
Then he brought me to the nave and measured the side pillars; six cubits wide on each side was the width of the side pillar.

Ezekiel 41:4
Verse Concepts
He measured its length, twenty cubits, and the width, twenty cubits, before the nave; and he said to me, “This is the most holy place.”

Ezekiel 41:2
Verse Concepts
The width of the entrance was ten cubits and the sides of the entrance were five cubits on each side. And he measured the length of the nave, forty cubits, and the width, twenty cubits.

Ezekiel 40:48
Verse Concepts
Then he brought me to the porch of the temple and measured each side pillar of the porch, five cubits on each side; and the width of the gate was three cubits on each side.

Ezekiel 42:15
Verse Concepts
Now when he had finished measuring the inner house, he brought me out by the way of the gate which faced toward the east and measured it all around.

https://bible.knowing-jesus.com/topics/Facing-East

“The stone the builders rejected has become the capstone" (Psalm 118:22).
​
The image comes from the ancient quarries where highly-trained stonemasons carefully chose the stones used in construction. No stone was more important than the cornerstone because the integrity of the whole structure depended on the cornerstone containing exactly the right lines. If the cornerstone was not exactly right, the entire building would be out of line. For that reason, builders inspected many stones, rejecting each one until they found the one they wanted. Rejected stones might be used in other parts of the building, but they would never become the cornerstone or the capstone (the first and last stones put in place).
When Peter preached to the Jewish leaders in Acts 4:8–12, he quoted Psalm 118:22 to show that Jesus is the rejected stone whom God made to be the cornerstone of salvation. They (the Jewish leaders) rejected him, but God not only accepted him but put him in the position of highest honor.
​
Peter pressed the point home with this powerful conclusion: “Salvation is found in no one else, for there is no other name under heaven given to men by which we must be saved" (Acts 4:12). These words are utterly exclusive. There is no other hope, no other way, and no other name than the name of Jesus. If we would be saved, we must come God’s way or we won’t come at all.
Do not be like the builders who rejected God’s Stone of salvation! Do not stumble over this rejected stone. The very stone the builders rejected has become the head of the corner.—the Cornerstone of eternal salvation! ❤️

​
Measurement instruments and systems

measurement, the process of associating numbers with physical quantities and phenomena. Measurement is fundamental to the sciences; to engineering, construction, and other technical fields; and to almost all everyday activities. For that reason the elements, conditions, limitations, and theoretical foundations of measurement have been much studied. See also measurement system for a comparison of different systems and the history of their development. Measurements may be made by unaided human senses, in which case they are often called estimates, or, more commonly, by the use of instruments, which may range in complexity from simple rules for measuring lengths to highly sophisticated systems designed to detect and measure quantities entirely beyond the capabilities of the senses, such as radio waves from a distant star or the magnetic moment of a subatomic particle. Measurement begins with a definition of the quantity that is to be measured, and it always involves a comparison with some known quantity of the same kind. If the object or quantity to be measured is not accessible for direct comparison, it is converted or “transduced” into an analogous measurement signal. Since measurement always involves some interaction between the object and the observer or observing instrument, there is always an exchange of energy, which, although in everyday applications is negligible, can become considerable in some types of measurement and thereby limit accuracy. In general, measuring systems comprise a number of functional elements. One element is required to discriminate the object and sense its dimensions or frequency. This information is then transmitted throughout the system by physical signals. If the object is itself active, such as water flow, it may power the signal; if passive, it must trigger the signal by interaction either with an energetic probe, such as a light source or X-ray tube, or with a carrier signal. Eventually the physical signal is compared with a reference signal of known quantity that has been subdivided or multiplied to suit the range of measurement required. The reference signal is derived from objects of known quantity by a process called calibration. The comparison may be an analog process in which signals in a continuous dimension are brought to equality. An alternative comparison process is quantization by counting, i.e., dividing the signal into parts of equal and known size and adding up the number of parts.

Other functions of measurement systems facilitate the basic process described above. Amplification ensures that the physical signal is strong enough to complete the measurement. In order to reduce degradation of the measurement as it progresses through the system, the signal may be converted to coded or digital form. Magnification, enlarging the measurement signal without increasing its power, is often necessary to match the output of one element of the system with the input of another, such as matching the size of the readout meter with the discerning power of the human eye.

One important type of measurement is the analysis of resonance, or the frequency of variation within a physical system. This is determined by harmonic analysis, commonly exhibited in the sorting of signals by a radio receiver. Computation is another important measurement process, in which measurement signals are manipulated mathematically, typically by some form of analog or digital computer. Computers may also provide a control function in monitoring system performance. Measuring systems may also include devices for transmitting signals over great distances (see telemetry). All measuring systems, even highly automated ones, include some method of displaying the signal to an observer. Visual display systems may comprise a calibrated chart and a pointer, an integrated display on a cathode-ray tube, or a digital readout. Measurement systems often include elements for recording. A common type utilizes a writing stylus that records measurements on a moving chart. Electrical recorders may include feedback reading devices for greater accuracy.

The actual performance of measuring instruments is affected by numerous external and internal factors. Among external factors are noise and interference, both of which tend to mask or distort the measurement signal. Internal factors include linearity, resolution, precision, and accuracy, all of which are characteristic of a given instrument or system, and dynamic response, drift, and hysteresis, which are effects produced in the process of measurement itself. The general question of error in measurement raises the topic of measurement theory.


Measurement theory

Measurement theory is the study of how numbers are assigned to objects and phenomena, and its concerns include the kinds of things that can be measured, how different measures relate to each other, and the problem of error in the measurement process. Any general theory of measurement must come to grips with three basic problems: error; representation, which is the justification of number assignment; and uniqueness, which is the degree to which the kind of representation chosen approaches being the only one possible for the object or phenomenon in question. Various systems of axioms, or basic rules and assumptions, have been formulated as a basis for measurement theory. Some of the most important types of axioms include axioms of order, axioms of extension, axioms of difference, axioms of conjointness, and axioms of geometry. Axioms of order ensure that the order imposed on objects by the assignment of numbers is the same order attained in actual observation or measurement. Axioms of extension deal with the representation of such attributes as time duration, length, and mass, which can be combined, or concatenated, for multiple objects exhibiting the attribute in question. Axioms of difference govern the measuring of intervals. Axioms of conjointness postulate that attributes that cannot be measured empirically (for example, loudness, intelligence, or hunger) can be measured by observing the way their component dimensions change in relation to each other. Axioms of geometry govern the representation of dimensionally complex attributes by pairs of numbers, triples of numbers, or even n-tuples of numbers.

The problem of error is one of the central concerns of measurement theory. At one time it was believed that errors of measurement could eventually be eliminated through the refinement of scientific principles and equipment. This belief is no longer held by most scientists, and almost all physical measurements reported today are accompanied by some indication of the limitation of accuracy or the probable degree of error. Among the various types of error that must be taken into account are errors of observation (which include instrumental errors, personal errors, systematic errors, and random errors), errors of sampling, and direct and indirect errors (in which one erroneous measurement is used in computing other measurements).

Measurement theory dates back to the 4th century BC, when a theory of magnitudes developed by the Greek mathematicians Eudoxus of Cnidus and Thaeatetus was included in Euclid’s Elements. The first systematic work on observational error was produced by the English mathematician Thomas Simpson in 1757, but the fundamental work on error theory was done by two 18th-century French astronomers, Joseph-Louis Lagrange and Pierre-Simon Laplace. The first attempt to incorporate measurement theory into the social sciences also occurred in the 18th century, when Jeremy Bentham, a British utilitarian moralist, attempted to create a theory for the measurement of value. Modern axiomatic theories of measurement derive from the work of two German scientists, Hermann von Helmholtz and Otto Hölder, and contemporary work on the application of measurement theory to psychology and economics derives in large part from the work of Oskar Morgenstern and John von Neumann.

Since most social theories are speculative in nature, attempts to establish standard measuring sequences or techniques for them have met with limited success. Some of the problems involved in social measurement include the lack of universally accepted theoretical frameworks and thus of quantifiable measures, sampling errors, problems associated with the intrusion of the measurer on the object being measured, and the subjective nature of the information received from human subjects. Economics is probably the social science that has had the most success in adopting measurement theories, primarily because many economic variables (like price and quantity) can be measured easily and objectively. Demography has successfully employed measurement techniques as well, particularly in the area of mortality tables. 

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