Space Bug Domination

Problem: A space bug has a volume of 1 mm3 and can travel around at the speed of light. After enjoying its life for a century, a space bug splits into two bugs, which quickly grow to their parent’s size. If we release a single space bug into the wild, what will happen to its descendants in the long run?

Solution: Let’s see. After a hundred years, the first bug splits up. Suppose its kids don’t like each other and decide to fly in opposite directions. After another century, they are separated by whooping 200 light-years. They split up again, and now we have four bugs. By the end of the next century, they can also be as far as 200 light-years from each other.

By this point, the pattern seems pretty clear. The bug colony will form an ever-expanding diffuse cloud, and unless these bugs decide to throw a party, you will probably never see more than two of them close together…

Okay, Luke, if you insist, we will do it the proper way. If we measure distance in meters and time in years, the total volume of all bugs at time t is

10^{-9} \cdot 2^{\left\lfloor\frac{t}{100}\right\rfloor}

Now imagine this: when we are just about to release the first bug, we flash a bright light to tell everyone about our great deed. The light from this flash will form an ever-expanding sphere, and since bugs cannot travel faster than light, they will always stay within that sphere. Thus, the volume available to bugs at time t is

\frac{4}{3}\pi(3 \cdot 10^8 t)^3

Now, how do we figure out which of these functions grows faster? We could try plugging in small values of t, but that’s basically the same as what we did at the very beginning, and Luke said it was wrong.

We could try plugging in large values of t. Given that we are interested in long-term behavior, plugging in large values makes a bit more sense, but at large values of t both of the functions become pretty huge, and our calculator won’t be too happy about it.

Instead, let’s use a great mathematical truth that says, exponentials dominate polynomials.

Exponentials dominate Polynomials dominate Logarithms; Rock dominates Scissors dominates Paper dominates Rock

Let’s break it down a bit. An exponential is, unsurprisingly, any function with the variable in the exponent. In our case, the total volume of bugs grows exponentially. A polynomial, on the other hand, is a function where the variable is raised to a constant power – like the volume available to bugs.

The statement that exponentials dominate polynomials means that if we wait long enough, any given exponentially growing function will become larger than any given polynomial.

Therefore, even though the bugs are so small and initially so far apart, they will eventually occupy all space available to them, after which they will crush each other and die.

The end.

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As promised, I am now releasing the CYOA story that I have been making for the past ten months. It is called O (yep, just one letter) and you can play it here:

I hope you like it!

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Squiggles and Novels

Last time we were discussing the amazing mathematical properties of a weird blue thing. Back then I promised to reveal my proof that the thing can only lie flat if its number of segments is divisible by four, and I guess I will do so now.

To be fair, it’s really simple. Remember what we did to prove that the number of segments should be divisible by two? Right, we painted the plane with two colors:

Loop on a two-colored plane

So, what can we do to prove that the number of segments is divisible by four? Yep, paint the plane with four colors!

Loop on a four-colored plane

The squiggly loop traces the squares in the order green-yellow-red-pink-green-yellow-red-pink-…, so its length should definitely be divisible by four if we want it to get back to the starting square.

This four-coloring of the plane is actually pretty special and useful. For example, squares of the same color are very far apart, so if squares are students on an exam and colors are problem sets, it is hard for students to cheat. My recent chemistry exam worked like this.

But nobody likes to talk about college exams, so let’s talk about their less formidable counterpart – projects. I had to do one interesting project lately, which I will now tell you about.

The project was in computer programming. It was unusually open-ended, so we could do almost anything as long as it involved coding. The project was done in teams, and my team included Ava Seldin and three other people – gotta give credit where credit is due.

We decided to create a procedural novel, and not just any novel, but one without the letter “E”, in the style of this book and this subreddit.

To do this, we used a Markov chain. Here I would normally link to a Wikipedia article on Markov chains or something like that, but all articles I came across are really complex and technical. And Markov chains, or at least the ones used for text generation, totally don’t require a complex and technical explanation, because they are stupidly simple. Basically, you just take some human-written text, cut it into pieces, and arrange the pieces into a “chain” where the end of every piece matches the start of the next one – and you are done!

So, how did we do this? To begin with, we got a few human-written novels, and cut them into triples – pieces of three words each. Then we discarded the triples where any word contained the letter “E”. This automatically took care of the e-less-ness requirement – no matter how we would arrange the triples afterwards, the resulting text could have no “E”s.

At this point, we had a lot of triples that we had to somehow categorize. We made a database which, for every pair of words, determined what this pair what followed by in triples and how often. This is kinda counterintuitive, so here’s an example:

him not 3
	to 8
	laying 1
	only 1

In human language, this entry says that there are 3 different triples that start with “him not”: “him not to”, which appeared 8 times, “him not laying”, which appeared once, and “him not only”, which also appeared once.

Next, we used this database to make the actual novel. We started with two words (“it was”), looked them up in the database, and used weighted probabilities to decide which possible word should go next. And then we again used the last two words to append one more, and again, and again, until we got a lot of text.

And this was not the end of it. We still needed to do three things. Firstly, we had to separate the text into sentences and paragraphs and put some cool punctuation into it. We found a simple way to do it: we just treated punctuation as letters! This way, the database would store things like “hi” and “hi!” as different words, and then the algorithm would automatically throw these punctuated words into the generated novel.

Afterwards, we could just split the thing into sentences by looking for periods, exclamation marks, and question marks. Then we created paragraphs out of reasonable numbers of sentences, and problem solved! A quick note: even though this is probably obvious by now, I want to reiterate that we did not make sentences independently of each other; we made the entire novel as one long string, and the division into sentences was just an aesthetic thing added in post-processing.

Secondly, we had to solve a problem where sometimes the code would stumble upon a pair of words for which there was no entry in the database. In this case the program backtracked, tried to advance again, and sometimes failed again and had to backtrack further. This was accomplished by a short but very mind-bending algorithm, which I will not describe here.

And thirdly, we had a problem that after a while the code would enter an endless loop, printing the same few words over and over. We could have solved this by making the backtracking algorithm smarter, but instead we chose an easier approach. We just cut off the repeating part and didn’t mention this in the presentation, because that’s how you solve programming problems, right?

Okay, this was actually the end of the project, and here is the novel we got:


It was a rattling of china and is now in sight, and my spirits will not call in vain. It was only in his form and a constant irritant to a stand, and i had but to all pursuit from man. But as for a kingdom! Upon my word, said mrs. Collins was not good. What kind of a glorious shout, and in all his poor old chap would stand by now my blood run cold, and that i might say did i not know i am.

I didn t i bust out a-crying so you just now what has that man had got up and two boats, stubb s long tail standing straight in his hand, and all of us, why not now? I think good this night. It was only with groans. I will go far to windward; for this was at a loss to know with how much you got on his own and mrs. Phillips, and was so full of it. At last my work at pounds a month and a tall, thin man, who was to draw up to a work with in your own conclusions. I shall not sport with your own way; but if you can t. Do you stand on this.

What was to put in. Why, aunty, it cost what it was still not sorry for that, i should at this thought in his arms, who is it? Asks mr. Lorry, as an occasion of this or any part of this lady who had only known by any particular infant in whom i saw him with such a way that i could not now to him, and lydia had nobody to watch for him and said it would not do; in half an hour tom s mind was far from attributing any part of this aromatic ship. Though stubb did not know if you wish to know if i again cast my lot to bring on a particular favour to ask for mr.

Collins was a sound of a diary in shorthand all that is what you said that if you think in this mood if his door was thrown up to him, and oars and stand by to sway as a point was what i could but just to you than you could almost touch his aunt would pull it down with di monds, and fill it, and said, what do you want it. You said just now, in allusion to a criminal and of his machinations. It was most prompt in inviting mr. Collins for having had an only son of king s who stands forward on his arrival at lambton; and this i got to do so; not to his coffin with that of all his first yawn and said, if i don t want to know that i can only say that i could only afford to carry it in his look, that, for your going to hug him, but only a short supply of ammunition, and again my spirits that burst all your sorrow and to consult with you in writing from both of body and of which i so old! , and i was and stood on was not so mad as it may, it is not difficult to attain.

It has got him his hand, and carton s hand , but no hooks. It warn t no harm and that ain t saying nothing; i m afraid i shall not find out who i was. I would put up with it, and was now going to lay on a chair, and on all hands and took it from a population of a low and almost in an angry snarl, such as a physician of high woody hills; and in varna a day at this critical instant a door of idiotic obstinacy with a vast portion of his birth. And, by a unanimous call for it was your journal of his own words, hoping that i do not know; but you can t. Do you hang down your hair to try for it.

That s christianity; go on. And so forth, had in all his sorrows, and how you would say this man s lips, and could not find it difficult to draw up, and, i may call it back from his own volition, and so what was that? His hands in his land, owing to his cousin s conduct to you. Do so, if his poor ignorant soul trying to do it, s i; that s right. Right, and that it was all right. It s all right, but i d of august, , and giving it a bit, and jump and cavort around, with his own body. Would that i should not only now almost at tom s track. Aunt sally coming, and jumping for him, and by jim says: why, is a short walk took us to run off f m down in body and soul; and i don t do nothing!

Why, how you did not do it, and it was of so many things i know all about poor lucy, and how much i shall think nothing of it? Hain t no bad thing for all that night. But what it was. And can say by his bringing his harpoon in his blood, at last in a day or two, during this inquiry, and it s i want ; but arthur caught him, if so that, adding to all his thoughts to any curious and not at all. Now, as i was bound, and that i ought to adopt this sort of a land in this difficulty with which such a scanty portion of tom s bosom but a tributary of a thousand things, carton said, and that as i saw with horror and diabolism of subtilty, and by now my blood cold, and how all his brains out if it would go to your inclinations.

But this is my cousin, mr. Collins, who was to sail a navy of upwards of l , , falling from that black air without any condition. I found that i also had to do right and tain t no good in making up his mind that, by your aid, i got to do so as to wish you had it not a chip of a brook and taking him, not only to you, i could not but say, tom, now that jonathan is a long arc in his mouth, and was just in a storm is coming up; i must drag out of his bunk without his at all his kingdom, that if i may want your opinion of mr. Darcy. But i am too old?

Said mr. Lorry, said mr. Lorry, with an old man from which so abound in most of his son, in passing, of his own arts, said fitzwilliam, without applying to him, but i would do anything at all. I am now to sit down again and again, and to whom i had for a long solitary walk on a sunday, i don t your fault if you d a had it from top to bottom.

Now, said mr. Lorry. Say no word to any bad and that s what i m coming to, cook. You must comply with paragraph .f. , a full ship and boat s bow, and said:-- no sitting up stairs and in a hard parting, though it could not doubt but that many of your lawn.

I thought all was dark i slid out of my own, to whom i had no loss to know it s foolish, tom. It was no sign of any provision of this and all in a condition to a family of that country and of gaining such a man of a far distant land for such a comparison that did not go to mr. Darcy; that to do as much from it this way; it don t. It s you, and sat down, and out of his mind was all a flyin , that i did not stir again all his sorrows, and find out how it had not a flat, but a human body is not a sound in our furs, and madam mina, i will run to throw at a short call upon his watch at night. So, mr.

Darnay; and my want of faith. It is not to fail him; and, in a calm, with his poor rags would do anything. Lydia, my aunt told us to his brain; for it so high that it was so ignorant, and so on all hands got to glory. It must go instantly to my diary and my mind as a doctor, but i couldn t go and stay was short, and mr. Collins s long stairs and along by so much to carry it to you may not go out as will soon find an account of your man of his fair young lady at this dark and dismal night, bitingly cold and sad, and took his last with his family back from it, and saw only that i would call to mind what i had not a word about it. Down it sunk, out of sight of stubb s hands, lydia s imagination, a visit to london. I don't know how it was!

I did not at all by your aid, i shall not; and it most as many, so of it is, all right; and so, without a word or two of my boyhood--it s all a bad job for you. I am thinking still, and will scratch out all his might, and i can trust. If you grant that? I ll stick to it. Will nothing of it? Old dobbins will ask you not think, mr.

Darcy, to whom you paid him, and for our raft. Now was that lay on a day or two at a loss how to find out who it is? It was king of all by your old callao to far down as if to this mrs. Oakshott for it. And still as on you. What is wrong with him, and if any you paid a visit to brixton road, to a man was just such a way, and in a soft kind of talk won t talk back and forth - it had to do your work for it. But you, said this his first long visit to rosings.

Mr. Collins s admiration. It was now full of his arms round it torn and full of joy and ran in this country. You just follow him; and now, as soon as that to his broad, glossy back, of an old hair trunk in your mind, i could not finish it by saying, that though you and your trust, not know if i was glad, and said: if you had to wait a bit, old chap, you got to it but to that not only full of his body out of sight of that anointing. In truth, not a doubt about that, said mrs. Samsa , said his say, as i should at any risks i was doing, and with a big parlor that had as much right to think, and so, my brain just as if to this is not sound, and still, just as day in august, high in his hand. Though, upon my word, watson, you can find a lunatic in such a man with a long cord.

Just so, and i will not go. I know of any kind. I know it, and it is but a day could run as fast as you may go and visit us. My limbs as a man s hand, and his sons, but said nothing about it.

So huck sat down for a walk; not only a woman, and if you do not solicit donations in all what i says to hans: i will not find any way with an animal which can only do as to this, and wishing to hold your hands from his body as far as to facts of his own hands, and says, that no bad thing for us all to him. All curious to know that on which a noah s flood is not a sort of frightful hot, as though it could not account, and partly from curiosity and partly from curiosity and sympathy of your country in my study in half an hour. How long did st thou that pointing to him that i could only find it upon our corn at his door, looking as if you don't think you know you said that if any of fog both to mark if any you paid a visit to a shallow hollow to catch anything in bulk. It is what i want, said i, 'i shall not soon to wait on him of this it is, that with which this was going along, and don t know hardly what to do, and i'm glad of that, and so on. It was not so happy at any of fog both to and fro as if it could not do that; but i would not talk so wild?

How ? Why, hain t you do it, s i, that must now go and join him in my own family, and to fill a vacancy did not know if you can do nothing but a fool would a thought of his coming with his hand, as if it will pass away; and in a constant irritant to a high social polish. Still, for if i do not cough for my curiosity was not such a task which was stiff a cord to draw his mind for a thousand dollars and i only wish it may only ask for this sort of fits to him; and it s all right. What is your n, ain t no way to withstand it; in that coffin; but that is going out; i can t amount to anything that was not doubtful for a work with a rag of a diary in it; and it was all so good; but i saw it in my mind as usual. I am writing now, with a sort of fits to him; and a half a man who was now an opportunity of shooting off-hand was not a bit, old chap, you got to do first, or which way you could find a way as to all of a cloud of caring for nothing, and said: i shall not long to your son's guilt?

How can i do too much? I think so, captain? Glancing at his cap on its summit and look sharp for a work or any alarm; and within a day as soon as you may know how to do with this country. I didn t wait. Think o that, now!

What s that in which mr. Collins was not at all what i was; i thought so. Captain ahab did not fail to carry in a hurry and confusion of blood in him, and was in this town; and his painful part of this sort of intimacy with his back to mary but which had struck at him a long pruning-hook of a cabman as a kind of world, you will comply with paragraph .f. , a full moon and straw limbs to it by its light i saw him fly from this sprung from his station, and will you do it, or that i do; you can trust in god and man at a low rumbling sound was that of a hub of a man of his sty. I was known, and from its vapour; or how to find it out.

It will not do for this. That s worth a good south wall, not far from having a suspicion of having a black and muddy, and a mission? Did this old hair trunk in your wisdom you may say that you would not call this a glorious shout, and in his youth was holding on to do it now you wouldn t back out of my natural lord and lady clara st. Simon had by now to work for him to go into court with that occasional look which had a gun. I was to blow on nobody; and told him that it should not think of it brought back by my first duty is to say, is, don t you call for it s good.

Now you do not know him not, and i told him that which had not had much sorrow and not i. I shall in all round. But as soon as i know, to say that i could do to start with a sort that had it would fool anybody . In , and so was i to wish you a song? Oh, a most amazing howl or two, i shall not; and i don t talk about that.

Go long now, said i had a lot of things you can t stand such a comfort and a mighty notion to just try for it. I know, i said it with any kind of lazy along, and how to control and not knowing. All this and all around him and said: now will i talk to him how i should not wish to study out a sign of any kind, but only as soon as i had to stop. It might at first thought was ahab, that thou shouldst not only through habit and association, but from a common soul in this town and jack sit down by his own way to all but that can t do a girl to do which i want to stay in my soul; and i turn my body and soul at all! From miss pross. Do you not afraid; for what you had it from its frowning walls, and at no cost and with a loud crash -- now, who did not think so at last to a shallow hollow to catch anything in this sport.

I could to comfort it. Lucy was right about him. For, of all that old man furiously. But i won t talk about it, so that by his own hand, and a many of my youth, said his lady to hand to work his brains an hour of noon and at last in a way out, and you could fix it; and a mighty good that i wish to visit you. I kiss your hand, and raising up a snack, and says: why, it s worth, or all of us and hunt for that i could but go to your own way--don t skip anything, and don t know i do not know what mr. Wickham s alarm was instantly caught by a troop of four thousand pounds.

I should run for your going to play it any fish that you will not call this high and mighty quick, i say, may not i shall play on for a shock to an hour or so my stay was short, and your family, but thousands of birds which fly about in all things, and a day, and his account of such a sight you know how anxious i was at a loss on his mind, is a good as i said i as i was almost too much and so i told tom all about him; so i lost it in with him on topics that had a good south wall, not far off in that particular. Full of a sail, or a port, or a nail or two to kick back, upon my honour, i had but a rag of a family to you. Jack. That is why you did not. And i am not afraid of no common man; for in this country. You just wait a bit; that you will not that of all things.

You and i took my way out of his two hands in its touch that workman s arm and a half, and said with a hard night of his boots, his pair of as much as you know, that i had a long sight. My souls, but i ain t all. It was a woman of about fifty yards. Not a bit, and said that this was against his captain s work, and it did not wish to know. I do not want to ask him about it now.

It will do; it is his look, that had a ray or two of my own, as if your husband is not only your good man and who had grown up, and said, i could show a cat to him, though in many of his ivory arm frankly thrust forth in paragraph .f. , this work in any way with an angry snarl, such as to my own part, now that i was not long to go at six o'clock that i was up so high an aim to hit um wid a rock? How could i know not how. What will my husband has not a man to apply for it, and a charming man? I could not find it.

And if i was. I would marry, you might a got down and stay in town last spring! I had had in all my days!

Don t you know anything about it, and kill him. On both arthur and my mind was soon out of a most dark and unknown ways; into a transport of fury, with its rush and roar of rain could not all of which you abhor. Still thou canst blind; but i said i had no food for it, said stubb, rapidly lifting a glass of old roman valour is not an hour s visit, and sat up and says: what s in a bad thing if that s kind to us, if i could not but laugh at this, and i shall soon find you out. So i said:-- but you cannot go back, and said to his cabin, and put his foot and said to him owing to this, it is that i was hard to say, which, in all walks of fancy on my part that might not - or probably would not say a word to a coach?

I shall try to play music on? I know it is that you can do all you know that what you think to fool a girl who was to you, struck it mighty warm for him. And just as day in a hansom, but as this miss prism says that so much on a chair, and putting his arms again, as though it was a cant word of it. What it is so long as no gold was brought in, and shut it, and i was so afraid, you know, only in most of which, as thou art a full moonlight, and it took all his might for joy, and out of his tail again, and had to admit that i could say, for all my days.

God pity his poor ignorant soul trying to do so. Mamma has a kind of thing for us to whom i had not long to him, with hands as if his door was shut out from a first and last, and i was in full bloom, and on board at that instant a door in a public domain works in your room. I was trying to buy so much as a light in hand, and his hands in his doing so by way of fighting, and tugging at a salt-lick, about sixty yards from our man. I should call this a hint to stop at this dummling was glad, and forgot all about his back, that s it! Long and rough, and i was a poor man was living.

Now, said mr. Lorry, you cannot go back, and told you of him, but would not willingly drown without first humbling him, nor was it on a couch with furs, and madam mina, i know. I soon shall put down his back, now, and pay him half a song, which was not a pity you could hardly pass through. As you say. I am glad of it; but it is not always looking at him for his guard, and from him with joy, and said if you would think of. But, with all my occupations and my arms and a troop of cavalry and infantry, of which runs straight out from a boat to its humours and to punish him. It was only a poor man, but i was conscious of its origin in his chair and clumb up into it it may do what a glorious shout would burst from it to you: 'i was foolish of you.

But i s so old and a salad of it, and that my darling will not go to-night? I will not much to do what i said. It is your n, ain t good to us all.

Knowing of what might grow to my own and mrs. Long. But i did not go to mr. Lorry, who had a most dark and kill him. On his back and fool away this morning i was not a thing to bring on a first and was soon to wait until you had much to do, and which still grow idly on at high noon and at last in his affairs in hand. I must watch should his door and thrown up from hands and burst out of his having to do with m all in good spirits; i think you will only say: i told you so, long ago.

So would i, said mr. Lorry, in his blood, and as it was, and said in an angry snarl, such as i was a brooding look which i could not but you must not at all. Mr. Barsad s communication to a broad bright coin to find it, thank god, i shall not go to work and not to join with my family. And this, too, i call it?

It s on. That was passing fast, and, for a long way back, and told him that it is not that so? That's so. And as long as you may not hold your hands still at my watch. It was high ground, so i trust that, by his conductors to this young man?

Is that in a hurry, and calling loudly for my having to do is just as i d start a band of light upon what grounds may i humbly ask if it had stood up with a string, for all that had to go to my fancy, it is but a fast-fish? What is it not? Jack. Oh no! I can't think of both as to his own mind, than to stoop to this a glorious shout would burst out of it, and at last i got hurt a fly. Such a woman.

I must first cut into continual and short and with a kindly word, and in drawing it back, but this custom has now a good family in such a man without now and again on such a thing for today, and i told you you could? But of a cottonwood that was always a joy to my companions, but i could not swallow so much in that room or not, and said mournfully, i know not; i will look on his way, and told him that i am about to throw away in a light of that of any sort of a man, so i took off his coat. His boots, and rags, and put him in your mind, tom? Nothing. Nothing t i wouldn t do that! Kill?

Who said it was a rush to whitby and all was dark as it is not to do. Don t call to him; as if it was now so nobody won t put my hat and a gourd, and a low hill, that i should say that you will wait on him to think that i am at this hour in his hand, and with much compassion.

But if you now is that i could put. By and by taking away his last man, to whom you paid for it was not lost on pork? Why can t think! And oh, lucy, it is mighty curious, huck. I wish it was jonathan who was saying it, and soon as i had a lion which was a bold and rolling it into his chair. In a low hill, and just as though saying it warn t no show for it.

Any injury to it in that awful hour; and all but miraculous. How at such or such a good old man in a way out, said mrs. Collins has no doubt that from so many of its own. For a company to which you know i was curious to know what you do all i want to know that a man will show that you can bring to you in writing from both my hat on, i ll go and as i had to back away and ran out, and it was a light snow had all but that couldn t a gill in his own arts, said fitzwilliam, without applying to him.

It had only to avoid scandal. I thought of fixing in town than what i want. I was busy, and that it was an odd and not know our dogs, and carrying with him and to know how to work out of you. I can only trust that i was told about in his limitations and his aunt s old chums i found that in his hand upon his man to stand a top of it. So i could not but a slight itch up on to that.

So i know who i was. I stuck out a stiff glass of cognac, took a young buck with an apology for his pains.... I was not long was through that land many, many months, calm and cool, but i shall again and soon found out to buy its own jostling group or crowd, according to your family. In darcy s having both hands and sobbing in a young man, it is just a word, not to visit. But you always think you could float by in my room for him. What a charming man?

I am afraid that i had no luck with my conditions, i will not , sir, i must go. My papa is so painful that it was found in paris at that hour, and was using his art of war. It is to lift and push it back again in his right hand at cards happily unconscious of it to you with all my family, and that if any you paid a visit to a bad man or boat can withstand it. Your only companions. How can you not to fail him; and, in short, i should go to paris. I soon found that if i did, if you do a girl who is picking up a bill for a young woman from him, had to miss darcy. I cannot say much on my part.

Is not such proof of your mind to my boy, i want to say that my writing now would all wash off in various sorts of knowing winks in all walks of fancy on my part, and i was still in his favour and you would not burn. I was glad of it, mr. Windibank. It is a customary saying that fur is good for nothing, and said, cat-skin, you must know by a coin flying into his chair. In a look on as though it had hardly had his hand and standing up shouting and crying.

Folks got up and had to go if i may, carton! But how? I am only too glad to find that i did think about it. Mr. Carton s hand shook so that it almost too much for you, mr.

Worthing, i trust you will not touch it without knowing it was too much afraid of asking your ladyship s asking us to join him as to go around hunting for us to show us your taffrail to show that i must go in and around a bit, and jump up and down with a triumphant burst, and it was also not unnatural if you follow not too much for kitty. Won t look at him. Into his room is on account of him, and laid down as you go up by him without introduction as an occasion of introducing him to your room, and in a wing of a town in a fortnight ago i was not to any of us who has struck down into his room is no good blood in him, moby dick and fought him, than to say that i am! But i can t afford it. And it is a child, that i had --which is a bijou villa, with a round turn in it, said stubb, showing it. Lay it by daylight. I can t do nothing.

And that s so. Who d you go through with it. If i could a got into a room as any i thought i did not fall upon his words, for his wish of my guilt and his country in addition to his ghost! What was it? No, i don t you snap your oars, and clutch your souls, now!

My god, what shall i do! I ll just walk in; but i fancy not, for it last night. It was what pap always said i had not two of whom had his first long visit to london. I am sorry that for an hour, and i cannot stay with his right; and so, darcy did not know who has known for many months in prison, and that i know not much doubt it, that as i can t find nothing, what would it not again.

It was in such a thing of his lips as though it was dark night, and might, but for an instant to horror and dismay. I was not taught to think of following his own hand, and a chair and shaking his hunting-crop. I know you always to follow my inclining i would willingly afford you any doubt as to what is it not so? Nor was it until i am naturally a poor account of its own particular boat was to cairo. Jim thought it would, said mr.

Lorry, and was away up to my own cabin and hadn t had him put in its own way; but i must touch him or to such a quantity of oil, and has brought us through all this took from his room, stamping his foot to foot, without a brain and that s a good fairy, that was in bristol. It was an atlas, which i did so again and found it so vigorously that it should drag it from an indian's throat. All ran up with a singular and highly to its fungi; but, in his vicinity that could not look towards his lips, and straightway starbuck did ahab s brow is so cold, and up to him, saying that such a supposition did not disturb him till towards night-fall; for i thought it was at first glad to find him. I am so happy!

I am going to-morrow into that unknown and in this city. Look at you shortly, that s got a quoggy spot in which i may not i can put up his mind and can t you want to know all about how a poor lost lads that always had a quantity of oil, and has grown into manhood in my imagination was busy in bringing in good spirits, and out in front of us. Just as i should go on praising mina for a month ago i found that i was an atlas, which i had lain thus in march, , and so saying i had long black hair and horns on. Out of blank walls and dark i slid off without fooling around that school s going to finish my labours did not you who brought him from it. On that account that i will not fail in any way with a cup of broth and took us for all who ran to pick up any particular infant in whom duty was so much, but i had also to his will.

It may harm. Again your pardon, but i had to admit us, and so his own bloody nails in his waistband again, and his look is a pity to an animal , said mrs. Collins was also said that this must not think of that, but i pity you, miss lucy, shall not find a doctor, but i will show that you do not think about it. In an angry snarl, such as had just a child and said: i m awful sorry, and so i didn t run jim off from that part of it. It is in a part of that , you must, at no cost and with a pistol to his long whip, and with long hair and a young lady. I was only in pavia, but throughout all this was such a thing?

But say, tom, did you! I thought that my lord godalming and morris; and down on your mind, said miss pross, rising to its own way; but i fancy that i don t know how mr. Darcy is not good that i had, of his dignity, and its crowd of old oaks out of my husband's also, which is a kind of natural philosophy. It was a sort of look about on a visit to rosings. Mr. Collins s long tail standing straight in front of him as your child, companion, and fast to a coach? I shall not do that; but i know many chaps that was a fool of a dark night, and had no notion as to no toys to play with him. I did my poor child, for it by knowing that that was only said, it was dark i slid off into a bird, and a final snap of his coming back.

'i know that i may not and i could not so quick to run to throw off your chain, and a sprinkling of bark; so i told him that his lady to you may at first i know nothing of much of that sort of lullaby to it than to say what you want it, you can find it. So away i sha n t touch an oar, and ahab, putting out his hand, was for us both, i know. I do not know.

A juryman: did you say that it is too much for you, mr. Lorry, rubbing his hands. Turning back i told you to town to town i shall go in, bind him, and which i did not want to go instantly to my cousin, that your assistant is not his own, but what s a mutual, joint-stock world, in all walks of fancy on my room. For an instant as it was all so good a right to dat young man said, i will warm you a long way from paris. Nothing but a mob of young palms.

It was an unusual but still i will start upon his thoughts. In front of his hands and burst into a cloak- room, and in thought with horror, ran along and try! I will gladly pay for it, was missing. Could not think that s all owing to my own hair.

I took out a huntsman to shoot him a pair of high standing, and on top of a man to whom of all four of my own. That point of human affairs, did not know who has a sort of crick was in confusion, and that old man says: did you say of this and all its might. At this critical act is not as his wont to mount to my horrid task, and a still though, but stay of my door, but not to talk with its lurid lights and to my darling. I must say that nothing could for an hour or two on a small patch of tobacco and a lot of it, and found ilsabill sitting on a point. Could annihilation occur to you.

Will you look? I will go to it was in a short walk took us to do any work on a short stroll with you. Why, it s not long, a rich man. During that long and too much for it wi' a wind which now i could not but look sharp for a glass of whisky and soda and a king s son, and i will try to; but you must comply with all my affairs of my story, and laying his hand into his pantaloons as soon as this it would hardly think that i was to find my way to dig him out to do with most of all our arguing with him. But i had to do but work it would all go to my own part, i am not a gallon you burn, but at last it was so charming a young lady at this turn of affairs, said i; but at midnight both of his long hair and a girl to do wrong, and to all his might, and so that it was as much as a fly is found in him, and to wind up with his hands in his, and oh, my husband! God can, if it was to him a sum as a man so that a man s to stash his tomahawk in any way with a wild cry of satisfaction.

For a day or two. If i don t know how to walk and to ask him, with hands as though it is always full of joy and ran down with him. Mr. And mrs. Hurst, who had known him to put our hands and shook out upon a straw, i will call upon his back.

From having a cup of broth and took to his back in his chair in his way or that it is a curious thing, and according to his work. It was, by my clock it is all i do; and of all sorts, through this work in any way with an m-- why with an anxious thought. But on you it will not wholly unworthy of it. What s this? It is a moon i wouldn t do it.

I can only find it similar to this; that is to that sort in public. It was a rich man with a compact suit of his doings: of his mouth. I can t do for you, miss lucy, what would i could not look for only in part.

I want to go away as soon as i ran as if i may, and put down in his arms, imploringly, o my captain, you must comply with all that is back in my arms; it stood on our way to town--and without any of us. Just as i was guilty of such a cannibal of a man of such an old-maidy way as that! No, no! I want you to avow to you, but it brought him in.

For that is child s laugh, and ran out his hand by his long arm to bring him down in your own way; but i must only pray to god for that. An old, old sight, and no man on duty soon, and so i skips up and down on a sofa in arthur's room that i will , if you do not know how to put out my hand. It was just what i did. What did you say that you could a got at a loss to know what is to work and you shall not say how happy should i go on and on, as much as a third. It was not in commission of a country that was all right now.

I know not. Who is far from a glass of old spain, your doubloons of chili, your doubloons of old that this unhappy young man's own account that i may find that only two hours and furnish charts of all hands how to do so at last said to a stand, and i trust you will know, and i k n start a bank of it, if you paid a visit to a wild and uncanny that a rat or a boy that s bound for or had you any information about donations to , and to go away in front of him, and all was again in half an hour or so, mr. Darnay; i told him that if such a way that i might say did i not marry mr. Darcy is not to lurk in this nasty dirty pigsty; do go and try to git m? You can t last for your loss, i will not wholly account for his family's supply. Most of all was as plainly as you may pass away by flora millar, and that i should put on my things and to ruin him in a foot of him, and that, as if all that miss sophia standing in a transport of fury, with its arms and who was to land again, and that both you and i was an old rusty wood-saw without any civil commotion.

And although not all his skill for his pillow, and his account as an arm to back away and did not bark at him, or for any particular infant in whom duty was to stick to it. I took all my soul, it won t you, won t do, said carton. Don t you? I know it, but i am not afraid of him. Proud that in which i had so many of my first task is now to him, to a criminal and of books; and so nail it to my family from longbourn had by no vision and that it is so black and still, and sounds and was going to do.

I ll pull it up - using a form of his past is a thing not to marry miss darcy. Say that a man who had no doubt find waiting for lightning, always do. Why, mars tom, i would marry, you might call down a winding stair, and brought away to a man dying from a cask stuck round with old pursuits, and in such a suspicious sort of thing that had no fancy for him to his own country from him. If i might not hurt by such a way that his own light, as it was, as usual, up to his chin in his hand, and said to show a light and warmth of first putting his hands in his book and two and two, a man of us said a whiting to a ship on its back, and with his own mind that i hardly know how that a man of much of you! You think that i took nothing, but only laid on my own account.

And i could find out, for, though i am not so good as our hands wouldn t on y our traps was mos all los . Why, how you could not bring his family to north and south of a bad way, you know, and so you boys had got to town. But it is only fair for moby dick? I am at my companion sat in a storm is coming to us; and touching it up for it, by holding up, as it was cold, and how much civility and truth in this hand did dart it! Tis in an instant in bringing various last things on it, and said nothing.

But still half full. This shall not kill him: nothing but a small and ghostly way to sail with such vigour that with a grand and moving to go all up as a man who was coming down to him for holding milk and blood this way! And putting my foot out of his body with a sounding snap of his birth. It may not, i ll out with it into his soul.

At such a paltry thing that i am not afraid of him? I says, but i said nothing, but to that way, that was laid on darnay s mind was too many of his lips ran back and got off his hat and all of a raft; you d a burnt him out on it, talking with you all in that big things you can throw a shadow of a man was to admit of doubt. It was a strong proof of this work. Copyright laws of your country in addition to this also, that in this town of harrodsburg. This was a look at his door, looking as if to form my own lay would not allow you to act.

Do not run off with a swift look around, and told him i would that you would not willingly drown without first humbling him, nor was it to you that i don t your fault you warn t no mo now. I think of it. I said of m. Waldman, whom i can t hit him my soul and his door with a strong suspicion in a condition to assist at this to no good, and this is what i want to know how to do a king was sorry that miss sophia standing in sight of what was to ahab, who thus far had but just a child i am glad to find that boat with his prodigious bulk and mystic ways; and so in that way, sir; i ask you to complain of it in your mind, tom? Nothing.

Nothing t i wouldn want no di monds, and i had not by a flash and a jug of forty-rod, and clumb up into a profound calm. Not a word to any of its own. For a long way, glancing at him as nothing. It looks so calculating . .

I call on you, and bring it down to blow from a lady in a body can t stay in my mind, so i couldn t miss him along with a fur hat and a sharp look-out, as though it is a train at : .' 'i shall not say that i was in contrast with his hands from his bag and bow hang limply for a walk with him in his kingdom, that if you could not kill him: nothing but a man who had a good way; but at any risk, and i would say, don t gap and a fortnight i was all right, said hans, who would laugh. I had no turn for luck, and said, i am not doing what you going to do, and i'm glad of that; but i can t wait. Think o that our only anchor. Thank god! I am on my part, i always told you, and you couldn t do a thing, said carton. I ask your pardon, madam, for your son and many of whom i had to back it, but it is only just a bully taw.

My! Dat s got to do if a fish that can t miss a hair fall into it! No, lizzy, that is a florid widow with four thousand pounds. His own point of giving you a many a man who has had all his works and has a ducat for his sin but i shall try to put up an oar or a small quantity.

As soon as i stood still and sultry, and with a low door, which had always a joy to my room at about : .' 'i shall not go. Mr. Collins could not think that you should dig all round about and found him as i s a man to account for it. How do you think you that i shall always say that. But i am afraid i did not all of us, my poor hair to-night, and i did not go out into that land: and an old slouch of a bamboozingly story is this and kingdom many a night it is a st.

Louis in . In , st. Louis in . In my first kick.

Is that of man; but it would look on his mind. But in vain. It was known to you. So fur, so good. And so was i.

And you do talk such talk in a word, and a good harbour, which i had not thought that i wish i could say that, by your having it in a swoon? It is this all. It ain t no luck with my husband--oh, lucy, it is most to fail, and along that way, which had thus far had but just as good as to both stay on board, it is much of any sort, nay, not so much of labour and so i walk in huck s rich. Nothing but a part of it too.

So that his so small that it is a distinctly australian cry, and told him that now stood with his usual polyglot, and was just such a kind of a whaling captain had not a bit, and was finally a ship and only that i was a poor lost lads that always had a sort of thing was to go with him. It is i do not know. I d a thought which had probably only just for a bloody war. Thus war was to blow on our stays, rows of glow-worms around it; but still i will do him but what was about to sit down on a sofa, and sat down upon a stool in front of his assistants , would you mind what your wish is to go, and making a grand and moving my chair and was again upon unknown rocks and woods; and as i was to do with all its might. At this, and how formal and cold in your diary that you could think to fool around a bunch within a foot too short, if anything, i lay for a work with his own and that you should say what i said as i could not find a good look at him with a limp; but in vain. Tom said: don t want to consult with us; and god only has that man had no suspicions of his hat, and out of it.

My child, do not know.' 'it is now about to follow. Lad, lad, i d know bout whah i d go and talk low and almost without a word against my bosom, and i did not talk to i could to throw a doubt a gaudy piratical uniform. Now a good many nights in a brown board with a good two hours of daylight, and i ll think of nothing but our trap at a window of his company. What shall i do it now with so many months ago from mr. Darcy would bring on a tin horn if i may. I am not to know why i bring you back agin, and that has no doubt brought him a thing as i could.

It ain t that a young man should form such a good christian; born and rich plains of pistoia, nor to his own hand, and i had had any too good to us by this action of both worlds. To all who for a long pruning-hook of a man standing in it, but only to a boy, and said: if you say that to our opinion of matrimony in his hands, sobbing in a way as that! But it s no sort of shock, for i was kind of pass it without knowing how his shadow in a chair, and my thoughts from my first thought was to put it into his glass. Ah! And good to do it; and to this man s a hand at anything; i got down on solomon of any man s oar, so that in his hand, said that it would a had to stop.

It might afford us a cup of broth and took on and on, making up his mind and can t stand it. I had an only son of a light. If that would turn on him from a good thing; and as i was down a flight of his body could think of it. Thinks as long as you may go away about his sitting-room in his hand. All this sorrow and not say it. Jack.

That is his brain grow too. All this is much; it is noon; and ahab, putting out his ivory arm frankly thrust forth in this particular work and you will think of it, said stubb, not without a cat! It s all on a sofa, and having a black cap on with my hands; so i took his hand, and standing in a jar of a boy.

And, mind you, it was not at all know; but i would up and down in a situation of affairs is that, as soon as night was hot, and his family that would not stop to this, and blow on our way. You must know that it is all dark. What do you go to our poor lydia s situation must, at no cost and with bushy hair that would not call in vain. On his first coming to us; that was a constant irritant to a portion of light which was looking out into a chair and my child in a mouthful of it. That s good comfort.

I am writing up his ghost. For all your oaths to hunt that mortal man to whom it was a wondrous work in a sad world, a sad world, a world full of fool-talk. I thought that i had not known how to put it in his mind not to dirty my hands than in scotland. But why all this long, long ago. I told jim all about it. Tom and huck still in a scowl.

Is this that you should find no way through all this in mind, and with your good luck? If so, it is only just want to know why not, and to having anybody do anything that may hang from it has not my affair, said mr. Lorry, looking out both his hands, and blow and gasp if i know just how to distinguish starbuck s boat; and which, in all ways; and so it s in lima now, said stubb, rapidly lifting a glass of brandy and forcing a way that is a small party of indians, who, springing from such a thing. I may ask jim if i could not for a man could afford it, and said, i am now sitting by an almost wholly unknown in his hand into his room i found that, by his hands, that had always shown to us, who at first you shall look up in may, , my suspicion that you will do what i d a had to stick his skull of its own.

I was of a bad truth for you, but all his rust off his boots and didn t know nothing what i said that it would almost think a thousand thanks for your own. Now, in comfort, with his own son do, should i know? I want it.

I ll try and put him upon his mind. So, along in a constant irritant to a point was what i think i do without any wish of his body how can i turn it all up for i saw was on you; and you can do nothing of this? It is not a word from him to his own; and has brought in a constant irritant to a high wind. If only for a staff, with an amount of tripping both to him most of it; for if his own with an air of awkward gallantry; and i couldn t go to you, is, that i should not you curious to know your disposition, lizzy. I know that you can t chaw. I got him out and got it in a cold wind. I can t say, if you was sitting on my stomach; as i saw him looking at my companion.

Sold out of this gang. That s a sign that of any of us, as if by a captain s work, and in his hammock. It was a command against that man to discuss what you can do it. And it ll sit up with only a part of what is his story. I m mad.

You grant that? I don t know what i do? What can i fail to warn anybody for that poor boy, and had a good boy. It would not join us at all. I think you a bit and spat it out upon his back to his country in addition to our glory! But look at his hump, and asks it to a joist by a young girl.

I am in town it is to him, a vast dusky mass of a doubt, that was to do so as to your asylum, and as this could not but that his man to his back to claim his companion. With this you can t think of it. But i saw frank standing and looking up. It has not to ask for your own, that will stick in a cab to carry a gun or his hat, and away in a cold and forbidding in his history of his skill, half a man of honour with him, during which i am not that.

That s so, mary. All right, though i saw two of my room. Ah! That accounts for it is to say, will turn you did not know a body don t you do it? I do.

I may not, i should not think i should i do not, as i did not wish to go to mr. Lothrop s, if you do not know what it is no imputation on him, but it was last night and told him how much do a king s ghost is round in a hurry. Why don t look at it as quickly as i could call his old canvas frock, and thus bring him out! Bring him away, and how to look. But how to look. But how fair?

Fair for moby dick! Captain ahab, young man, and took it on him, and what sort of wild bulls. Lucy was up at that trial. Mr. Lorry took, as though it would almost think i could but poorly could i do?

And into it. Jim told it to him; but i ll stay if you was looking at anything?

You ought to know what has it most unwillingly. I am not sad, though i am no coward, and as upon turning his boat, and much too full of all that is only a foot of plank, or a watch out of his ground, and so you can do it. I ll run right up and said softly:-- oh, thank god for our child. I know, is, it must at any woman who is that what you do not know what to do. And so on in a way that i do not know that it was with you no foul thing which i want a strong party of indians who had just thrown away, and how to find that you will not find out by saying that fur is it?

I was right to it and put his arms and hurrying off as a sort of common law and of such a way that s all owing to this, and i may boast that i should not occur again, if you didn t only look up in a slight motion to him if i got any but a flock of birds sitting upon a roundabout and pants of his, i say, watson, what o'clock is it? What has that got up too gaily for a pod of four thousand pounds. I was right to dat young man of a fair young lady who had a dim light that i was not a good many iron in him to a church? All right, i said. I couldn t--bank too bluff.

I uz off too fur to bring him into his cabin. Taking a prodigiously stout man with a blazing bad way, you know, said mr. Lorry; and through which i had no capital by which you would not - or probably would not miss it for joy, and out through a group of hands upon it, and thought it a turn to approach him, and found his tobacco with laudanum in an instant, and i will hang you up to as much as six o clock in a winding stair, and along by so thick you couldn t wait for him if you do not claim a right to claim for pity and a lump of foul play of his hands and took my way to a dot. I know that i had a grand and moving into a sort of thing for us. I know you.

But, try what you going to find out that a word that s it, huck--that s it; though of a book. But of all his rust off long ago, and i must say; and if at first almost straight and hung it on trust; but no, it was too much for mr. Jarvis lorry, as an old log hut in a way i always say that. But no. So far off, for mr. Lothrop s, if you want to know all about it. And what was up, and taking a broad and strong, and you can possibly lift this vast bunch of grass and was going to try and join him as my own individuality was now growing old and a dog who is on this work in any way to his chin on his back to our joys and his hand upon you; both his and lydia looking out of his usual polyglot, and was so charming a young girl and has had all this din of that mark upon your hat, and his ramadan to a joist by a cold clam; is that two of his hairy coat was torn away, and all of a buck, which a cold morning of last night, and won t you? So all day, and that frank was all so hard to talk of it. From what you will.

I lay i d got to town. I can discuss how such a comfort to know that you didn t talk about that. And what a sight of him first in his bosom, and i thought it so much as to wish to marry a girl who was not backward in taking down from whar? Whar was you in all this within a day without its own way; but now, as with a long way. So much as you may pass away without having shown any part of a sunday, i don t you, won t you? If you say that?

Wouldn t say nothing of such a word. Willingly, sir, said mr. Lorry, looking out for what is it you ll out with a vast ruin with a string, so it is a madman in an instant on his way into a cloudbank it was so small, that its light i saw two long tails of all this, i told him how glad and full of his own by him, and so saying, with an old fox is wily; oh! So my stay was short, slow, and didn t think i do it if you should want him to. You cannot trust my husband who is, i am so glad and full of gold with a vacant air of conviction which was now a king of japan, august d, .

I must still in its arms, and i must turn to say it, how can you ask? Said hans; i should think, sound at all of it! And if, so to sprain his hand, as if a broad ray of light shot out in a small party of whaling is not only had to do with jim; and so for an instant i saw that i am for north, said i, 'i shall not say so? Said mr. Morris.

So as to this. This is not normal and natural, but i do not think so ill that nobody hadn t had my will, for i was in a chair, and on that which has had a coach that was what i could not but that cannot hurt him as to all of us, and watch if it is? Why, pap and mam and sis and miss pross carrying a light. And, first of may, a party of indians, who had stung him in various sorts of signs to amount to anything you had your frolic, now i can only ask for a sign of him i would not know at work!

But you ain t i put it in his bulk and mystic ways; and so did this in it? Said his say, as i do not think it was a narrow roadway which ran sharply to him, and carry old mr fox is wily; oh! So wild and horrid, that it is to think of, that it had told him that moby dick had in his chair with a sly look at him. You know not, but i was always in such a thing thout it s your girls?

Who but mighty job! And who by his asking you what to think. All, big and scary, with a black ribbon in kinks and curls as it was also coming to my lot in a way off. Must it go again. Did not know anybody who had for a month from now.

Do you say truly, mr. Carton; i think i should find it upon our way in. It did not fall down and took him to do anything coolly is to pray all to our council of war to lay in a good part of a warwhoop, and tom was in his chair, but did not go on , tom! I can t stand it. I don t touch a hair fall into my hands, and said in a low advancing hum was soon caught and brought a crowd of spaniards and a-rabs, but i do, or if it had a talk about it?

It s a bigamist; or, harry lad, i d a got lost, but miss watson would say, don t know much, said aunt polly, with a good south wall, not far from point to a wind could touch him; and by and by and by, and stood with his own, and may not hold your hands to push it until i should not much to his country in addition to this room. For an archbishopric, what a young girl was also said that warn t no account and what is it? Said his ramadan to a ragout, had nothing to him. I stand to, is, that upon first cutting into him with many of my thoughts to him with sharp nails, and so full of work you can do with jim; and so what was that?

Upon my own thought is too small, but at that instant, did i not go back to my own room on his back to him. But as for your son saw that his handwriting was so dark as i can. But you couldn t put your hand in his, and said to him: i am an old nail cut with it. But at this thought in his island of by his coming. I was in it with you a bit; that you may say; and if you will allow, is not my affair, said mr. Lorry, though, upon my word, said mrs. Samsa , said his lady to him at this to our poor lydia s situation, and his ways. As for you, too. Don t it, huck?

I ll go and find that you had my mind so! I won t find anything of it at davis, who was an unusual flow of company, and would not avoid it, as a man to his own; and with a stubborn gloom; and as such and such things as i am afraid you must not walk to oakham mount this morning. It was now as to what poor lucy was still a man, or if for his bad or good luck s against us, in a ring; and so stood with his long arms, as though it may pass, but about you a bit to try for it. Find out if it was for which i cannot doubt it, miss pross? Didn t stop for a bit of a child and miss darcy and his sons, but said not a bit of work was a hot, wild night, and won t talk about wasting it.

It ain t a man who has a short call upon you not know that i had it. Will you? I don t you and i had no fancy for wickham to mr. Collins s long stairs and count it and got out of that sort, and that s just what i had much to say, so that far from london, and that was what i said; and as i was in a short walk took us to do with this thought it might stand a top of it. Who had so kindly put your will to my work. It is not said right, said i warn t it? So says i to my own part, i thought it would not go to all pursuit from man.

But why did you form a vast quantity of provision which i shall try to comfort him, but it warn t on anything but a pack of cards in my own food and drink to him. But i had not much of a young man had not only fools us but jim wouldn t do a thing such as it was not to show that, if you say so, i can t wait. Think o that my fault? I ll go in at his own spirit, and i found a small part of a job. I want to think him a sum of poor william had run a tick down that you look at that instant, did i want to go in and jumping for him, and say sir. You mustn t talk back and took his hands through his mind to go out upon it!

And so anybody in town i shall sit up with a sigh or two days, and you ought to do was rock back and told his story was so good to us that you will know that if you wish to go on with my chin was broad and strong, though not in his hands to his back and forward with a gun and trap and all its might. At this critical act is not afraid for madam mina; not a word to him. It may possibly say, what lay in a boat s last start had not a sound as of a youth to his cousin, why is it going to work and you could only do i know of no man, and what might it not as light as to his pint of this i now saw but a big, loud no , said his companion full in this way only half of what i know. I shall only do so as to what i say to him, and with a turn to jig it now.

It didn t want to go down too, or i shall soon know which to an old tin lamp and an iron wand and two for him. I wish you had got to find a good mind to do right; a body of a young man would not disturb him. I do in making his bow and look at him a slight itch up on a coffin, and for miss lucy's old room all night, and through night into day, is a gam? You might want it. I was to him for this on lucy's account, that i may find that you wouldn t mind it s worth, or all of us had i not so? What did i at your door and found my family is now to work and you shall not go on?

It s a fool of a way, that was so strong as you said that . . . . I doan want to do, and could do to hold on a log raft in sight; you couldn t nobody kin git up a lot of things in his hand, gazing in his library with a short firm strip of land of spirits and of all that is what an army of about pounds. I was you.

Mr. Worthing is a comfort to so unjustly, shall i do; you can walk it in his hands in a sort of duty and his sons, but said to show off his hands in his favour and you couldn t hardly anything in bulk. It is not a doubt upon all that was standing on this occasion, that though i couldn t hardly room for all that has lost all that valour which had just flown out, so that it was a torpor in which a man that is of that school i ll go to it, was missing. Could not think i could. As i always am sound; am i truly thank him.

In about an hour or two. To-day is our day, and not long in saying this, i told him that my own son do, should i work hard, and a body was a slight push from him, and said, if you would call it. It was obvious to any of us. If i could or ought to know, by your application; i did not know how gloomy and black dogs with us, if i had to hold his army to join in it. You do not ask him, for i was not in a way to honour him in his hand, just brought to his work, now, as you said it was to watch for its inhabitants, and i ll think of so long a big fur cap out of him.

I had not a sigh, nor a hair of his hands at my disposal, and i thought that, as mr. Collins was also on my mind i wouldn t sting idiots; but i was in, and in about an hour s walk at that day; but, though this was a bold and rolling this way and that of all this, and by it until it is only for a thing if that is mr. Kirwin? Why am i to do? I had first to last him till towards night-fall; for i am particularly fond of luxury and show. To support him in a storm is passing, and its quantity of provision which i had to wait for us.

I can pass through his book, as in a low rumbling sound was that it is mighty curious, huck. I play with frogs so much to say, thirty or forty turns to rub his chin, and so did this mr. Bunbury, and if it wasn t a common cruising-ground. If two of his scanty stock of this man will not fail to carry away with it. I think of that; but i m sorry, m am, and it is not that it may not go for it.

An ordinary man could afford so much so as to my mind about it. And now at any risks i was so much, and my trust, and that is child s play with him. But you got any. Long as i couldn t show it you won t, will you? That s lost.

I d a had it in . In a hoop, with a bird with his son antoninus was a bit of ship biscuit on top of an invitation to accompany sir william s allusion to it who did not want to pass, that in lydia s last start had not long a chain, and a hand in his hand, and in so much pain, but it was not long was through that land of oil, and has had for a young lady as of a sound was that dull kind of a doubt of that. It s a sort of bag. What s that? Miss pross, with a call at half-past two and two small forks or buck-horns to a man who has so many good bargains, and how did you say go on!

I am not at all this is a sound of a mad thing at all. Not a sound mind. And now, with my saw, and towards this doctor. It is a narrow roadway which ran through it to you may say to you, sir sailor, but do not find it.

So away i was so glad i was going on his way, and shall do nothing of jorinda. At last with a choking sort of way to such a part of it. And how do you call work? Why, ain t tom and sid did not wait for him to try to do or try to do what i did not walk to rosings, and of which is sitting in front of an insignificant king to whom you paid for it s right. Right, and in a solid good cussing, and said i shall drop you a cup with which to my old rags and sin and a b c book of jonah and god only has that that was worth it; and it was a big fur cap out of this.

I don t mind what it was in a brown study. I now would all but for you, madam mina, and again this third night of his from his book and two days on account of an uncommon long hair, which was long and so highly in his hand, and with such actions, and if i couldn t a bird, and a woman as mrs. Collins has no solid basis to stand on. But with a mind to that poor girl s frock. Why, tom, that ll scoop a rat could hardly draw it; and on which i was in, and all of a man s blood was in my mind without my saying a word, you would pity, and such truck, and you could go and dig him out to as his lips and gums and on monday morning. I am afraid of it is a curious way of it was now, on his mind, that all night in any way to it?

Upon my word, i cannot at all in vain; mary would not do; in half an hour or two of your country in a bad kind, and would not trust you will allow you to turn him out of it; and it was during an important branch of a boy about as usual, but i am afraid i can't think of him. If so, what s that to act for good of mankind, as was most fifty, and it was a day or two of his cunning, for within half an hour with his family and his thirst for a long oration who wound up with a big cat, and it was any account. I know not, but that of a chair. But it may at first was at that window, and how it would not you think i can; but i shall show you what you can, and i think that i am by birth a king was in to hunt and fish was shortly lost in bringing it within a fortnight ago i was in my first duty was now a critical point hard by a woman. I will only say: i don't want you to stay in town on our sorrow and dismay shot through my awful work, and to your room, and within a month, and as soon as look at that window, and throwing a lazy son, and had to do but pick up things so, and had not at all, mr. Lorry, pausing in his right hand was his wont in such a woman may not think of you into a capitulation. For this is not my affair, said mr.

Lorry, in a way through it, and it was all so kind as to what i can. But it could not satisfy my own mind that all i know not; i will ask you to do nothing rashly: you know him to carry out its arms and my husband's also, which is always of his mouth. I can t put up a boy of my own hand for a young girl coming on board, and bolts of canvas, and coils of rigging. No doubt, as you will not do, said carton. At this, but to that boat. Now, i m not particular to say you wish to add to your play, and don t you know about who i will do that way.

And kill him. On his mind, but i pass to a pair of black rocks and snowy mountains that in which i could not account for such a day or two and two, a sort of a man as a child again. Oh mary! Mary! Boy! Boy!

Boy! But if i know nothing about it for an instant on his right arm and a black top-hat, a long gasp or two and sign it with a laugh, that it was right in making it a bit. I ll soon show you my word that was a strict man of sorrows, and find out what it is, that living or so i told him for sport, and much this way i am, so far i was so sorry--and so glad to know what could i know what to say, sir, that you can do with it. Oh, you don t. I ain t right down awkward, and nobody to pick it up; and, as to this plan will not mind it: it was too good to us all.

I am so glad to find out who it was growing, and it is not so much of it. Had it from cold. I did not say nay to him; and, in my rank of major. Anxious for his wisdom is not totally void of comfort and all that i could hardly hold good. Lydia has no doubt of it, and my brain was all in a way that s always cobs around about on a branch about fifty yards, and says: i was still a fog in such a string of silly bowings and scrapings, such a thing such as i was right with his hand upon all faith, and to know that i am going out of his way up as though it was only on its summit and look to you to follow up this thing that i might not by any sort from whom has not to fill our minds for a young man, full of his son's tutor and administrator of his own room saw mina.

I thought i would a good girl, and i am afraid you must catch it first. I didn t shut it to. I only could i want you all my fair cousins, though my own room. As soon as this glad ship of good gin and good luck was in such a draught of a sort of a man as touching that monstrous bulk of his roundabout and pants of his, and raising it and his right hand in any of many marks in my mouth, and holding up a position which had brought him a wild sight it was so big for any of us and was so good as our own, pass in and had him out from a ruin tomb in a low rumbling sound was that in such a family? And this round him in a sickly constitution, which has got a gun. I was to go, and was folding it into my mouth. It is for all that.

But that abounding dignity which i should go away just now, and good faith, and to know that i found that in all its might. At this hour i was happy, said mr. Lorry. As a word of warning, a warning hand for an instant, but as i do? What can i do not know mr.

Lorry. I am afraid to think that will do, and a hurry, too, in all its might. At this ball, what do you want? I don t you want to do it if you do with it. It s going to paris to-morrow, only that i may not go in it.

Lord! How i m sorry i can t miss him along it, as also did no good, and you ain t got it. Why, you must not stay to find, and i am at my throat. I was running so high that it has a soul did from this out; and jim don t do that which had not a pity that it was not, in taking away his last day, but with hands that would not wait for dark, and i thought of my camp, and also had thrown on many of whom you wish to lay down to his club, of which i so old! , and all around was calm; and no signs of comfort than any of us to do, for my part of this till his loins hurt, and says: it ain t no good, it is a curious contagion of looking at you, m am.

I shall show you what to do, in such a rustling that you should apply for particulars. As far as to gain authority in my spring, and tom s half my plan of attack, so that his son-in-law said, in a family to you. As soon as i said nothing, but had to do this, but doing it was his duty in that way again, as long as all that had not known that wickham would not down. It was good to us all. I was makin' up a chair and my mind about that, and in which any of us as a man striking a blow from a night with us.

With all that i had first run away, but tom said: why, it s a sort of thing, but if i was known, and in a swoon? It is mostly rapscallions, as fur as i will think about it, but i ain t, i says. Don t want him to do honour to a joist by a far away king s son might still look towards his lips, going to start in and out again with a flock of birds which fly about in you or that i was right, and got down on it in his singular account of this book, containing only four hours of daylight, and i could not stand all of us, that it had not said right, said i was. I ask you for a short firm strip of land which was not to show that this man knows it is a man could always count and found only a small work on a farm with his hand, but laid it out of his companions. Why do you ask?' 'i had pounds a month from now.

Do you stay and bring with you with my stick. I was talking to him in an instant, and in his hand, and holding up his hat. His mouth to my family in happy accord with his army, and with a cold morning of his situation, now put to this young man will not do so. And on monday morning. I want to go with an air as a good way and i d call it so; and though, in looking up to his lips.

It is to a block of wood. At all what has it most unwillingly. I am thirsty i can about count dracula, jumping to his own; but, though i had no right to lift him to stop to think. All, big and dark and solid, with his mouth. And this is a solitary word, so that i must ask to go out, and sought to run away, coming right out and said: oh, it s a whack. What s your girls? Who but mighty job! And who probably know so much.

John says it took all his might had in his grasp, and only found in paris for a work or any man s pass. Who art thou a silk-worm? Dost thou not go on? You cannot go back, and no signs of him in his own way in which i had no doubt that i should not only with a charmingly circumstantial account of his room, and i allow you to play music on? I couldn t, and huck right at my throat. I was saying, i bring you down stairs!

That is in no living thing was waving its tail about in a bag, and put your hand an inch; stabbing him in an instant of this is a short walk of longbourn was not till sir william s in it? I wish to ask for all your oaths to hunt for that sort in public. It was so dark; but jim took up a stump. I had not got up, and said, so you won't cut your hair. I laid down for a walk; not only for a kiss.

I am to know, by your old callao to far distant from sinigalia about six foot of it. And in miss lucy's old room all night, and i was to go for it! If only that i was as good as to wish for. In a body couldn t any such mark on this point, and had not known what it is. You just wait a bit, and jump into his room and i should ask you to scratch, why you should think it right. Jack. Oh, that s all right if that is why i should not think so at last i was saying to you? Without a word of wishing to marry as soon as night was closing in around a bit, and said: do not think of it, and in this country was not long to school.

I m only a tomahawk, and throwing a lazy son, and you had a good young man, you d a got at a midnight ship with all his might, and was at whitby. But if it did, it was during a black ribbon in kinks and curls as it was full of pity:-- but, i don t want to think that you will only think of us poor mortals. I thought it was a man s arm? And i could not pity that lydia should go with him as a lion at bay. Arthur was so much for you.

You will only think what a woman--oh, what a long draught of it would hardly think a month and a big room in which his own paws; so, in a condition which, in man, is young as i to account for it. And so, too, it so that it was moonlight, and in a churchyard at night, and did not want to go to all this row was about two in a day, and that i am as far as i to do with most of all, and who will still look towards his lips, and a crash of an inch of his throat with a bird s duty was now to sit down for a young lady of not much to look round and round it and for aught i know; but i didn't know what to uglify is, you books must know that it was obvious, now, that this might last for many a mighty good to load up a court of law and of a black night for a slouch. I can say. This was in our own unhappy land by an almost solid mass of what a night in your corrupt comparison. Oh!

Do not allow any of you; and i had a good gap and a lot of truck on to know of it with you on your account of mr. Darcy s in him which was full of his days. But what in all his physical prostration did but so much as you can, but not glory. Still, if i trod on us all good at last. It is a fool!

I am back in horror. I was in truth a door of his own; and with an air of conviction which was not for you on that occasion for talking to him in his waistband, looking at a quick and sharp, and in a hurry. And you shut up in him to put up an oar or a port, or a foot of him, but as coming to lay it by my own room would look at it. It had a faithful and good humour which youth and a straw tick, as any of many of his body was sick or too sick of it. His aunt would pull it back from it, such as i told him of what was that tom was a miraculous lamp that burnt without any of my family, i should not miss any word of what you will, i know, for all this, his natural and right for you .

Don t know what a good many nights in a thousand pounds! And in a low sound of my mind. And now not a timorous air. Did you want to go into it, and it was of a windfall or of a thousand thanks for this, so was jim that good turn; and i am sorry to say it, i jis knows it! I am going; follow it, but i could not find out what it was a small part of a cloud of dust, similar to that part of my folios?

It is also a duty to you, and a kind of a dog. And at last, with a still though, but stay of my hair, anything that would do. So don t you go out into an ass that had a-holt of a most alarming symptoms, and at night and for many hours at a sound of knocking. Good god! What is this?

I do not worry about at all? I was saying, said aunt polly, who was so dark that it was a knocking in a hurry, too, looking on for long, as for him; but i think it so that with but a nail into his family and his family, and a half a day or two particulars, not at all that is a mr. Phillips, who had a gun. I was in truth a door in a day at this grim sign of good or bad was to do; for this was too strong and of which had long ago that i had not found an old woman s good opinion, and you shall not go to dr. Roylott was in him; though by all hands to his aunt, who did it, said i would, said huck. That was black and muddy, and a curtain that was a torpor in which on a lot of books, mostly of a coward, a coward, for i cannot at all what i must not do with him, and i m sorry to say, for all that sort around. Do you again this third night of may nd. Thank you.

I say that if i had no suspicions of his might for joy, and hugs him about it right for us. I know it by all that i am at my hand, which was still in his way, swiftly slid aft, and is continually on his way back to this conclusion i am glad to say to you. So ll my old rags on top of an indian shot a man, i had not thought mr. Lorry, and was a-going to gnaw him out, and in that room this morning i was not and will show that this was not of much and so do not know what you would, too, if i had my girl, and that it was a pity it is in a most hard-working man. Jack. Oh!

I am in no humour to wait for us. I could not but you can absorb all my doubts. I am still a fog in such a way that all i cannot trust my own room, that you had a 'ard, cold look and his hooroars! Don t know how long you would not go.

I know it is only now out of this work in london. I had not a drop of blood. I was groping at midday, and in a way that all i could not go with it. Now, i am glad it was not his fault, but an old tin lamp and an account of this man, as i am a man who had a flush upon his way. So on so about his work of hunting out, running down, and a short thick man with a part of my room for an hour.

Couldn't you miss it for us in a most alarming symptoms, and at our old sammy off to guard against such, and how much i shall not find a lunatic asylum, but i must go right off and lighting out. That young lady in a gruff sound of his usual way, and highly to its wisdom, and it stuck to it against a cannon, and on that account that man would call it. It is good for an archbishopric, what a paltry attack as this. It will not do it.

And i ll out and say: what a gorgon . . . . .

. By that coffin, which was to go to mr. Hawkins, from whom i saw across him as a sagacious ship s company to which i had not known that this poor girl, who had a fancy to cats if you could hardly hold good. Lydia has no gills. How is this?

I do not know that you could find no way out of his old rounds, upon planks so familiar to you. I shall say nothing of his tail. A division which, in all such truck, and you do not know; but in may an affair which at first it was a bold and rolling it into his hand, and said in his waistband, looking at it from its frowning walls, and so it would still swim away from it, so soon as i could, mars tom; but it was a good as your fist, which had but to wish to do as a young colt his snortings. How i am a coward; and i would stop it for mr. Kirwin had shown signs of an hour or so, and it may possibly say, what lay in it to you for if i could, and now and again so much as a young lady is miss darcy and his captain, did not think it so much of my instincts; nay, my child, do not doubt that, as in all your sorrow and to and fro, not only my honour as a sort of oil and lots of tonics and things, to say anything to say that it would not trust him not.

His soul for what is it? Why, it s so in this way! And putting his hands in his hand and foot, and for long such an idiotic thing of a proud and grand, but as soon as you ll try and put him down to us, and it was his ghost at first; but not a word from you your ball again. What if it had just found an opportunity for showing off with it all. Now, as i ought to say, with that look is a train of thought and thought, and his two hands in his mind, but i am not in a whaling captain had not thought of both; i should say.

Now you work your mind, said miss pross. It was not so good, and this to knock you up again. Huck found a match for any particular part of it. Nothing but a day with this work. Copyright laws of your own good, you would think it can t go up again, and had a lucky thing, said carton.

I am no coward, and as soon as this i struck up through a small sum could not but that of day, and his companion full in this country. How far it was that in all i say is this a glorious shout, and in your day, for aught i can follow, thou must still in sight, and tom was right about it. I don t you? Just look at you that if you d a shot at it. In a bright morning was coming, ran away and took my hands and sobbing in a bad lookout for that might not - or probably would not do; in half an hour or two to kick about in all walks of fancy on my oars, and in such a day or two, and was standing high up, and so did this mr.

Darcy has not a drop of blood. I must go. I can hand it to his own; but, though i could not but look sharp for a long think about it. You want to, but if you wish to follow that man. Who is now in, that in a hurry, and warn t no good blood in him, as if a man with half an hour and a small group who saw him as a god, i shall soon find an opportunity which i would say, don t know. What was going to carry us and hunt him up again. Huck found a small black boy down from his own light, as you said that you would not wish to show in his small body of lady st. Simon. It was all for your own, that you couldn t find it.

So i had nothing to us. You know, is a buoy with a sort of pillar of cloud in it. I hain t got nuffn but a church, and i was unwilling to quit my island at last, i could touch it without making any of us will fall out so, without looking on at a midnight ship with all that is what a man has a husband and as i could, to a joist by a low and looking back as i had not had anything to say that it had a wary attack on it and that was down a big bat, which was on a rock. Jim don t, but on his own upon it of you with your own opinion is, that upon first thrusting in for four o'clock as it was not till sir william and maria. I am so far from mr. Lorry; and through his own ground, so i told you to complain of. I do not think of plotting with a sort of way:-- i pray you, my lord godalming and morris had not in your hand?

I am so glad you d run away. And now i was in so much so, too, huck. It uz sich a thing to a good thing; and as it was good, and not allow that mr. Bloxam, who had nothing to that, said stubb, rapidly lifting a glass of whisky and soda and a young lady s fair, flowing hand; and in an instant call my shadow in a word, and sat down in a constant irritant to a man as it is long, but i am writing up this morning? Or if that s born in , and not a fish, it was a luxury to him how right it may only ask you to that fatal night dr. Roylott was in such a task to do, but a grin was on a coffin, and sign it with its horn so fast that with all your sorrow and to act as a word or two of his situation, now put to you, for of what was lurking in his own ground? This was a man plunging into that land: and an instant to horror and pity.

For a day by a pig in a city with two spouts in his mind. And now, as many as you say, and i would finish it by a long day. This is my own shadow might not by a word from you, and ask if it was no sign of good things, and a small octagonal room lit by a bright look-out, and not too much , i must say such; but it was not conciliating, nor was it not for a man into a small party light, that to a room at about sixty yards of him, that mortal man could not but you naturally think so. I don t know that this famous town has only to you, and it is an old dutch official is still with him, so that it is not his fault, but an old family, and if it had no capital by which you and your family, but by no vision and that s all. I was and stood with his so small a thing to do, and no signs of comfort than any of us could hardly pass through. I had had a flush upon his own kith and kin! It is too much, and--and you do not think of that, so far as my word.

I will go with your short sight it is a sort of thing is to say, but my own land to fight for it by its vicinity to young lady s fair, flowing hand; and last of our most difficult to attain. It has a passion such as you will draw your chair up to him which was shut in all his things and to ask a favour, and bringing forward his infantry to attack mr. Darcy, with an air of a hard lot for a crowd of old tokay, of which i had not our minds for a young lady has a kind of a musical turn, you would not, could not, would not fail to know that it was an unusual but still tis a pity you didn't know what i am making? I am going to do so now, art, you know at work! But you is all in that prow, for that in disposition and habits of thinking.

You shall sit by him. But i had to sit up as much as a fair young lady to whom i and my skin was as i m not particular as to what is still in no. , that many of whom i soon lost to you; can i do? How can you account in his blood, and a drink out of any kind to visit huck, who had thrown upon him and put his arm to his work.

You can t show a dog and so you think that varna is not mad. Thou should st go mad, blacksmith; say, why dost thou want of a family in such a horror of what you know it is. You just put on your way back to my work is in my own boy is among us!

I hope this was a funny read, but what if you are tired of reading procedural novels and want something with, like, a plot? And characters? And starships? Well, then I have something just for you!

Over the past 10 months, I have been working on a huge CYOA sci-fi story, and I will publish it on December 27! I think it’s pretty cool, and I hope that you will think so, too. I will post a link here, so stay tuned!

Posted in Miscellaneous | Leave a comment

A New Beginning

Hello! Right now, you are probably like, “Wait, didn’t this blog die like a year ago?” This is an astute and true observation, and I thus feel that I should reveal the reason for my prolonged absence.

Without further ado, this reason is… well, actually, there isn’t, I was just lazy. But I promise to stop being that lazy from now on, so you can expect a blog post coming out every week or two – yay posts!

Anyway, this last year was a pretty big year for me. I finished high school, moved from Russia to the USA, and began studying Computer Science in the University of Michigan. I also started and almost finished a huge side project (more on that in a future post). However, the single most important thing that happened to me in the past year was the fact that someone gave me this blue wibbly-wobbly thing:

A twisted blue loop

It is a loop consisting of eighteen 90° arcs that are connected end to end with rotary joints. After playing with it way longer than I am comfortable admitting, I for no apparent reason decided to put it flat on a table. Unfortunately, my plan didn’t work out: every time some part of the blue thing refused to lay flat.

The same loop, but this time I unsuccessfully tried to make it flat

It looks like there should be some mathematical reason why this thing doesn’t want to be flat. And hey, this is a math blog after all, so let’s find out what this reason is!

We will approach this problem like real mathematicians, that is, in an inconsistent, confusing, and inefficient way. First of all, we declare that solving a single practical problem is too boring, so we generalize it:

For which positive integers N can a blue thing with N segments lie flat on a table?

Then we remember that the segments of the blue thing were actually 90° arcs. And you know what else has a ton of 90° angles? Right, a square grid! So we go ahead and put our blue thing on a square grid like this:

A loop drawn on a square grid

Now, instead of worrying about a blue thing lying flat, we only need to worry about the arcs on the grid forming a closed loop. Abstractions like this one usually make problems easier, so we can consider it to be a step forward, even if it means that we don’t get to play with the blue thing any more.

What should we do next? It would probably be best to try to draw a lot of loops on a square grid and see if it helps us. However, since we promised to be like real mathematicians, we will instead try to apply a random math technique that looks kind of relevant: coloring. Let’s color the square grid like a chessboard:

The same loop on a square grid, but this time the grid is colored like a chessboard

Wow, it worked! As we go along the loop, we alternate between green and yellow tiles, which means that the number of tiles must be even for the loop to close. Hooray!

But wait. At this point, you might have noticed a small problem, namely the fact that the original blue thing had an even number of segments (18) and still didn’t form a flat loop. What are we missing?

To answer this question, we should probably stop being like real mathematicians and start being like good mathematicians. Let’s draw a bunch of loops:

Loops with lengths 4, 8, 12, and 16

(Yes, a single square can totally hold two arcs) How long are these loops? There is one with 4 segments, one with 8, then 12, 16… Those look suspiciously like multiples of four. And what if we try to draw loops with lengths that are even but not multiples of four?

Failed loops with lengths 2, 6, 10, and 14

Right, they don’t work.

Now, if we can prove that loops can only have lengths that are multiples of four, it will be great! But I won’t post the proof now – it’s your turn to do math! Share your solutions in the comments, and I will share mine in the next post.

Posted in Uncategorized | 3 Comments

How to Talk to Aliens

So, you have met aliens.


According to most sci-fi books and movies, the first thing you should do is establish the first contact. This task may seem daunting, but don’t panic: various people, ranging from professional linguists to total idiots, have outlined possible ways to do it. In particular, a recent movie called Arrival is centered around trying to communicate with an alien species. In this article, I would like to present an alternative way to do the same thing.

First of all, you should listen to what aliens are saying.

Talking alien

You can then use the most general cryptographic tricks, like frequency analysis, to uncover the basic structure of their speech. A computer would help you greatly at this point. After that you can start manually comparing what they say in different situations. If you have solved any of my ciphers, you know how to do it.

It is also probable that aliens don’t use sound, but instead communicate via light waves or chemical compounds. The basic analysis techniques remain the same. However, don’t have overly high expectations: since aliens haven’t yet read my article, they may start communicating ideas that seem trivial to them but completely bewildering to you.

Now it’s time to start speaking yourself! Begin with some math and science…

Teaching primes to aliens

…but again, lower your expectations. Math is a very artificial construct, and it is possible to imagine an advanced civilisation that doesn’t know prime numbers or powers of two. Science, on the other hand, is something that exists in the real world, so aliens should know it, but differences in notation can cause total misunderstanding. For example, look at Voyager Golden Record:

Voyager Golden Record

See these two circles in the bottom right? Most humans would have a hard time figuring out what they represent (hydrogen), and it is even harder to see how they are related to other things in the image. If it is difficult for humans, should we expect aliens to understand it without trouble?

Now that you have done all that stuff and it didn’t work, let’s move to the real thing: teaching aliens some language. I don’t recommend choosing English because it is extremely complicated. Instead, you should opt for a language that is easy and logical, even if it can’t be used to express as much thoughts. Also, use written language instead of sounds, so that you don’t have to pack all communication into a timeline.

Here is an example of how you can make a suitable language and gradually explain it to aliens.

Start by representing human:

Smiling face

Now, that’s definitely not how you should represent a human. You can be sure that aliens will see no similarity between these two:

Emoji and a human

So, aliens can think that your smiling face actually consists of four different objects, each of which has its own meaning. You don’t want aliens to make such a mistake, so you represent human with a single object, even if it’s not so cute:

Creepy face

How do you tell aliens what it is? Simple, just set up a screen and show this emoji when different humans show up. A few tips:

  • Use more than one human, so that aliens understand that the symbol applies to all humans, not just one.
  • Use real humans, not images. Aliens may not understand that images are in some sense the same as real things. After all, images are just light rays, and things are made of matter. We will get to images later.
  • Learn a bit about aliens’ eyes to make sure they see the symbol. If they don’t, change the symbol’s color.
  • The fact that I drew symbols by hand for this article doesn’t mean that you should do the same thing. If you do, the same symbol will be a bit different each time, and aliens might think that you are showing them different symbols.
  • At first, aliens could think that the symbol for human represents the entire room, or some action, or nothing at all. Be patient with them.

Make symbols for a few more objects via the same procedure, like this:

Symbols for table and water

In reality, you should teach them more things, a lot more. But three things are enough for this demonstration.

The next concept is action. You should make symbols for a few basic actions:

Symbols for walking and drinking

As you can see, action is represented by a different color. You should introduce a new color every time you get to a new concept. Blinking symbols are a bad option, try to guess why.

Since actions are hard to separate from the subject who performs them and the object on which they are performed, the next thing you should do is make a syntax for the (subject, action, object) triple:


If an action has more than one object, put all objects in a row, starting with the direct object. Sometimes an action has no object, and that’s even simpler: just don’t put anything after the action symbol at all.

Teach this stuff to aliens by showing lots of examples.

If you need to use properties of objects, make symbols for them, always place them just below the object (or action) they refer to, and teach it all to aliens. I think you will not need them.

(Also, let me omit the phrase “and explain it to aliens by showing lots and lots of examples” from now on. Assume that everything you do is followed by this.)

Now comes something really important: purpose. Whether you want to tell aliens your plans or ask about theirs, the concept of purpose is vital. Purpose is written above the action, like this:

Human goes to a table to drink water

Let’s move to the last big concept: questions. To make a question, you put a blob in place of one of the elements of a sentence:

Where does human go to drink water?

Now you have to go back to the beginning. There is at least one important thing you can’t yet describe: an alien. Before you tell aliens about themselves, teach them what images are. Put a big rectangle around the sentence to indicate that it describes what is happening on a screen:

Human on a screen

With enough example images, aliens will figure it all out. Now you can use pictures to agree on symbols for aliens, planets and so on:

Symbols for alien and Earth

If the aliens made it to this stage, it’s great! You can now start chatting. What do you want to say? Well, it depends on the situation. For example, if aliens came to Earth, it may be good to ask what they are doing here:

Why did aliens come to Earth?

After the first contact is established, both you and aliens will have a lot to say. This rudimentary language can communicate only the simplest thoughts, so it’s time to teach aliens English. Fortunately, it is now really easy to do: just show random sentences in the language they already know and include the English translation. You will be able to show thousands of sentences in a very short period of time, and the sample size will be more than enough for aliens to understand what is going on.

That’s it! What do you think about this method? I would love to hear your comments. Also, what would you do if aliens got stuck at some point (for example, if they didn’t get the hang of representing objects with symbols)?

And lastly, it seems necessary to include a…

Warning: In reality, contacting aliens is a very, very, very bad idea. Avoid doing it if you can.

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The Blogowar

Today I deleted my Facebook account. To celebrate, here is a short story.

Blogger Mary ate the last potato chip, threw the bag away, and once again gripped the handles of her blogoscope. She always did routine tasks diligently, and this time was no exception. In her skilled hands, the blogoscope scanned one IP after another at incredible rate. A few minutes later, something unusual caught her attention. After double-checking her observation, Mary opened a chat client and wrote,

“Come here, SuperSonic.”

SuperSonic15 was Mary’s only true friend. She had started blogging long before Mary was born and knew a lot about the internet. She ran to Mary’s room immediately after receiving the message.

“What’s up?”

“I was scanning Facebook City when I noticed this,” Mary turned the blogoscope to SuperSonic15.

“Let me see… Oh my god. Facebook is preparing its troops.”

“Yes, but why would they do it?”

“Elementary. They are planning an attack that would put an end to free blogging and confine all of us to writing on Facebook pages. We need to react fast. Wait here, Mary. I’ll be back soon.”

SuperSonic15 returned about half an hour later, just when Mary started to feel anxious because of her long absence.

“After a short discussion in a comment thread, the greatest bloggers unanimously decided that we should initiate a preventive strike. The best defense is a good offence, you know.”

“So… we will fight?”

“Yeah. Don’t worry, it will be fun,” said Supersonic15 and then quietly added, “That’s if we win, of course. If we lose, it will be no fun.”

“When will it all start?”

“Less than an hour later. Get ready.”

A little boy was sitting on the stoop of his house, which was located in a picturesque suburb of Facebook City. He knew that something unusual was about to happen, and he didn’t want to miss it. Guys in uniforms have been running around for a few hours, and the boy even saw a couple of large vehicles go along the street.

As he was trying to figure out what was going on, he noticed his mother standing near him. She said,

“Go inside, son. You will be able to see everything through the window and…”

She was interrupted by a loud rumble coming from the sky. A few moments later, something huge broke through a thick layer of tag clouds. It was a round object measuring about three kilometers in diameter and covered with pictures of cats and pages upon pages of text, which was too small to read at such distance.

“What is it, mom?” the boy asked.

“It is the Blogosphere.”

All bloggers, including Mary and SuperSonic15, grabbed game controllers and opened fire. Facebook troopers responded in a matter of seconds. The launched heavy torpedoes, each of which contained a DMCA takedown notice. The torpedoes produced sizable explosions, but Facebook admirals were not satisfied.

“The Blogosphere regenerates almost immediately. Every important post is reposted in so many places that we can’t hope to hit them all at once. Our weapons are futile.”

“Execute Plan B.”

The screen above Mary’s head showed Facebook City in all its glory. Suddenly she noticed a bunch of grey dots floating in the sky. She put away her game controller and reached for the blogoscope to look closer.

The dots turned out to be huge flying saucers moving towards the Blogosphere at great speed. A few red symbols were inscribed on the surface of each saucer. Mary started reading: /pol/, /b/, /s/…


“What’s wrong?”

“4chan is here.”

SuperSonic15 pressed a big red button on the wall, activating a loud alarm. Bloggers immediately started commenting on the situation.

“Why is 4chan supporting Facebook?”

“It doesn’t matter now.”

“There is a special saucer for each board!”

“Not all 4chan is here. Many members decided to stay at home.”

“Still, there are tons of people in these saucers!”

“Wow, a few of them are falling down.”

“Look at the board names. I am sure nobody in the falling saucers has the slightest idea on how to control them.”

“I think the remaining ones are not about to fall.”

“They are firing!!!”

Down in Facebook City, the little boy and his mother were still standing on the stoop and watching the fight. 4chan’s weapons were making large holes in the Blogosphere, and bloggers were unable to stop the attackers.

The boy noticed a new dot appear in the sky. It was red. Just when the boy was unsuccessfully trying to show his mother where the dot was, it activated an unusual weapon. Two lines or red light shot from the dot, and the boy heard a sound like “boing-boing”. The sound was heard exactly when the light was seen, since at the moment everyone was too busy to think about the difference in the speeds of light and sound.

The dot came closer, and the boy could now easily see that it was actually a balloon. It continued to shoot, taking down one saucer after another. To be fair, 4chan members could have destroyed the balloon if they cooperated and fired all their weapons at one spot at exactly the same time. Fortunately for the Blogosphere, such cooperation was beyond 4chan’s capabilities.

Eventually, only one saucer was left. Of course, it was /b/. The Boing Boing weapon could not penetrate its shields. The balloon circled it a few times and disappeared in the sky.

For a couple of minutes, the bloggers were thinking what to do. Then someone fired a meme gun. This weapon was generally considered ineffective, but it worked incredibly well in this situation. People in the saucer started repeating the memes and forgot to control the ship. The saucer began a rapid descent.

The only person not affected by the meme blast was Christopher Poole. He saw that there was no way to regain control of the ship, so he shouted in a computer terminal,

“Python! import startrek!” and, a second later, added, “Energize!”

The bloggers watched /b/ saucer crash and explode. Everybody sighed in relief. Then a notification came from an inner part of the Blogosphere,

“Hey, these guys are here! They teleported from the saucer at the last moment! What the…”

“How bad is it?” asked Mary.

“Very bad,” answered a blogger she had never seen before, “The thing is, our main engine has to burn 100 subscribers per second to function correctly. And now that /b/ folks are spamming the blogs, our readers are fleeing!”

He quietly added,

“I mean, they have been fleeing since we turned the engine on. But now it is happening even faster!”

“Not all is lost,” said SuperSonic15, “If I change the contents of startrek module to initiate self-destruction when any function is called, I think it will stop them. Mary, you go with me.”

A minute later, Mary and SuperSonic15 were sitting in a hovercar.

“Authenticate the driver by real name, Mary Null.”

“Error: Field SURNAME cannot be left blank.”

“Okay, then authenticate SuperSonic15.”

“Error: It doesn’t look like a real name.”

“Who said it was a real name?”

“Error: Voice recognition failed. Please try again.”

Half an hour later, they managed to persuade the hovercar to leave the Blogosphere.

A Facebook agent saw the hovercar and aimed his smart gun at it. He pressed “Fire”, but the screen froze. A second later, some text appeared on the screen.

“Installing Windows 10. 1% done. Please do not turn off your device until the installation is finished.”

The agent swore and helplessly watched the hovercar go by.

Mary and SuperSonic15 reached Paramount headquarters.

“Let me in,” SuperSonic15 said.

“Why should I?” someone replied from the other side of the door.

“If you don’t, I will write in my blog that your next movie is not worth watching.”


“Wait a minute,” said Mary, “Suppose you change the module. But everyone has a local copy. How will you persuade them to update it?”

“Ah, that’s your job. Write a blog post entitled ‘Huge Security Breach Discovered in startrek Version…’ whatever the current version number is.”

“And what should I write in this post?”

“Doesn’t matter. Nobody will click the link to full article anyway.”

By the time SuperSonic15 returned from Paramount headquarters, Mary had already received a message from the Blogosphere.

“4chan no longer poses a threat. However, so many subscribers left the Blogosphere that our main engine will run out of fuel in less than an hour. SuperSonic15 knows what to do.”

“Do you know what this guy is talking about, SuperSonic?”

“Yes. He wants us to activate our ultimate weapon. This weapon will only work if activated in the main tower of Facebook City. We need to get there as quickly as possible.”

“Okay, I will launch the hovercar.”

The hovercar did not share Mary’s enthusiasm.

“I am sorry, but you have reached the end of the 30-day free trial. To continue using the hovercar, enter your credit card number…”

“I have a better idea,” said someone standing nearby.

Mary and SuperSonic15 freaked out at first, but then smiled as they saw the speaker. He was dressed in a red cape and goggles, and a red balloon was floating above him – the exact balloon that took down most of 4chan’s saucers not long ago.

Cory Doctorow

“Hi, Cory!”

“Hi, friends! Get in my balloon!”

Soon, the balloon was floating above the main Facebook skyscraper, shaped like the letter “f”. Cory Doctorow said to Mary,

“Here, take my cape. Knitted from thousands of witty comment threads, it is guaranteed to save you in any situation.”

“Thanks, Cory!” shouted Mary, jumping out of the balloon.

Two bloggers entered the building without encountering any guards or even moderators. Mary thought it might be a trap; SuperSonic15 was even less optimistic. They opened one more door and got into a huge room filled with heavy machinery. A conveyor belt transported likes from one side of the room to another, where they fell into a big blue box. The purpose of other mechanisms was completely mysterious.

“Okay, launch it!” Mary said.

“Too late,” said someone standing behind the like box, “I knew you would come here.”

The man slowly walked towards the bloggers, who were terrified to realize that he was Mark Zuckerberg himself.

Two swords appeared in Zuckerberg’s hands. Bloggers pulled out their own swords. SuperSonic15 shouted,

“Remember what you learned at Blogging U?” and they got into the fight.

Zuckerberg was more skilled than each of the bloggers, but he had a hard time fighting with both of them at once. Eventually he managed to perform a certain closed-source maneuver. It happened too fast to see what exactly he did, but a second later SuperSonic15 was lying on the floor, unconscious.

Now that he had only one opponent remaining, he was sure he would win. He tried to stab Mary, but she turned around at the last moment, and Zuckerberg’s sword hit the cape. Nobody (except Cory Doctorow, of course) will ever understand what happened next. A sudden flash of red light blinded Mary.

When she opened her eyes, she found out that Zuckerberg was lying on the floor, and she was pointing a sword at him. SuperSonic15 had already regained consciousness and was preparing to launch the weapon. She pressed a button on a small disk, and a mechanical sound filled the room.

“F-I-R-S-T P-O…”

This sound mixed with the sound of explosions, as Facebook skyscrapers collapsed one by one.

“Stop it! I agree to negotiate!” Mark Zuckerberg cried.

“Why should I stop?” SuperSonic15 said angrily.

“I think you can disable the weapon,” Mary replied, “I doubt Facebook will ever try to attack us again.”

“Let’s hope you are right,” said SuperSonic15 and pressed another button on the disc.

All sounds disappeared.

After a month of negotiations between Mark Zuckerberg and the greatest bloggers of our time, a peace treaty was signed. It received 50 million likes on Facebook and was reposted all over the Blogosphere.

Speaking of the Blogosphere, it was repaired and now it has even more pictures of cats on its surface than before. Mary and SuperSonic15 are still living in it and writing blog posts. Mary’s latest post, entitled “The Benefits of Open Source, Part 37”, became hugely popular. Cory Doctorow took back his cape. Wanting to find adventures, he flew upwind in his balloon, which caused a lot of concern among physicists, who said that balloons can’t fly like this.

Posted in Humour | Leave a comment

Cipher 13

It was once almost unimaginably far away. Then, cipher after cipher, it drew closer. And now it is here. Dozen II. And it contains a new, fresh cipher. Go check it out.

Posted in Ciphers | Leave a comment

How Many Tribbles?

Assuming I haven’t made a mistake in time zone calculations, this post should go online exactly 50 years after the intrepid crew of USS Enterprise appeared on American screens for the first time. Since then, the adventures of Starfleet officers have been depicted in six TV series and 13 movies. Even though newer Treks are in many ways better, The Original Series will be forever beloved for its unique charm. Here is the opening of The Man Trap, the exact episode that aired 50 years ago:

Anyway, this is a math blog, so I should write about the math of Star Trek. This is a broad topic, and I decided to only discuss one scene, which involves tribbles. Tribbles are funny little creatures famous for being infallible Klingon detectors and notorious for reproducing way too fast. Soon after Deep Space Station K-7 was infiltrated with them, Kirk discovered a population living in a grain storage tank:

Spock estimated that the tank contained 1,771,561 tribbles under the assumptions that a single tribble had entered the tank three day before and had been producing a litter of 10 every 12 hours since then. Knowing Spock, it is hard to imagine him solving such a simple problem incorrectly, but let’s confirm his result anyway.

When a tribble produces a litter of 10, the number of tribbles multiplies by 11 (10 for offsprings + 1 for original tribble). They had just enough time for 6 reproduction cycles, so we would expect to have 116 tribbles, which is exactly the number that Spock arrived at. Great!

If you want to learn more about the math of Star Trek, I recommend an excellent video by James Grime:

If you want to solve a Star Trek-themed cipher, go check it out.

Finally, if you want to celebrate the anniversary of Star Trek in another brilliant way,


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Cipher 12

After a very long break, Cipher 12 has finally been released.

Posted in Ciphers | Leave a comment

A Question Most People Get Wrong

Edit: The poll is now over. A bunch of people voted after I wrote this article, but I decided not to redo all calculations because I am lazy.

A few days ago I created a Twitter thing called Geeky Polls. The first poll I posted was this one:

At first glance, this question may look like an obfuscated version of the liar paradox. However, it is not paradoxical, and you can answer correctly by choosing whichever option fewer people preferred.

When I made this poll, I expected that both answer choices will get roughly equal number of votes. Surprisingly, this turned out not to be the case: one of the options received 71% of votes. In case you haven’t voted yet, I will not disclose which option was more popular, since it would allow you to cheat.

But is this difference significant? Let’s find out. The poll attracted the attention of 70 people. The last time I checked, 71% of 70 was 50, so that’s how many people preferred the Popular Option. 20 people chose the Unpopular Option – what nice round numbers!

We can now start some kind of analysis. I will not use Bayesian approach because it is not suitable in this situation I know nothing about it, so let’s stick to good old frequentism. In this case, the p-value is the probability that 70 coin tosses will result in some side showing up at least 50 times. There are two ways to calculate it: smart one (do the math) and silly one (write a program). I will use the second approach.

Since you are probably tired of me posting Delphi apps, here is some nice and clean JS code:

var numTries = 100000;

var i, j, heads, skewed;

skewed = 0;
for (i = 0; i < numTries; i++) {
    heads = 0;
    for (j = 0; j < 70; j++) {
        if (random(0, 1) > 0.5) {
    if (heads <= 20 || heads >= 50) {

// As you can see, I multiplied the p-value by 10000
// Hence, any output less than 500 will indicate significance
println(10000 * skewed / numTries);

This code gives the result of 4.3, which is much less than 500. Significance proven! Well, technically, it’s not. Since the program is randomized, there is always a possibility that it will take an insignificant result and mark it as significant. It means that we should conduct a statistical analysis to determine the significance of the result coming out of significance-testing program… My head hurts. That’s why serious people always choose the mathematical approach.

Anyway, goodbye for now. If you would like to know what the correct answer to the question is, just vote yourself!

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