Tamarajo is an avid Bible Studier who loves nothing more than to seek out the treasures in God's Word and share them with others.
God's Word is more extraordinary than one could ever imagine. His will and ways are, remarkably, not only conveyed in written form but are also communicated and confirmed in scientific, mathematic, and geometric terms.
The patterns and mathematical conclusions, in nature and science, follow similar arrangements and structures in Biblical text that can many times illustrate for us spiritual truths.
. . . since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made.
— Romans 1:20
In this writing, we will be looking at how the Genesis creation account is not a mystical or magical event but a very scientific and even mathematical one. We will examine how God's Word creates and how the snowflake illustrates and confirms this process.
God's Word Patterns the Created World
The patterns of nature and its mathematical and geometrical expressions are well noted in math and science. This phenomenon is most commonly attributed, in the secular world, to evolutionary processes. God's conversation with Job offers us a much more significant consideration.
“But now ask the beasts, and they will teach you;
And the birds of the air, and they will tell you;
Or speak to the earth, and it will teach you;
And the fish of the sea will explain to you.
Who among all these does not know
That the hand of the Lord has done this,
In whose hand is the life of every living thing,
And the breath of all mankind?
— " Job 12:7-10
The realities of geometry and mathematics confirm what we read in the text of God's Word and reinforce the faith that we proclaim.
“Holy, holy, holy is the Lord of hosts; The whole earth is full of His glory!”
— Isaiah 6:3
God has designed His Word and world so that no matter how we measure and compare the two, the same truth is consistently revealed and confirmed.
There are infinite treasures to be discovered and mined in these spectacular and privileged God-given resources of His written Word and the created world.
"There is a language in nature that speaks of the existence of God. It is the language of order, beauty, perfection, and intelligence. Some time ago a scientist told me that when he gave serious thought to the majestic order of the universe and its obedience to unchanging law, he could not help but believe in God. He had become aware that God was speaking through nature."
— Billy Graham
Sonoluminescence—Let There Be Light
Before we discuss snowflakes, we will study the two most fundamental elements of the created world; water and light. Both play an integral part in the processes of snowflake development.
The first chapter of Genesis describes the earth as a dark, formless, dysfunctional mass of water.
And the earth was without order, and empty; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
— Genesis 1:2
The first act of creation involved God's voice and light. A scientific discovery known as Sonoluminescence animates God's speaking over the dark and watery chaos and bringing forth light in the Genesis beginning.
. . . the Spirit of God was hovering over the face of the waters. Then God said, “Let there be light”; and there was light
— Genesis 1:2-3
Sono, meaning "sound," and luminescence," "light," illustrates how the frequency and vibration of sound, delivered with enough intensity and power, moves through the water and produces light.
In praise of God's holiness and majesty, King David makes a double mention of God's voice moving over the waters.
The voice of the Lord is over the waters;
The God of glory thunders;
The Lord is over many waters.
The voice of the Lord is powerful;
The voice of the Lord is full of majesty.
— Psalm 29:1-4
The video above explains a part of the process of producing light from sound and involves what is known as acoustic cavitation. Cavities form when an intense and powerful sound wave moves through the water then collapses. According to a Nature.com article, this type of collapse produces internal temperatures up to thousands of degrees Kelvin.
Acoustic cavitation—the formation and implosive collapse of bubbles—occurs when a liquid is exposed to intense sound. Cavitation can produce white noise, sonochemical reactions, erosion of hard materials, rupture of living cells and the emission of light, or sonoluminescence. The concentration of energy during the collapse is enormous: the energy of an emitted photon can exceed the energy density of the sound field by about twelve orders of magnitude, and it has long been predicted that the interior bubble temperature reaches thousands of degrees Kelvin during collapse3
The process of cavity formation from sound involves the splitting or tearing apart of water molecules. The creation narrative that exhibits God's spoken word describes something that sounds very similar.
Then God said, “Let there be a firmament (space) in the midst of the waters, and let it divide the waters from the waters.
— Genesis 1:6
Separation of Waters: A Horizontal and Vertical View
In the book of Exodus, we see a type of creative cavitation that includes the splitting and collapse of waters; God created a nation by causing His people to pass through a parted sea.
. . . the Lord said to Moses, “Why do you cry to Me? Tell the children of Israel to go forward. But lift up your rod, and stretch out your hand over the sea and divide it. And the children of Israel shall go on dry ground through the midst of the sea.
— Exodus 14:15-16
The above case was a horizontal event. There was a vertical splitting of waters defined as above and below at creation.
God made the expanse, and separated the waters which were below the expanse from the waters which were above the expanse; and it was so.
— Genesis 1:7
Combining these two images in horizontal and vertical imagery allows us to see a cross in the created spaces. Each symbolizes a physical (horizontal) and spiritual (vertical) transaction that joined what once had become separated. These combined scenes are reiterated at the cross with the tearing of the temple veil and the splitting of rocks.
Now it was about the sixth hour, and there was darkness over all the earth until the ninth hour. Then the sun was darkened, and the veil of the temple was torn in two . . . and the earth quaked, and the rocks were split . . . Jesus had cried out with a loud voice. The tombs were opened, and many bodies of the saints who had fallen asleep were raised.
— Luke 23:44, Matthew 27:51
At the moment of this chaotic darkness, following the creation pattern, a loud voice issues forth and then comes the light.
. . . Very early in the morning, on the first day of the week, they came to the tomb when the sun had risen (light) And they said among themselves, “Who will roll away the stone from the door of the tomb for us?” But when they looked up, they saw that the stone had been rolled away—for it was very large. And entering the tomb, they saw a young man clothed in a long white robe sitting on the right side; and they were alarmed. But he said to them, “Do not be alarmed. You seek Jesus of Nazareth, who was crucified. He is risen!
— Mark 16 3-6
Light Resurrects Water
Light and resurrection are connected. Sunlight calls up the water droplets from below into the skies above. (separating waters above and waters below in Genesis chapter one).
After the division of waters on day two of creation, productive inhabitable land appears on the third day in a type of resurrection from the dark, chaotic waters.
Then God said, “Let the waters under the heavens be gathered together into one place, and let the dry land appear”; and it was so . . . Then God said, “Let the earth bring forth grass, the herb that yields seed, and the fruit tree that yields fruit according to its kind, whose seed is in itself, on the earth”; and it was so.
— Genesis 1:9,11
Much Like the third day of creation's resurrection of land and vegetation following a dark and dysfunctional mass, Jesus is resurrected from the dead on the third day after the darkness of the cross.
On the first day of the week, at early dawn, they came to the tomb bringing the spices which they had prepared. And they found the stone rolled away from the tomb, but when they entered, they did not find the body of the Lord Jesus. While they were perplexed about this, behold, two men suddenly stood near them in dazzling clothing; and as the women were terrified and bowed their faces to the ground, the men said to them, “Why do you seek the living One among the dead? He is not here, but He has risen. Remember how He spoke to you when He was still in Galilee, saying, ‘The Son of Man must be delivered into the hands of sinful men, and be crucified, and the third day rise again.’ ”
— Luke 24:1-7
In this case, the masses of people depict the chaotic waters.
Woe to the multitude of many people
Who make a noise like the roar of the seas,
And to the rushing of nations
That make a rushing like the rushing of mighty waters!
— Isaiah 17:12
John's Gospel declares Jesus to be the light just before Christ's water baptism.
There came a man sent from God, whose name was John. He came as a witness, to testify about the Light so that all might believe through him.
— John 1:6
In the baptism scene, there is also a parting of the heavens. The Hebrew word "heaven (שָׁמַיִם)" includes the word "water (מַיִם)." This again links us with the beginning creation event.
When He had been baptized, Jesus came up immediately from the water; and behold, the heavens were opened (Mark says parting) voice came from heaven, saying, “This is My beloved Son, in whom I am well pleased (Recall the Spirit of God hovering over the face of the waters in the beginning).
— Matthew 3:16-18
In connection with baptism, Moses led God's newly created people through a type of baptism by passing them through the sea. Paul picks up on this link in his letter to the Corinthian church.
. . . our fathers were under the cloud, all passed through the sea, all were baptized into Moses in the cloud and in the sea.
— I Corinthians 10:1-2
Moses prophetically declares a future Messiah who transforms us into new creations by His spoken words and our faith in what He has done.
The Lord your God will raise up for you a Prophet like me from your brethren. Him you shall hear in all things, whatever He says to you.
— Acts 3:22
Stephen, also in the book of Acts, reiterates.
This is that Moses who said to the children of Israel, ‘The Lord your God will raise up for you a Prophet like me from your brethren. Him you shall hear.
— Acts 7:37
Creation Through Vibration Frequencies
The following Psalm congruently testifies to God's creation of the heavens and the earth through the vibrational frequencies of His voice.
The first section concerns the heavens, and the last part discusses the earth. Sandwiched between heaven and earth's praises is the reason for such glorious praise. He commanded, and they were created—all of the creation dances to the tune of His commands and decrees.
Praise the Lord from the heavens;
Praise Him in the heights!
Praise Him, all His angels;
Praise Him, all His hosts!
Praise Him, sun and moon;
Praise Him, all you stars of light!
Praise Him, you heavens of heavens,
And you waters above the heavens!
Let them praise the name of the Lord,
For He commanded, and they were created.
He also established them forever and ever;
He made a decree which shall not pass away.
Praise the Lord from the earth,
You great sea creatures and all the depths;
Fire and hail, snow and clouds;
Stormy wind, fulfilling His word;
Mountains and all hills;
Fruitful trees and all cedars;
Beasts and all cattle;
Creeping things and flying fowl;
Kings of the earth and all peoples;
Princes and all judges of the earth;
Both young men and maidens;
Old men and children.
— Psalm 148:1-12
The videos included in this section and the next are an excellent visual of how sound can construct order and pattern to randomness by transferring sound wave energy into things. This process is called resonance.
The whole creation is nothing but the visible curtain behind which radiates the exalted working of God’s thinking.
— Abraham Kuyper
From Death to Life
God called and summoned everything into being out of a deep, dark, and dead chaos, then transformed it into a constructive living organism by His command.
. . . God, who gives life to the dead and calls those things which do not exist as though they did.
— Romans 4:17
Death is exhibited in the process of decomposition, disorganizing, disintegrating, and dissolving. It is a turning of something into nothing. Alternatively, a highly organized composition occurs when human life is formed within the womb. This process involves constructing, arranging, and developing what seems like nothing into a valuable, meaningful, and productive someone.
The Bible speaks of a necessary new birth of a vertical or spiritual nature. We have all been born a living physical being on a horizontal level tainted by the darkness and deadness of sin, but God has granted, through His Son, the opportunity to be made new.
For it is the God who commanded light to shine out of darkness, who has shone in our hearts to give the light of the knowledge of the glory of God in the face of Jesus Christ.
— II Corinthians 4:6
Therefore, if anyone is in Christ, he is a new creation; old things have passed away; behold, all things have become new.
— II Corinthians 5:17
When Jesus speaks to Nicodemus about being born again, He speaks of first being born of water and then the Spirit. This all, without fail, follows the pattern set for us in the Genesis beginning narrative with sound, water, and light.
Jesus answered, “Most assuredly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God . . . the light has come into the world . . . the friend of the bridegroom, who stands and hears him, rejoices greatly because of the bridegroom’s voice . . . (final sentence spoken by John the Baptist, witness of the Light)
— John 3:5,19,28
The snowflake, primarily made of water, offers us a vivid and detailed exhibit and illustration of the creative force of God's spoken Word.
The uniquely intricate snowflakes patterns are something many have marveled at for centuries, especially since the invention of the microscope. Johannes Kepler, a late fifteen-early sixteen hundred's astronomer and mathematician, was the first to analyze these sophisticated natural wonders of crystallized water. As we shall see, the snowflake illustrates the intricate beauty of God's Word that invites us to be like Johannes Kepler and take the time to examine His truth microscopically.
O magnify the Lord with me . . .
— Psalm 34:3
Another consideration from the book of Job is entering the treasury of snow.
Have you entered the treasury of snow?
— Job 38:22
The word treasury above refers to a storehouse of precious things. Undoubtedly, there is a storehouse of valuable treasures to be discovered in thoughtfully examining snow's development and properties.
Snowflake Development—Order Out of Chaos
Snowflakes result from water molecules developing into a unique hexagonal (six-sided) shape. This process testifies to the biblical account of the heavens and the earth created in six days and represents the handiwork of God's Word based on the ten times "God said, and it was."
God saw all that He had made, and behold, it was very good. And there was evening and there was morning, the sixth day.
— Genesis 1:31
When water is in its liquid state, its molecules are in a chaotic arrangement. They tumble around randomly, much like the watery dark void "at the beginning." This scene also depicts our lives without Christ. When water resurrects into a cooled atmosphere above, it is transformed by its molecules' organization into hexagonal patterns as it freezes. This part of the development illustrates how the Word of God can change our lives through the resurrected Word of God that is Christ.
Elihu Job's friend describes this scientific process in the natural quite correctly in this statement.
From the breath of God is frost given, And the breadth (widely spaced) of waters is straitened (constrained and narrowed).
— Job 37:10
God's breath animates the crystal-forming process of water vapor condensing as it cools. "The breadth of waters" describes the once warm water molecules spaced widely and randomly apart and then are "straitened," which in Hebrew translates more correctly constrained and narrowed. This type of organization accurately describes how the molecules begin to pack together tightly when the water droplets are cooled. The water molecules are no longer random but form and grow into highly ordered intricate designs.
Snowflake development is a fascinating visual perspective of the creative attribute of God's speech bringing order out of chaos.
Anne Marie Helmenstine, a chemistry expert, also writes a similar descriptive process of the purposeful design from chaos, referring to the formation of snowflakes.
. . . water molecules arrange themselves in predetermined spaces and in a specific arrangement to fit the spaces and maintain symmetry.
From this description of the process, we understand that the created world animated by the snowflake was specifically arranged and pre-determined by God Himself and maintained by Him.
. . . by him were all things created, that are in heaven, and that are in earth, visible and invisible . . . and by him all things consist (are held together).
— Colossians 1:16-17
. . . upholding all things by the word of his power.
— Hebrews 1:3
He has made the earth by His power; He has established the world by His wisdom, And stretched out the heaven by His understanding.
— Jeremiah 51:15
The prophet Jeremiah tells us that God established (ordered and prepared) the world by His wisdom. We see this accomplished in Genesis chapter one via His spoken Word. According to the above verse, His Words have substance and power.
The one who was before all things (Col 1:17), and by whom all things were made (John 1:3), developed the created world by the following.
His word was with power.
— Luke 4:32
God's invitation to an ordered productive life with Him is found in the book of Isaiah. In the fifty-fifth chapter, otherwise known as the Gospel of Isaiah, God uses the metaphor of snow coming down from heaven to animate for us His word that goes comes down from above and makes things useful and productive.
. . . as the rain comes down, and the snow from heaven, And do not return there . . . So shall My word be that goes forth from My mouth; ( . . . and God said) It shall not return to Me void, But it shall accomplish what I please ( . . . and God saw . . . that it was good).
— Isaiah 55:11 / Genesis 1
A snowflake's intricate, organized development from disorganized water molecules demonstrates how God's spoken Word from heaven can bring order and function out of chaos. In the above verse, I have interwoven, in parenthesis, the Genesis creation account that parallels this portion of Scripture.
Moreover, the description of snowflake development metaphorically describes and illustrates the concept of resurrection, connecting us with "the beginning" narrative.
"Grant me intention, purpose and design—That's near enough for me to the divine."
— Robert Frost
The Math and Geometry of Wisdom
The numeric part of this story is equally fascinating. The ancient Hebrews did not have a separate numbering system, and therefore letters were representative of numbers. The first letter of their alphabet would have been "one," the second "two," etc. By adding or multiplying the number/letters of Words or phrases in the Scriptures, common themes were discovered to be associated with specific numbers and could formulate geometric patterns. By understanding that words represented by numbers can form geometric shapes, we might be able to see how God's Word did frame the worlds. God's speech was not a magical abracadabra event; it was a very scientific occurrence.
This reasoning makes God's intelligence particularly stunning in that the master mathematician could design a written text that could contain and express multi-dimensionally His Word world and its functions.
A Sphere of Hexagons
The Hebrew word for wisdom referred to in Jeremiah 51:15, noted in the "Snowflake development" section, is chokmah. Its letters added together ordinally (Ex. 1,2,3 . . . ) equal 37, which is a hexagonal number meaning 37 dots arranged together to form a hexagon. It is the foundation from which snowflakes build and illustrates the wisdom with which God created all things.
The numeric presentation for the Hebrew word for wisdom "chokmah," added together, according to standard Hebrew Gematria (letters 1-10 count ordinally after ten letters represent in units of 10 such as 10,20,30 until 100 then letters count in 100's), is 73 and is considered a star number (number of dots in a star pattern as displayed in the image heading this section).
We could view the ordinal formula and its hexagonal form as a representation of the earth. In this case, a sphere consists of hexagons. The Gematria value that forms a star, we might say then, represents the heavens, confirming and testifying that He created it all, the heavens and the earth, not just verbally but mathematically and geometrically. There is nothing mystic about God. He makes perfect sense out of what is seemingly random.
The snowflake pattern includes both numbers. If we were to line up all the digits of these two numbers, we would see 3773. If we overlay the sevens by joining earth—37, a hexagonal number, and heavens—73, a star number, overlaying one seven—the number of God's fulfillment, upon the other, we see the number 373. The number 373 is a fractal expression of a snowflake. A snowflake is a seemingly useless speck of dust joined with the purified resurrected water in the heaven/sky above.
A couple of significant Biblical phrases with a Gematria of 373 substantiate this entire topic.
— Proverbs 31:21 (373)
"The voice of the Lord is full of majesty"
— Proverbs 29:4 (373)
The Greek word Logos, when expressed numerically, also values at 373.
In the beginning was the Word (Logos), and the Word was with God, and the Word was God
— John 1:1
The first sentence in the Bible that sums up creation adds up to 2701, which is the equivalent of 37x73.
The number three in Scripture is consistent with solid, real, and substantial things and is exhibited in three-dimensional objects. It also illustrates the realities and credibility of the spirit realm.
. . . faith is the substance of things hoped for, the evidence of things not seen (spirit) . . . By faith we understand that the worlds were framed by the word of God . . . he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him.
— Hebrews 11:1,3,6
Faith is full of substance. God, a spirit, and His Word are real and solid as a rock. They are undeniable realities.
He only is my rock and my salvation.
— Psalm 62:2
The number seven in Scripture speaks of fulfillment, satisfaction, and completion. This interpretation is evidenced and imaged by the seventh day of the created universe when God saw all He made, and it was good. The very first sentence in the Bible consists of seven Hebrew words expressing and summarizing the fulfillment of the creative events that follow.
The following experience I am about to share continues to substantiate the hexagonal foundation of crystal formation and God's created order of things via His Word.
22 Degree Halo and Hexagonal Ice Crystals
On the 10th of April, 2014, our church hosted a "Jews for Jesus" presentation on Christ in the Passover, with the actual Passover being the 15th of April. The young lady who hosted the presentation lodged at my home that night. We arrived at my house after dark. When I stepped outside the car and looked up at the sky, the moon was encircled with a beautiful halo.
A moon halo, otherwise known as a 22-degree halo, occurs when light from the sun or the moon is refracted through "hexagonal" ice crystals in the atmosphere at 22-degree angles. As I looked this up, I couldn't help but recall the 22 letters of the Hebrew Aleph-bet and the Bible Wheel discovery.
The 22 Spokes of the Bible Wheel
The Hebrew aleph-bet, with which the Old Testament is written, consists of twenty-two letters. The entire written Word of God itself contains sixty-six books. Sixty-six is the equivalent of 22 x 3. If you laid out these books in a linear fashion and rolled them up three times like a scroll, you would have a circle that consists of twenty-two spokes, each containing three books of the Bible each, as shown in the diagram above.
Notice that each spoke is headed with a letter of the Hebrew aleph-bet. The Hebrew language is a pictograph language meaning that the letters, in their most ancient form, were represented by an illustrative image that aided in understanding the concept of the word in which it was used. Each spoke in the Bible wheel is spectacularly and consistently themed, with aspects of the pictographs representing it in each of the books included in a particular spoke.
Three Divisions Perfectly Organized
The divisions of the Bible can also be neatly organized in this format. If you look closely, you can see the top of a cross behind the most central circle representing the New Testament in the image above.
Let There Be Light
The 22-degree halo gives us the visual of God's light refracting through the wheel of His Word, illuminating the darkness as we saw in Genesis 1:3 earlier in this article.
Honestly, how can a book spanning so much time with so many authors make this happen? It's because there really is only one author, namely God Himself, who orchestrated it all.
It has recently been discovered that Saturn has a hexagonal (six-sided) storm on its North Pole. It is the sixth planet from the sun and is known as "Shabbatai" by the Jewish people. This name refers to the Sabbath day of rest that honors God's six days of creative work. What an image in that the six planets revolve around the sun representing that all of our days and work should revolve around the Son Jesus, the light of the world whose work on the cross made us new creations.
. . . if anyone is in Christ, he is a new creation.
— II Corinthians in Christ
The storm is theorized to be bordered by some jet stream. Once again, we see the stamp of God imaging in space His creative patterns and power and containing and ordering of chaos. He is in control of all things and sovereign.
God Calculates With Precision
The heavens declare the glory of God;
And the firmament shows His handiwork.
Day unto day utters speech,
And night unto night reveals knowledge.
There is no speech nor language
Where their voice is not heard.
Their measuring line has gone out through all the earth,
And their words to the end of the world.
— Psalm 19:1-4
Did you catch the measuring line part? Everything He does is precisely calculated as well as evidenced and displayed in all that He has made.
Who has measured the waters in the hollow of His hand,
Measured heaven with a span
And calculated the dust of the earth in a measure?
Weighed the mountains in scales
And the hills in a balance?
— Isaiah 40:12
The writer of Hebrews explains.
By faith we understand that the worlds were framed by the word of God, so that the things which are seen were not made of things which are visible.
— Hebrews 11:3
These formations of hexagonal structures are further revealing to us how God's Word has creative integrity.
This section concludes the Snowflake exhibit of the Word of God.
We began this article with our foundation in Isaiah 55 that connects the imagery of snow and God's Word. This chapter is also known as the Gospel of Isaiah. I will wrap up this part with its simple yet profound invitation.
Seek the Lord while He may be found,
Call upon Him while He is near
Let the wicked forsake his way,
And the unrighteous man his thoughts;
Let him return to the Lord,
And He will have mercy on him;
And to our God,
For He will abundantly pardon.
— Isaiah 55:6-7
The next time you see snow, I hope you will consider God's Word's intricacy, power, and accomplishment.
3McNamara, W., Didenko, Y. & Suslick, K. Sonoluminescence temperatures during multi-bubble cavitation. Nature 401, 772–775 (1999). https://doi.org/10.1038/44536
© 2014 Tamarajo
Tamarajo (author) on June 16, 2014:
Hello Deborah, Amen He truly is awesome.
‘Ah, Lord God! Behold, You have made the heavens and the earth by Your great power and outstretched arm. There is nothing too hard for You ~ Jeremiah 32:17
We certainly can trust Him and what He has said. I have much I am trusting Him for as well concerning my family. May God continue to strengthen and confirm our faith as we look to Him alone as our Rock and our Refuge!
I am pleased that this revelation was a blessing and faith builder for you as it is for me as well. His wonders never cease. It is easy to see how we will spend eternity learning and discovering His awesomeness and goodness because it is so infinite.
God bless you for stopping by to read and I appreciate your confirming comment.
Deborah L Vasquez from Palmdale, California on June 13, 2014:
All I can say is Wow!! You are amazing the Lord has truly gifted you for ministry! I am going through something with my youngest daughter who has five children,I found my self worrying and praying,your teaching made me see that all I spoke over her and taught her has already made a difference in her life! And that casting my cares on the Lord because He cares for me has brought me peace concerning my daughter! We serve an awesome God and nothing is to hard for Him! Wow your teaching gives me a whole new understanding on that Scripture! Thank you so much Deborah
Tamarajo (author) on June 07, 2014:
Thank you Bill. I was hoping that the presentation would do just that...glorify Him! Because it sure glorified Him in my eyes as I was learning all of this. It all confirmed what I already believed. He is true and reliable in all ways!
Blessed as always for your read, input, and encouragement. Thanks for visiting and commenting
William Kovacic from Pleasant Gap, PA on June 07, 2014:
Good Morning Tammy,
Up, and across (except for funny). I really enjoy the detail you include in your hubs. it all speaks of our wonderful Creator God and glorifies Him for who He is. Looking forward to part 2. A beautiful piece of work. Thank you.