Unsupervised Learning

Here's an R code that implements unsupervised learning.

vdmulearning.R

Here's the code to display the hexagonal outputs you see in this page.

vdmhexplot.R

This is a specific instance of an unsupervised learning network used by Von Der Malsburg, hence VDM. He was interested in getting the network to exhibit similar behavior to what is observed about the human primary visual cortex. In humans, the primary visual neurons are organized in a columnar fashion according to their sensitivity and selectivity to visual line orientations. That is, each neuron in the primary visual cortex is maximally active for a specific orientation of lines that it receives visual signals from in the environmental space. Furthermore, these neurons are grouped together such that adjacent neurons are each sensitive to close orientations.



This R code implements the VDM network specifically using the following line orientation stimuli. The stimuli consist of 19 input units selectively made active (1 or 0) to give rise to "orientation". In fact, the input stimuli is realized in R as a matrix of 1s and 0s in the right positions.





At first, the network outputs a roughly clustered pattern of activity to a particular orientation (bottom left). But after several training iterations (about 100 cycles, which is quite fast!), it displays columnar organization (bottom right).













Interesting directions to pursue from this code are: object-level representation, color, moving stimuli, 3D representation, binding, repetition suppression.

Here's my paper which describes the model in greater detail [VDM.pdf].

Perceptron Neural Network: Backpropagation

Here's an R [http://www.r-project.org/] implementation of a backpropagation network.

trainnet_perceptron.R
testnet_perceptron.R

The network learns by propagating the input activity to the output layer, then comparing the resulting output with desired outputs. The difference is computed as an error which is backpropagated to the lower layers to effect a weight change that will reduce this error magnitude.

The network is then tested with original or distorted inputs. In general, this network can compute input-output mappings effectively (within network limits which are a function of the number of bits of information required to distinguish inputs, and the number of hidden layers and units). However, it is poor at generalization and distorted inputs compared to the Hopfield network.

Check out my paper that explains in greater detail [Backprop paper].
Also check out this website http://www.gregalo.com/neuralnets.html

Hopfield Neural Network

Here's an R [http://www.r-project.org/] implementation of the Hopfield, auto-associative network.

trainnet_hopfield.R
testnet_hopfield.R

Here's an brief on how it works. Every unit in the network is connected to every other unit (see weight matrix configuration in figure). Input patterns are used to trained the network using Hebbian learning. The network learns by additively changing its weights to reflect instances of unit co-activation. Unit dissimilarities and inactivations are ignored.

The network is then tested on original or distorted inputs, and it will robustly return one of the original trained inputs (within limits).

Check out my paper that explains in greater detail [Hopfield paper].
Also check out this website http://www.gregalo.com/neuralnets.html

Parko Beero!

The blind pig. Here lor. Even though hor, its Spring break lah. This is a one week holiday. So we all supposed to be relax lor. But then suddenly got so many works to do. Is very siao one. Suddenly is Thursday already. The whole like disappeared like that. I dunno why. So I say lah, we all go Blind Pig to have a beer to relax. How can not relax? Is Sprint break mah! So the lab came. Fun fun. I had two beers, one is call er...dunno what, an India pale ale (7.2%), and the other is the famous Delirium Tremens (8%). Blind Pig very good lah. I think so is my favorite pub in Champaign. Got character. Feel like an old English pub. Got one of the most selection of beers in town. You even got beer you dunno inside got what. Anyway, we talk talk talk, and then we go home. At least got relax a little bit lah.

Soba Tempura

This is a set meal consisting of cold soba noodles, vegetarian tempura, and miso soup. I will be explaining how to make this as a set, rather than as individual portions, so the descriptions will overlap as I found this the best way to save time and hassle while making the meal. It is worth it though. Really really good!

Ingredients
For soba:
Soba
Soba sauce
White radish

For miso soup:
Spring Onions
Silk Tofu
Miso
Fish stock (dashi)
Dried seaweed (kombu)


For tempura:
White onion
Carrots
Shiitake mushroom
Anything else you want to fry
Flour
Oil
White radish
Sesame oil
Soy sauce
Fish stock

Method: Initial preparation
Batter
Place a bowl of flour into the freezer, this is to make the batter, and it is lighter cold. While waiting, prepare the soba.

Soba
Boil the soba noodles until soft. Drain the noodles and rinse with cold water to stop the cooking. Place the noodles on ice cubes in a bowl and put in the freezer. Prepare the tempura pieces.

Tempura
Slice the onions, carrots, mushrooms and others into bite size pieces.

Method: Ready for the frying
Prepare the batter. Take the cold flour out and set aside a small portion on a flat surface, this is the coating flour. Take the rest and pour water to mix in small amounts while stirring. Add and mix only enough water so that you get a sticky mixture with some lumps in it, this is the dipping batter.

Heat up enough oil so that the tempura pieces can float in the fry. Heat the oil hot enough by testing it with some of the dipping batter. Throw some in and if it floats, then the oil is ready.

Take one tempura piece and coat it in the dry coating flour, then dip it into the dipping batter. Make sure it is well covered. Fry the tempura in the oil for about one minute, constantly turning and watching. The tempura is done when it becomes relatively stiff and floating freely in the oil. Remove it and drain the oil on a napkin. Prepare the miso soup.

Method: Miso soup
To make the miso soup, prepare the fish stock by either dissolving some pre-made fish stock or powdered dashi. Boil the stock. While waiting for the boil, prepare the seaweed by soaking bits of it in cold water. Cut the spring onion into small pieces for soup, and the tofu into small cubes. Dissolve the a spoonful of miso into one cup of cold water. Once the stock is boiling, add the miso mix under low heat. Add the seaweed and cubed tofu and let the soup warm under low heat. Do not over boil miso soup, it will taste bad. Serve the miso soup with the chopped spring onions.

Method: Sauces
Soba sauce
Shred some white radish and chop some spring onions. Pour some soba sauce in dipping bowl and add the spring onions and the shredded white radish. The soba sauce is ready. You can add wasabi and raw egg in it if desired.

Tempura sauce
Prepare the tempura sauce. Mix the soy sauce, a little sesame oil, the fish stock, and boil the mixture. Add shredded white radish. Serve in another dipping bowl.

Method: Serving
Take the soba out from the freezer. Serve the soba on ice cubes, the tempura pieces on a plate, the miso soup, and the soba and tempura dipping sauces. Recommended to serve with a cup of green tea or roasted tea (hoji-cha).

Enjoy your meal!

Lake of the Woods

This is a park about 15 min drive away from Champaign-Urbana. Not bad lah. A little small, but got lake. As you can see, its all frozen over, can walk and skate on it if you want...good for Sunday afternoon picnic.

Science and Intelligent Design I

One debate that is current is that of the existence of Intelligent Design. There are two basic camps. On one side, people believe in a God who started it all. On the other, people claim that there is no such thing, and things are simply the expression of physical laws that govern space and time. People from both camps can get quite heated and emotional argueing for each case. But I don't see why they should. When dealing with this matter, it is of utmost importance that one keep personal emotions and preferences and predispositions out of the arguments. One MUST sit down and cooly think through with reason the merits and pitfalls of either accounts of life as we know it.

I prefer to think of this matter in this way. First, how can we think about things or argue about the matter at hand? Here, we have to assume one thing. That anything which considers anything, and anything which communicates anything, must do so within the boundaries of logic. That is, if my opponent were to form conclusions from what I say that did not follow from prior premises, then there is no way to proceed, because the arguments would be arbitrary. Anything goes, and therefore there is no argument, no final goal for a truth. So, we must debate this within the confines of logic, or insofar as it is necessary, inference.

Second, are things real? Or is everything we experience part of a dream, or non-substantial, and thus inconsequential? Descarte had a brilliant answer. Cogito ergo sum. I think therefore I am. He approached the problem by doubting everything. But in the end, he realized that no matter how hard he tried, there was one inescapable truth (yes, there is apparently such a thing), that he could not doubt that he was doubting. It was impossible to think of such a state since to doubt that one was doubting, one would in fact be doubting, and end up concluding that if anything ever existed, it would be doubt. And to doubt, is to think, and to think, requires a thinker. Hence, cogito ergo sum. So, the thinker exists. And if a thinker exists, something exists.

More to come...

Catfish Creation

Ingredients
Catfish fillets
Broccoli
Potatoes
Carrots
Thyme
Parsley
Mustard seeds (black)
Olive oil
Chilli powder
Gin
Lemon
Salt
Pepper
Portabella Mushroom
Milk

Method
Season the catfish in a stock of gin, lemon, chilli powder (just a little), salt and pepper. Let the mix set in the fridge for about an hour or so. In the meantime, cut up the broccoli into bite size pieces, the potatoes and carrots as well, and the mushroom. Boil the broccoli, carrots and potatoes. Once well cooked, remove and set aside the broccoli, seasoning it with salt and pepper. Place the boiled carrots and potatoes in a mixing bowl. Season with salt, pepper and add some milk, and mash the mixture.

Heat some olive oil in a pan, and some mustard seeds. Lightly fry the mushrooms for just a little while, then remove them and set aside. Next, lightly saute the catfish in the olive oil, mustard seed mix, with the seasoning sauce as well. Let the mixture simmer over medium fire for about 10-15 min.

Arrange the broccoli, mash, mushrooms and fish on the plates. Pour the sauce over the fish. Serve with White Zinfandel (chilled).

Blizzardy Evening

Storm finish. From top left to bottom right: Snow pile in Beckman Circle lot, Walkway lit by lamps in Beckman Circle lot, Charlene's car stuck, my car stuck, block of snow, bigger block of snow!

Lots of cleaning up, but even today, there's another snowfall, another 2-3 inches. But its not as bad as the previous one. Here's a video report of the day.

Post Blizzard Desert

So, let's start from the very beginning. It was a dark and stormy day. The wind was blowing at about 40 mph, snow was beating down of the roofs. Schools were closed, the University was closed. The University! That which has never closed in 30 years finally fell prey to yukimon! Everyone stayed at home and peered their eyes out the window to see whiteness falling and falling, growing, wafting, blowing, twisting, and they sipped their hot chocolates and tea.

The next morning brought better news. Sunlight. Something we haven't seen in a day. In all its glory. But it shines through the aftermath, through my kitchen window. Yet, the warmth is welcome as I have my coffee.



Of to the lab then! Stepping out, we are greeted with what appears to be last nights deposits. People will have to dig their way out of this one.





And yes, its about a foot of snow, but in some places it comes up to your waist. That's me in the middle, see where the snow stops. There's another view.










Onward still! Charlene's feet are in a foot. The cars are all under, and I had to dig my car out of its icy prison.



















Finally, we arrive at the Beckman again, it is still standing. This monolith, impervious to yukimon. Impervious I say.










So coming into the Beckman, we hang around and work a little, then we go for coffee. Here are some shots taken while on coffee break. And then eventually head back for the classic approaching Beckman shot again.

Blizzard!!!!

According to wikipedia, a blizzard ain't a blizzard until:
1. There is snow or ice precipitation
2. Visibility must be reduced to 1/4 mile (400 km)
3. Wind speed must be at least 35 mph (56 kph)

Here's footage of a blizzard happening outside my door right now. [blizzard movie]

UIUC never closes because of snow, but today, classes are canceled and movement is down to almost nil. The snow ploughs are working over time and the snow just keeps coming and coming...estimated about a foot or more of snow by the end of today.

Joseph's life as an example of Christ

I just discovered for myself this amazing message in the story of Joseph. Joseph was most favored, and also was "worshiped" by his brothers and father in his dreams. Joseph was then betrayed by his brothers and sold into slavery in Egypt. Just as Jesus was crucified at the hands of men, His brothers, and took on our sins, and also became limited from His divinity during His time on earth, a sort of Egypt. While Egypt is rich and has comforts and wonders, it is temporary and it worships false gods. That is, they stop short of the ultimate reality. The true God. Instead, they attribute the wonders they see to half-way icons, idols. Just like here on earth. That is what we do.

But Joseph, even though he was in Egypt, he prospered it. He established it. In fact, if you read carefully, it was Joseph who brought Egypt and Canaan under Pharoah's control, and its seemed as if Pharaoh and the other Egyptians weren't doing much at all. It seemed that Joseph brought the lands and servants under Pharoah using economic superiority and also established a 20% tax system (the first national tax ever with priests exempt? at least the first mentioned in the bible - Moses might have later taken this up in the 10% tithe to God, and the Levite concept). We think we do great things on earth. Might it be that it is the Creator of the earth that actually knows how it really works that does these great things for us?

And later, Joseph is instrumental in saving his brothers and father from the famine as he is revealed to them, and also in sharing all that he has in Egypt (the world) with them. How he was once dead but is alive again! And more than alive, he brings his family with him into prosperity. In return, they are to take care of livestock, use their skill to prosper Egypt in kind. Sound familiar? It sounds like Christians, being blessed to bless in return, being saved by Christ in a "foreign land".

Note though, that there is a sense that Egypt is not the final destination for Israel. There is an even greater finality. And that is played out in layers upon layers, cycle upon cycles of biblical records. Moses, David, Judges, prophets, Abraham, Isaac, Joshua amongst others and finally the ultimate reality all these are pointing to - Jesus. Note also that this story of Joseph was probably written by Moses. And he probably had access to some historical records in Egypt to investigate how things turned out they way they did at that time. In faith then, he wrote this down, and we now have the benefit of the the revelation of Jesus to see how when Moses wrote this down, it was truly the Holy Spirit writing in him to tell us of Jesus that is to come. Who He is and what He does. Also, we see how God uses human knowledge to reveal a little of His plans to us. And even more so, we see how those who did not yet have a change to know Jesus at that time, since He had not come yet, could still hope in God through these themes of God's deliverance, and that is credited to them as righteousness through their faith and His faithfulness.

John 3:1-21

Nicodemus, Pharisee, ruler of the Jews...

This event occured while Jesus was in Jerusalem, after He has cleared the temple. Nicodemus' question shows that he has been considering Jesus for quite some time, along with others. And this reflects a certain contemporary thought at the time: that the Jews were expecting the Messiah to come and deliver. Jesus seemed to be a suspected candidate, but the things He did did not square with a lot of their conceptions about what Messiah would be like. And there, they were tripped up in all their thinking, even as Pharisees.

Note how Jesus begins the conversation. It has nothing to do with Nicodemus' statement. But Jesus knows his heart even before his mouth spoke and started the conversation immediately on what is important for Pharisees to know: the idea of being born again, to be saved.

"The wind blows where it wishes..."

Somethings happen, we experience it, and we believe that it is there. The wind. And we do not question it. How is it that we cannot bring that same faith into spiritual matters? That is the point in Jesus' declaration here about being born in the spirit. To be born again means to be born in of water and the spirit. Baptism? This is linked with John the author's references to baptisms before and after this passage.

"We know and testify what We have seen..."

Simply this, the only way to really know, is to believe the testimony of the one to whom true knowledge is found. We can try to increase knowledge through observing for our own, to believe only when we see things or experience things. But how often, even though the truth is before our very eyes, we still refuse to believe, but choose to explain it away by other "theories" or worse, ignore it. So then, perhaps this is something to consider with respect to philosophy of knowledge, perhaps the only true knowledge can only be obtained by faith in another. And this Another is the ultimate Another, who has seen what is the truth. So we can rest assured in His testimony.

"For God so loved the world..."

The famous verse. The only hope we have. Note, how we cannot do anything to have everlasting life other than to believe. And how this all stems from one point only. God's love. Love that saves, but also, love for which the rejection of is unimagineable.

Jesus' pleads here are entirely logical and reasonable. He who does truth comes to the light. Why then do people still not believe in the One? Choosing other alternatives? If they truly do what is true? What is their thinking and answer to Christ's words here?

Japan House Winter Tea

Atsunobu, Charlene and I take a short walk in the Japane House, Arboriteum area in Urbana, IL. We also stop for some hoji cha and make some snow angels. Check out the movie Snow Angels: [click here for movie]. The temperature is 11F (feels like -1F). The hot tea in the hut warms you up, and feels good in contrast to the cold environment. The brown tea contrasts with the white snow. We also had cookies and some rice crackers. Some people were cross-country skiing and sledding down the hills, the highest natural point in Urbana. Highly recommended!

Breaking Breaking News!

The snow has stopped. I estimate at 6-8 inches.

Guess what this is in the Beckman?

Can you figure out what this is?
Clue: Its in the Beckman.

Put your answers in the comments.
Answer will be posted soon!

Ugli Fruit

Sad sad name for fruit.

If you were called Ugli fruit
And that was your name
Would you feel ashamed?
Would you fade in fame?
Would you say you were lame?
Would you find someone to blame?
Ugli fruit, Ugli fruit
Sad sad name for a fruit
Sad sad song to toot.

Breaking News: SNOW!!!!

So its finally here. Today, temperature is -13C (-6F). And its snowing and snowing all day...these two pics from left to right, Beckman Institute, and The Boneyard Creek. Here are some clips as I walk from Psychology to the Beckman.
Snow1, Snow2, Snow3, Snow4, Snow5.

And here's one from Starbucks at Green Street: Snow6.

As you can see, plenty of the white white thing. About 6 to 8 inches maybe!

Olive Oil Chicken Pasta

Light yet solid taste, a satisfying meal for a gentle evening.

Ingredients:
Spaghetti
Mushrooms
Chicken
Parsley flakes
Garlic
Shallots
Asparagus
Pepper, salt, chilli powder
Olive oil
White wine

Method:
Slice mushrooms and chicken into bite size pieces. Cut asparagus bottoms off. Mince garlic, and slice shallots. Boil spaghetti in seperate pot first. When done, rinse with cold water to stop cooking and set aside. Fry garlic and shallots in olive oil until golden brown. Add chicken, asparagus and stir fry until chicken starts to turn white. Add spaghetti, mushrooms, pepper, salt to taste, a little chilli powder. Stir to mix and fully cook the chicken. Add white wine and let mixture simmer a little. Add more olive oil and parsley flakes and mix it in. Ready to serve! Serve with tomato soup and Beringer White Zinfandel recommended.

Breaking Arctic Blast Newses!

As if in answer to the warmer than normal December, today's temperature went down to a feels-like of -8F! Flurries all day, and tomorrow. Little snow powder falling down all day long.

Another news, Bill Meier said he would step down this July, to move on to another ministry. Kinda sad. He is a good man and pastor. He shared that he felt that he had completed all that God had led him to do at TCBC. And this was God's calling for him to move on. May the peace of God and the fellowship of the Holy Spirit go with him.

The Wii is sold out at Target and Meijer's. It is supposed to be selling at $250 USD. Hopefully it will be in stock again in a couple of months. In the meantime, save up.

What is this thing at the back of the Beckman?

Well, its acherly a liquid nitrogen tank lah. The water tend to steam around the pipe, so when its cold, the ice accumulates like that. See, it accumulate until it come out of the fence.

Winter Shots of Champaign

Here are some pictures I took while walking around. The best depiction is the movie clip in the post a few days back, but these capture the idea pretty well too. From left to right, UIUC Quad facing south, the Boneyard creek in Engineering Quad UIUC, outside my apartment, my apartment parking lot.

Birthday 2007

Aiyah, lau liao lah. Sa chap huei! Acherly hor, is not so bad lah. It was a nice celebration. People many many. And we eat steamboat. Very re nao. And "Wife Swap" was on TV. Good cake, good food, good friends. What more can you ask for?

Photos not I take one, but I got them and put them on my photo site anyway, see them here.

What is consciousness = What am I?

I am a wave of existence/influence in the medium of space and time. I have a defined peak and full-width-at-half-maximum. I change the medium through my existence in it, as it, in turn, limits me.

Walk through Champaign in the snow

Finally ah, the snow all lau chut lai liao. See, white. About 2 inches only lah. So I think not very much...last year got a lot more. So we walk walk through West Side Park and downtown, Champaign, Illinois. Got people making snowman, snow things, really chia bah bo si zo you know. By the way hor, its still snowing lor...on and off. I think this winter is very bu san bu si lah. Like ai chut mai chut like that. I mean, if you want to snow, then let it all out, but if you like that, then people very frus, dunno whether should believe you or not. So in this movie we take a walk and see the pretty sights of this tiny town. Warning, it is a large file. I recorded with my Samsung z230. I make on mac. Also, since it is handphone video, the quality is of course not top notch lah. So watch too long might give you headache. Don't say I never say ah!

[Download movie]

John 2:13-25

"Zeal for Your house has eaten me up". "Do not make My Father's house a house of merchandise".

These events occured after the water to wine miracle in Cana. Thus, we assume that Jesus and His disciple made another trip back to Jerusalem for this Passover, but this was before His final trip to Jerusalem for His crucifixion.

During the Passover, a sacrifice was made. This was the Passover lamb that was eaten in remembrance of the Israelite exodus from Egypt. The lamb symbolized a few things: substitution of the object of judgment on sin (the lamb for the Israelites), forgiveness of sins, identification with God, protection (from God's judgment), grace, providence, cleansing, and probably many other wonderful things. It is therefore interesting to see how Jesus is the complete fulfillment of all these symbols, as the actual thing rather than just a symbol. Back to the passage, a sacrifice was made during the Passover, and therefore, since not all were farmers, and not all could afford lambs, and also, because there were other types of sacrifices to be made at the temple other than the Passover sacrifice, people bought animals from others, conveniently around the temple at Jerusalem.

It is apparent from Jesus' reaction, that this practice of buying animals for the sacrifice was being abused. What was the main problem of buying and selling animals at the temple, since sacrifices were needed? Note, there were also money changers doing business! The sacrifice was a ritual that was to bring about remembrance and worship of God. But in elevating and playing off the role of money, the sacrifice came to be ironically cheapened. It no longer became about God, but about money and men profiting off a holy ritual. Consider this, a family tradition such as a reunion dinner, and the commercialism that surrounds the food required for the dinner, how that affects the meaning of the actual dinner and tradition if we are not careful. Case in point, think about Christmas and Easter, and New Year celebrations.

Futhermore, the temple of Jerusalem is the footstool of God, and the house of prayer, God's house. God of the universe. The Most High. Do you sell and change money for profit in the house of such a being? How atrocious. Men substitute the most holy and meaningful of all things that has intrinisic value, with value of something else that is in fact meaningless, money. What is money that we should want it so much at the expense of the real thing, God? What is any other value in life that we should want it so much at the expense of the ultimate creator and source of all true values, God?

Jesus' anger is obvious and reminiscent of how God chases and drives out the inhabitants of a land who's sin has disgusted Him. Recall, the Israelites war on the Canaanites, driving them out from the Promised Land because of the sins of the Canaanites. Recall, the Babylonians and Assyrians driving Israel out from the Promised Land because of the sins of the Israelites. Now, Jesus drives out the people from the temple. The place is made holy because of God. Unholy men with their deeds have no place there.

And as if they thought they Jesus' actions were unjustified, they had the gall to challenge Him for a sign to appease them since He has done these things! John uses this to illustrate the blindness of the people (the Light has come, but the world did not know Him), and mentions this later on in Jesus' conversation with Nicodemus. For they did not understand His sign of the raising the temple in three days, nor did they see who He truly was (since He kept Himself from them, v24) even though He performed many signs while in Jerusalem at this time.

How many times, when we are going on with our daily profiteering, as subtle as it can be, we are being in stark opposition to the holy purposes of God? And how often we refuse to believe because we are too proud to acknowledge the higher and most valuable of values, that God has put into place.

Winter Trip to Starved Rock

Took a trip to Starved Rock Park about 1 and half hours away. So what happen here is the Indians had a fort on the rock. Then they kena got war lor. Then they retreat to the top of the rock to defend themselves. But then, the enemy surround them and basically they cannot get supplies to eat or anything. So slowly all of them die. I think they dig up about a hundred bodies. Ok, not say the bad part, the park itself is quite good lah. Got canyons and got bluffs. I never bluff you. They is got many bluffs. Is not bluffing. Then the waterfalls in the winter they turn into ice. But then ah, you know lor, this winter is very the gu-niang one, so not cold enough. The waterfall still falling water. Not complain lah. Is still quite chioh looking. Then got nice pub there to get a beer after a long hike. I recommend you to go lah. Oh by the way, entrance is free. Check out my movie and my latest photo album.

Parklab Singapore Trip

Ok ok, so I know this all look like we do nothing but eat and eat, but then, you have to understand lah. Singapore is small country, don't eat then do what? We got work also lah. Anyway, we go Sentosa to relax a bit on the beach, then eat then work then eat and work again. In this movie, you will see the lab people eating various Singapore cuisine. We had sushi at Sushi Tei (Far East Plaza, 5th floor), Frog Legs Porridge (Geylang Lor 3), Tow Huay and You Tiao (Geylang Lor 9), Durian (Geylang between Lor 3 and a bit off), Thai food at Sukothai (Boat Quay), Zhi Cha at corner coffeeshop (off Cantonment Rd), Bak Kut Teh at Ah Hua Rou Gu Cha (Tanjong Pagar). Don't worry, its all good for your brain. All very healthy, cooling and heaty in the right places and in the right amount.

Free Will?

Interesting article about free will.

NY Times article

John 2:1-12

"On the third day... Cana of Galilee..."

The actual location of Cana is not certain, however, we do know that it is situated somewhere around Galilee. Possibly a few kilometers north of Nazereth, Jesus' hometown. Cana is also Nathanael's hometown (John 21:2). In any case, Jesus, His disciples and Mary, His mother, were guests at this wedding, so they must have been at least acquaintences with the wedding party. This event happened the day after Jesus met Philip and Nathanael. So they had made the trip since then.

This is the first miracle sign in John's gospel revealing the divinity of the Christ. The exchange is interesting, almost telling of the relationship between Jesus and Mary as one in which the mother is conversing with her Lord, both familiar and at the same time not. The miracle itself was not made public during the wedding, and unlike other miracles, it was not about healing or a demonstration of authority of nature. Rather, it was simply about providing wine to a party that had run out of it. But this description is still included as a sign that manifested His glory, and that led to belief in the disciples. Perhaps this is related to what Jesus told Nathanael the day before since he is from Cana? Nevertheless, this sign serves as a buttress to testimonials of the identity of Christ.

We are not told what the significance of the six waterpots of stone according to purification manner means. However, John the author states this for the purpose of informing his non-Jewish readers.

Following this wedding, Jesus and His troupe went to Capernaum, a city by the north-west coast of the Sea of Galilee. Interestingly, this was the city of Peter, James, and Andrew (see other gospels), rather than Bethsaida. However, it could be that they moved from place to place around the coast, as these cities were quite close to each other along the northern coast of the sea. Capernaum was the center of Jesus' ministry subsequently, but later on, they rejected Him and He uttered a curse on the city. Note that this city was cursed later, despite the miracle that was done. Consider this for yourself, how quick we are to blind ourselves to what God does right before our eyes.