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### extending Mandelbox fractals with shape inversions

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#### hobold

• Fractal Phenom
• Posts: 57

#### Re: extending Mandelbox fractals with shape inversions

« Reply #15 on: September 11, 2018, 03:44:55 PM »
Somewhat offtopic, but coincidentally related. This past weekend I saw an exhibition of works from the very beginning of computer generated art (in Bremen, Germany, in the "Kunsthalle").

Most of the pieces were from the late 1960s and early 1970s, and were made with technically primitive tools from today's point of view. Quite a few academics, researchers and engineers authored these early works, simply because pretty much no other playful minds had access to these priceless machines back in the day. Still, there were few academic publications back then. The scientists didn't think their dabbling was science, nor did they think of it as art; and artists were initially not involved with computers.

We (the community of people interested in fractal-related imagery as medium of expression) have progressed a lot further in that regard. There are a few papers of "pure math", there are a few papers from computer science perspective, and there are "engineering" publications about the industrial production of fractal imagery (e.g. for movies). Artists, mathematicians, computer scientists, are still dabbling in this field out of sheer enthusiasm, and thus hobbyists are still free to join even before they acquired expertise in any of the aspects. (And this forum here is maybe the best place for such chance encounters.)

The fascination with fractal imagery has already produced original mathematical research, original computer science research, and it has made big money on the silver screen. Seems the topic already got quite a bit of recognition. Beyond that, what we do is not an exception; a recently coined term is "citizen science". Throughout the history of science there were always "dilletants" who could not publish - the internet merely makes them more visible today than before.

BTW, of the several dozen works being on display in the Kunsthalle Bremen, only a single one is actually fractal based. A dragon curve from 1971, produced by a working group under physics professor Herbert W. Franke (I only knew him as author of hard science fiction and had been unaware of his involvement in the early computer art exploration). We were there right from the start - we just didn't know it yet. :-)

#### utak3r

• Fractal Phenom
• Posts: 58

#### Re: extending Mandelbox fractals with shape inversions

« Reply #16 on: September 15, 2018, 11:31:56 PM »
just finding the time to look at improving those interfaces (subject for another thread)

BTW, take a look at Synthclipse, which is a generalized GLSL tool. It has many things similar to Fragmentarium, but what I love here, are animation tools.
Of course, not only that - I do use it, because I use it not only for fractals.

#### utak3r

• Fractal Phenom
• Posts: 58

#### Re: extending Mandelbox fractals with shape inversions

« Reply #17 on: September 15, 2018, 11:36:14 PM »
templates for your favorite work processor (MS Word or Latex)

Wait... there are people using Word for preparing their papers?
The first time I was writing my own scholary paper, I was trying to use Word for this... yes, it was LONG time ago, but I don't think nowadays Word suddenly became a paper publishing tool   so, yeah, of course LaTeX is the only proper choice

• 3f
• Posts: 1536

#### Re: extending Mandelbox fractals with shape inversions

« Reply #18 on: September 16, 2018, 01:08:28 AM »
Wait... there are people using Word for preparing their papers?
The first time I was writing my own scholary paper, I was trying to use Word for this... yes, it was LONG time ago, but I don't think nowadays Word suddenly became a paper publishing tool   so, yeah, of course LaTeX is the only proper choice
It depends on the journal, but most I've encountered allow Word. All I know about Word is how to open a Word document, so I agree with you on that.

#### utak3r

• Fractal Phenom
• Posts: 58

#### Re: extending Mandelbox fractals with shape inversions

« Reply #19 on: September 16, 2018, 02:00:20 PM »
most I've encountered allow Word.
I don't mean they allow it or not - what I meant is, you can very easily go gray, while preparing your doc in Word    I switched to LaTeX right after my paper was destroyed by Word.

#### CozyG

• Fractal Freshman
• Posts: 7

#### Re: extending Mandelbox fractals with shape inversions

« Reply #20 on: October 04, 2018, 03:16:00 AM »
I've been making some videos using these shape inversion extensions to the Mandelbox. Just posted one on YouTube, a visualization of a 4D Mandelbox where the inversive shape is a linear blend of hypercube and hypersphere. Each frame is a 3D slice through the 4D geometry, with the parameterized fourth dimensional coordinate changing over time. I've been calling these HyperMandalas:

#### Alef

• Fractal Phenom
• Posts: 52
• catalisator of fractals

#### Re: extending Mandelbox fractals with shape inversions

« Reply #21 on: October 04, 2018, 02:09:28 PM »
Offtop.

Realy so called spherefold of mandelbox consist of spherefold and sphere inversion. It's beautifull shapes is mostly a sphere inversion, then less of a boxfold. And it is just slightly modified by spherefold.

If I remember correctly:

//So called spherefold:
if magnitude of z < 0.5:
z := z * 4   /// spherefold
else if magnitude of z < 1:
z := z / (magnitude of z)^2 // sphere inversion!
catalisator of fractals

#### Alef

• Fractal Phenom
• Posts: 52
• catalisator of fractals

#### Re: extending Mandelbox fractals with shape inversions

« Reply #22 on: October 06, 2018, 02:53:08 PM »
Most of what is decribed in paper I had done in JIT formulas for Mandelbulb3D. Exept in higher dimensions.
It is https://en.wikipedia.org/wiki/Lp_space

Code: [Select]
//===modulus==in==Lp========()==================================/// calculate radius in Lp space where circle is circle (2), square (1) or smartphone shape (4)// Using just int values - faster.intPow:=round(v_Lp_space); if intPow = 1 then  // choice 1. If curvatures is 1 then use fastest formula begin modulus  := abs(x) + abs(y) + abs(z); end   else if intPow = 2 then  // choice2. If curvatures is 2 then use standart formula   begin modulus  := sqrt( x*x + y*y + z*z); end else  //choice 3. else use heavy formulas begin invPower:= 1/ intPow; temp:= intPower(abs(x),intPow) + intPower(abs(y),intPow) + intPower(abs(z),intPow); modulus  := power( temp ,invPower); end;
And use this as sphere inversion radius.
It just = abs(x) + abs(y) + abs(z) or = sqrt( x*x + y*y + z*z);   or = square root of 4( x^4 + y^4 + z^4);

But sphere inversion in 4D hypersphere must be different and 4D hypercube inversion alsou is something different. But then it could be done with hypersupersphere.

But radius can be calculated with different power in each direction. I used integer powers only to speed up calculation:

Code: [Select]
intpowerX:=round(sCurvatureX);intpowerY:=round(sCurvatureY);intpowerZ:=round(sCurvatureZ);//inverse of geometric mean, calculates necesary root value invpower:= power(intPowerX *intPowerY *intPowerZ,-0.33333333333333333333); temp:=  intPower( abs(x),intPowerX) + intPower( abs(y),intPowerY) +intPower( abs(z),intPowerZ); radius  := power( temp ,invpower);
I alredy posted this in fractalforums.com. Here it have different p powers in each axis. 1,2,2 Stretched eye corners are where p=1.

Sorry if I 'm repeating myself.

Alsou boxfold can be made with different lenght in each dimension - more control over its gabarites and if FOldZ=1 a possibility to make something like Amazing Surface formula.
« Last Edit: October 08, 2018, 02:00:25 PM by Alef »

#### DarkBeam

• Global Moderator
• Formula crazy engineer
• Posts: 7
• 2 plus 2 is 4 minus 1 is 3 quick maffs

#### Re: extending Mandelbox fractals with shape inversions

« Reply #23 on: October 24, 2018, 01:02:37 AM »
Seven years  ago I created ABoxVSShapes for Mandelbulb3D...
http://www.fractalforums.com/mandelbulb-3d/custom-formulas-and-transforms-release-t17106/
it cannot be considered your invention.The concept of tweaking inversion shape was shown to me by Aexion I think

#### CozyG

• Fractal Freshman
• Posts: 7

#### Re: extending Mandelbox fractals with shape inversions

« Reply #24 on: October 24, 2018, 04:10:16 AM »
Seven years  ago I created ABoxVSShapes for Mandelbulb3D...
http://www.fractalforums.com/mandelbulb-3d/custom-formulas-and-transforms-release-t17106/
it cannot be considered your invention.The concept of tweaking inversion shape was shown to me by Aexion I think

I'm certainly not claiming I was the first to come up with the idea of modifying the "SphereFold" part of the Mandelbox formula. Nor the idea of "shape inversion" in general (see my paper for references on earlier work by others, and I can list more that couldn't fit into the paper if anyone is interested). But I do think that the idea of replacing spherical inversion in the SphereFold with shape inversion is new. I could be mistaken, but I pored over a lot of code from Fragmentarium, Mandelbulber, and MB3D, and a lot of old fractalforums posts before coming to the conclusion that this hadn't been done before. I posted some of my initial work on this last year on the old fractalforums site: Generalized shape inversion applied to the Mandelbox, asked if anyone knew of similar pre-existing modifications, and mentioned MB3D's ABoxVaryShapes formula(s) as the closest I had found but pointed out what I think is the difference:

Quote from: CozyG
I think this may be a new technique to add to the Mandelboxen toolkit. But it's also possible that I've been exploring ground that's been covered before. I've only been deep diving into the Mandelbox for the last few months, so I've been playing catchup on many years of great brainstorming sessions on the forum! And looking at lots of Fragmentarium fragments and MB3D formulas for similar ideas. And there is a set of formulas, probably best represented by MB3D's ABoxVaryShapes, that on first glance may seem similar. However, as best I can tell these all modify the calculated distance from the origin of inversion to the iterated point --
what I've labelled above as d(OP). Whereas the shape inversion that I'm implementing modifies the distance from the origin of inversion (and following the ray OP) to the boundary of the inversion -- d(OS). Does anyone know of similar techniques applied to the Mandelbox?

The two techniques (modifying distance to iterated point, and modifying distance to shape boundary) can also be combined, one modifying the numerator and one modifying the denominator of the inversion scaling. This has been done in other contexts that use spherical inversion, for example see Pseudoinversion Fractals (Gdawiec, 2016) or the Inversion variation that I added to JWildfire last year. I will try to implement this technique combo for a Mandelbox formula in Fragmentarium and post again soon, to illustrate similarities and differences in code and images.

#### lkmitch

• Fractal Friend
• Posts: 17

#### Re: extending Mandelbox fractals with shape inversions

« Reply #25 on: October 25, 2018, 05:00:22 PM »
The Bridges conference, to which the original paper was submitted, is a very nice mixture of accessible and rigorous. Anyone can submit a paper and the formatting guidelines are provided in Word and Latex. The audience is wide, from mathematicians to artists (of all stripes), so a wealth of technical knowledge is not assumed. In fact, overly technical papers are sometimes rejected for not being sufficiently accessible. But all submissions are peer reviewed, leading to (if not guaranteeing) high-quality work. I encourage anyone with an interest in math & art and with something interesting to say to consider submitting a paper.

#### Softology

• Fractal Fanatic
• Posts: 33

#### Re: extending Mandelbox fractals with shape inversions

« Reply #26 on: November 29, 2018, 10:32:21 PM »
Where must you be to access those earlier papers without paying through the nose?

Sci-Hub
https://en.wikipedia.org/wiki/Sci-Hub

• Fractal Phenom
• Posts: 56

#### Re: extending Mandelbox fractals with shape inversions

« Reply #27 on: November 30, 2018, 12:11:14 AM »
Quote
I wonder about all that amazing work from previous years -- do any of you involved back then ever think nowadays about publishing some of your work as a more traditional journal article or conference paper? There is still very little published (in the traditional peer-reviewed sense) about the Mandelbox and other fractal graphics developments that have first appeared in fractalforums.

This might not be a published paper but it is a very well formalised analysis of the Mandelbox, by Rudy Chen at the University of Waterloo: http://digitalfreepen.com/mandelbox370/

I published one paper about using fractal dimensions in image enhancement: http://digital-library.theiet.org/content/journals/10.1049/iet-ipr.2014.0642 (paywall)

A lot of people who don't have the time to push through a peer-reviewed journal (it is quite an effort) use arxiv or researchgate. Here's one I did on variable dimension surfaces:
https://www.researchgate.net/publication/309391846_Three_Variable_Dimension_Surfaces

I agree that publishing is a worthwhile exercise, if nothing else because no-one is going to cite you and extend research on your topic if they can't cite a paper (hopefully this will change).

On the other hand I agree with Softology and others, why should I spend months pushing through the slow publication process only for it to be behind a paywall. More than this, forums and websites allow loads of images, videos, interactive webGL examples etc. I do find most journals to be really behind the times... some still don't even allow colour images!

• 3f
• Posts: 1536

#### Re: extending Mandelbox fractals with shape inversions

« Reply #28 on: November 30, 2018, 01:59:00 AM »
This might not be a published paper but it is a very well formalised analysis of the Mandelbox, by Rudy Chen at the University of Waterloo: http://digitalfreepen.com/mandelbox370/
Thanks for that link. I've been searching occasionally for something like that about the M-box for years. Search engines are not everything...

#### mclarekin

• Fractal Fluff
• Posts: 378

#### Re: extending Mandelbox fractals with shape inversions

« Reply #29 on: November 30, 2018, 09:47:25 AM »
Quote
This might not be a published paper but it is a very well formalised analysis of the Mandelbox, by Rudy Chen at the University of Waterloo: http://digitalfreepen.com/mandelbox370/

that is good, ( i skipped the maths, far too hard for this old man), the paper explains the concepts very well.

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text:
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# Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.$y = \sec^2 x$, $0 \le x \le \pi/3$

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Okay, drying the graph. We know this shaded region as the area as we can see, We're looking at the integral from the bounds of 02 pi over three. Seek and squared acts. Detox is 10 acts 02 pi over three. Plug in now. Tan of pi over three, minus 10 of zero. A squirt of three months here, which is simply squirt of three, which matches up with a rough estimate over here. If you were to do one times approximately three and then half of that because we know this is one and this is three out. But remember, this is no a rectangle. It curved over here, and this matches up.

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# Exponential Function

## Exponential Function: 4^x + 6^x = 9^x

Let $x$ be a real number that satisfy the equation

$4^x + 6^x = 9^x$

What is the value of $\left(\dfrac{2}{3}\right)^x$ ?


text:
# Electrons and Atomic Mass

Is the mass of electrons covered when talking about atomic mass. For example, the mass of Carbon is $$12.011\space\text{amu}$$. If this is including the mass of electrons (assuming the atom is neutral) the nucleus' mass is $$12.011-6(\frac{1}{1840})=12.00773913$$

The reason I need to know is I'm studying mass defect in relation to protons and neutron. If I inadvertently include electrons in my calculation, my binding energy will also be wrong.

• Good question. The mass of electron is so small relative to neutrons/protons that it can be neglected in binding energy calculations. Electron mass in amu is 0.00054. You can try both approaches and see the differences. – M. Farooq Nov 20 '19 at 3:42
• Note that 12.011 amu is the weighted isotope average mass. The mass of a neutral carbon-12 atom in the ground state (electronic and nuclear) is 12.0 amu (exactly), defining the amu. So, yes, it includes the mass of the 6 electrons. – Jon Custer Nov 20 '19 at 14:19
• (And, it is kind of funny that this was asked by a user named 'Dalton' - you'd think they would know their own definition!). – Jon Custer Nov 20 '19 at 14:20


text:
# An Anatomy of Key Tricks in word2vec project with examples¶

The python implementation is mainly for educational purpose, as I found myself understand the original code quicker by trying them in an interactive env.

Its implementation is by no means optimal and thus you should not expect its running performance would be comparable to the C version.

Some implementations have been simplified during the translation to better illustrate the idea.

Those are purely my personal understanding of the code.

In [8]:
import numpy as np
from collections import Counter
import mmap
import re
import networkx as nx
import math

## Precomputed Exponetial Table¶

• It is a table that pre-calculates exponetials of logistic function $$F(t) = {1\over1 + e^{-t}}$$
• For speeded-up access during the runtime
• The values in the exponetial table are later used as objective function
In [3]:
MAX_EXP = 6
EXP_TABLE_SIZE = 1000
EXP_TABLE = np.arange(start = 0, stop = EXP_TABLE_SIZE,
step = 1, dtype = np.float64)
## Exponentials of [-MAX_EXP, MAX_EXP]
EXP_TABLE = np.exp((EXP_TABLE / EXP_TABLE_SIZE * 2 - 1) * MAX_EXP)
## Logitstic Regression of [-MAX_EXP, MAX_EXP]
EXP_TABLE = EXP_TABLE / (EXP_TABLE + 1.)
## SO to use the EXP_TABLE, the value f must be in range [-MAX_EXP, MAX_EXP]
## and first transform the f value to range [0, EXP_TABLE-1]
## and then get the value from the table, e.g., to get logistic function value of f
f = [-6., -3., 0, 3., 6.]
## (f+MAX_EXP) / (MAX_EXP/2) transforms f to [0, 1]
index4exptable = lambda f: int((f+MAX_EXP) * (EXP_TABLE_SIZE/MAX_EXP/2))
f_index = map(index4exptable, f)
logistic_f = EXP_TABLE[f_index]
print f
print f_index
print logistic_f ## values in [0, 1] for logistic regression
[-6.0, -3.0, 0, 3.0, 6.0]
[0, 249, 498, 747, 996]
[ 0.00247262  0.04688669  0.49400029  0.95092101  0.99740611]

## Hashed Vocabulary¶

• In the C implementation, the vocab is a combination of hashed vocabulary and Huffman tree.
• A hashed vocab is a vocab and a hash of its elements' index. The elements in vocab is a vocab_word structure (simulated as a dict here) including fields frequency (frequency of word), word (string repr of word), path (point in c-version, all parent nodes of word in Huffman tree), code (binary repr of word in Huffman tree)
• The hashing is for fast searching of whether a word is in the vocab
• The vocab_words are sorted by their count in the vocab
• The hashed vocab and the tree are built from a train file (a list of words)
• The implementation below ignore the </s> tag as used in the original version, for simplicity
• a very good illustration of constructing Huffman tree can be found here
In [4]:
class HashedVocab(object):
HASH_SIZE = 30000000 ## max hash size
## count threshold for a word to be in the vocab - ignore infrequent word
MIN_COUNT = 5
@staticmethod
def file2ws(fpath):
"""
file to wordstream: lazily read words from a file as an iterator
"""
with open(fpath) as fin:
word_pattern = re.compile(r'(.*?)\s')
mf = mmap.mmap(fin.fileno(), 0, access = mmap.ACCESS_READ)
for match in word_pattern.finditer(mf):
word = match.group(1)
if word: yield word
def __init__(self):
## vocab stores vocab_word dict
self.vocab = []
## vocab_hash stores the index of vocab_word in vocab
self.vocab_hash = np.empty(HashedVocab.HASH_SIZE, dtype = np.int64)
self.vocab_hash.fill(-1)
## house-keeping - total number of word occurences in training set
## it will be used as an estimate of training size later, which
## affect the adjustment of learning rate of the deep structure
self.n_train_words = 0
def fit(self, word_stream):
"""
build hashed_vocab and Huffman tree from word stream
the word_stream is usually from reading a word file, e.g., using file2ws
"""
## word counter
wc = Counter(word_stream)
## total occurances of training words
self.n_train_words = sum(wc.values())
## Sort the words by their counts, filter out infrequent words,
## construct vocab_word (a dict) and put them in self.vocab
self.vocab = map(lambda x: dict(zip(['word', 'count'], x)),
filter(lambda x: x[1] > HashedVocab.MIN_COUNT,
wc.most_common(len(wc))))
## if vocab is already too big for hash, either (1) ignoring more infrequent
## words (as implemented in C by ReduceVocab), (2) making hash size bigger
## here we simply raise an exception for simplicity
if len(self.vocab) > HashedVocab.HASH_SIZE * 0.7:
raise RuntimeError('vocab size too large for hash, increase MIN_COUNT or HASH_SIZE')
self.build_hash()
self.build_huffman_tree()
return self
def index_of(self, word):
"""
Get the index of word in vocab by using hash,
return -1 if it is NOT there
"""
word_hash = self.get_word_hash(word)
while True:
word_index = self.vocab_hash[word_hash]
if word_index == -1:
return -1
elif word == self.vocab[word_index]['word']:
return word_index
else:
word_hash = (word_hash + 1) % HashedVocab.HASH_SIZE
def __getitem__(self, word_index):
"""
get vocab_word in vocab by its index
"""
return self.vocab[word_index]
def __len__(self):
return len(self.vocab)
def __iter__(self):
return iter(self.vocab)

def build_hash(self):
self.vocab_hash = np.empty(HashedVocab.HASH_SIZE, dtype = np.int64)
self.vocab_hash.fill(-1)
for word_index, vocab_word in enumerate(self.vocab):
word = vocab_word['word']
word_hash = self.get_word_hash(word)
return self
def get_word_hash(self, word):
word_hash = sum([ord(c)*(257**i)
for i, c in zip(range(len(word))[::-1], word)])
word_hash %= HashedVocab.HASH_SIZE
return word_hash
while self.vocab_hash[word_hash] != -1:
word_hash = (word_hash + 1) % HashedVocab.HASH_SIZE
self.vocab_hash[word_hash] = word_index
return self
def build_huffman_tree(self):
"""Build the Huffman tree representation for word based on their freq.
The vocab_word structure in self.vocab is a dict {word, count, path, code}
where vocab_word['code'] is the Huffman coding of word, and
vocab_word['path'] will be the path from root to leaf
"""
## for a full binary tree with n leaves, n-1 internal nodes will be needed
## for the 2*n-1 long data array (e.g. count and binary), the first n will be
## for the leaf nodes, and the last n-1 will be for the internal nodes
vocab_size = len(self)
## workhorse structure for tree construction
## count - the count of words (leaves) and internal nodes (sum of leave counts)
count = np.empty(vocab_size * 2 - 1, dtype = np.int64)
count.fill(1e15)
count[:vocab_size] = [vw['count'] for vw in self.vocab]
## binary - boolean repr for leaves and internal nodes
binary = np.zeros(vocab_size*2-1, dtype=np.int64)
## parent_node - storing the path for each node
parent_node = np.empty(vocab_size*2-1, dtype = np.int64)
## construct the tree
## DESCRIPTION: iteratively group the two ungrouped nodes (leaf or internal) that
## have the smallest counts
## Since the vocab is sorted in decreasing counts order (first half ) and
## the newly created internal nodes (second half) will be the order of
## increasing counts (the algorithm invariant), so we only need to check
## the two nodes in the middle of array to look for candidates, that is the role
## of min1i and min2i
## start searching for min1i and min2i from the middle of array
pos1, pos2 = vocab_size - 1, vocab_size
## construct the vocab_size -1 internal nodes
for a in xrange(vocab_size-1):
## min1i
if pos1 >= 0:
# min1i = pos1
if count[pos1] < count[pos2]:
min1i, pos1 = pos1, pos1-1
# min1i = pos2
else:
min1i, pos2 = pos2, pos2+1
else: ## running out of leaf nodes
min1i, pos2 = pos2, pos2+1
## min2i
if pos1 >= 0:
if count[pos1] < count[pos2]:
min2i, pos1 = pos1, pos1-1
else:
min2i, pos2 = pos2, pos2+1
else:
min2i, pos2 = pos2, pos2+1
## count(parent_node) = count(child1) + count(child2)
count[vocab_size + a] = count[min1i] + count[min2i]
parent_node[min1i] = vocab_size + a
parent_node[min2i] = vocab_size + a
## binary encoding for min1i is 0 (left), for min2i is 1 (right)
binary[min2i] = 1
## put the built Huffman tree structure in the vocab_word in vocab
## for each leaf node
for a in xrange(vocab_size):
## b starting from leaf, along parent_nodes, to the root
b = a
code, path = [], []
## traverse along the path to root
while True:
code.append(binary[b])
path.append(b)
b = parent_node[b]
## stop when reaching root
if b == vocab_size * 2 - 2: break
## path (or point) is from root to leaf, with an index offset
## -vocab_size
self.vocab[a]['path'] = [vocab_size - 2] + [p - vocab_size
for p in path[::-1]]
self.vocab[a]['code'] = code[::-1]
def inspect_vocab_tree(self):
"""Draw the built Huffman binary tree for the vocab
"""
g = nx.DiGraph()
vocab_size = len(self)
edges = set()
for vw in self.vocab:
tree_path = [i + vocab_size for i in vw['path']]
tree_path = [i if i >= vocab_size
else "%s(%d)" % (self.vocab[i]['word'], self.vocab[i]['count'])
for i in tree_path]
edges.update(zip(tree_path[:-1], tree_path[1:]))
pos = nx.graphviz_layout(g, prog = 'dot')
nx.draw(g, pos, with_labels = True, arrows = True)
return g
In [36]:
## examples of buiding the hashed_vocab and its associated Huffman tree
## simple.txt is the first 50K words from original text8
hashed_vocab = HashedVocab()
hashed_vocab.fit(HashedVocab.file2ws('data/first50k.txt'))
print 'totally %i words were used to build vocab' % hashed_vocab.n_train_words
print '%i of them go into the vocab' % len(hashed_vocab)
totally 50000 words were used to build vocab
1179 of them go into the vocab
In [37]:
## simple example to illustrate the built Huffman tree
%pylab inline
hashed_vocab = HashedVocab().fit(HashedVocab.file2ws('data/first300.txt'))
hashed_vocab.inspect_vocab_tree()
Populating the interactive namespace from numpy and matplotlib
Out[37]:
<networkx.classes.digraph.DiGraph at 0x10e8743d0>

## Unigram Table¶

• Unigram table is used for word sampling based on their frequencies.
• Unigram table is built on word frequencies in the hashed_vocab.
• Here the sampling probability of a unigram is proportional to the its frequency to a powe of 0.75
• The advantage behind using the power-law sampling and the number 0.75 is NOT really clear to me. See my question
• To use the sampling table, use a uniform random int as the index to the table, the word (index) sampled by the table follow a power law distribution based on their frequency estimate
In [5]:
class UnigramTable(object):
TABLE_SIZE = int(1e8)
POWER = 0.75
def __init__(self, hashed_vocab):
self.table = np.empty(UnigramTable.TABLE_SIZE, np.int64)
vocab = hashed_vocab
vocab_size = len(hashed_vocab)
## normalization factor of all word's frequency's power
train_words_pow = sum(math.pow(vw['count'], UnigramTable.POWER)
for vw in vocab)
## doing the sampling in the table
## the sampling probability of a unigram is proportional to its
## frequency to a power of POWER (=0.75)

## i marks the index of current word in vocab
## d1 marks the accumulative power-law probability up to the current word
## a / TABLE_SIZE marks the sampling proability up to the current word
i = 0
d1 = math.pow(vocab[i]['count'], UnigramTable.POWER) / train_words_pow
for a in xrange(self.TABLE_SIZE):
self.table[a] = i
## compare accumulative sampling prob with power-law accumulative prob
## move to the sampling of next word if they start not matching
if a * 1. / UnigramTable.TABLE_SIZE > d1:
i += 1
d1 += math.pow(vocab[i]['count'], UnigramTable.POWER) / train_words_pow
## put the rest as sampling of the last word (round-off)
if i >= vocab_size:
i = vocab_size - 1
def __getitem__(self, index):
return self.table[index]
In [7]:
## check how satisfying the sampling strategy is to the Zipf's law
## http://mathworld.wolfram.com/ZipfsLaw.html
hashed_vocab = HashedVocab().fit(HashedVocab.file2ws('data/first1k.txt'))
unigram_table = UnigramTable(hashed_vocab)
sampling_probs = [sum(unigram_table.table == i) / 1e8 for i in xrange(len(hashed_vocab))]
plot(1./np.arange(1, len(hashed_vocab)+1), sampling_probs)
xlabel('$1/rank$')
ylabel('$probability$')
Out[7]:
<matplotlib.text.Text at 0x10e823b10>

## Neural Network for Feature Learning¶

• In terms of neural network architecture, it could be cbow (continous bag of words) or skip_gram
• In terms of learning method, it could be hs (hierarchical softmax) or negative (negative sampling) or both
• see the reference paper in the original code base for pros and cons of different combinations

### 1. Continous Bag of Words Model¶

The main data structures of CBOW (and for Skip_gram) are syn0, syn1 and syn1neg. All of them can be viewed as feature reprs of the words in the vocab, but the words are combined in different specific ways. For example,

• syn0 are the feature repr of words (also the leaf nodes in the Huffman tree) to be learned, and the words that are fired in syn0 are a continuous sequence in a sentence (neighbors in semantic matter).
• syn1 are the feature repr of internal nodes in the Huffman tree. The words that are fired together are similiar to each other in the way that they are common parents of close words (in terms of similiar frequency) in the Huffman tree. Parents of word nodes in Huffman tree are analogy to prototypes of clusters formed by words.
• syn1neg are also feature repr of words in the vocab, but those words are selected via negative sampling. The words are sampled based on their frequency.

The basic idea is to learn both syn0 and syn1(and/or `syn1neg1). It might be helpful to understand the code in the following way. Again this is my personal understanding of the code, if it is wrong, it has nothing to do with the original project.

1. The cbow net can be thought of as a two-layer network. The nodes between two layers are partially connected.
2. The first layer (input layer) are syn0 for both hs and negative-sampling.
3. For hs, the second layer consists of the parent nodes in the Huffman tree. For a certain word w, there is a group of nodes in layer0 corresponding to the neighbor words around w in a sentence; and there is a group of nodes in layer1 corresponding to the parent nodes of w in Huffman tree. The connections only exist in the two groups in layer0 and layer1, and the weights of the connections are syn1, which is specific in each parent node in layer1.
4. Similiarly for negative-sampling, but here the connections between nodes in layer0 and layer1 are actually randomly sampled - the nodes in layer1 are selected based on the power-law sampling given in Unigram Table. #### ================= Trained with HS ====================
5. The computation happens in two directions.
6. The forward computation first calculate neu1 as the sum of the related nodes in layer0 (syn0 vectors). The output f is calcualted as the logistic transformation of inner product between neu1 and syn1.
7. Since the nodes that will be turned on in layer1 are parent nodes in Huffman tree, it is like training a multi-classification problem via the network. Here the pesudo targets for the output layer are the binary encoding of the corresponding parent nodes for the certain word. The reason behind this is that the parent nodes (and their encoding for a certain word) are a sparse and deep representation of the word - it is similiar to a hierarchical clustering with cluster prototypes as the parent nodes.
8. So we have the output f and the psuedo target binary encoding of the word, we can calucate the cost function and thus gradient. By making the output and pseudo-target close to each other, we enforce that the feature represented as syn0 (based on a word's context information in a sentence) can be used to approximate the distribution of the word in terms of the encoding by the Huffman tree. The gradient is calculated as g in the code (actually just part of it, the gradient is g multiplied by the input vector for a logistic regression training).
9. Both syn0 and syn1 are updated according to the gradient, interleavingly and iteratively. That is, syn1 are updated based on gradient, and all the connected syn0 (neighbors in a sentence); and syn0 are updated based on gradient, and all the connected syn1 (parent nodes of the word in Huffman tree). #### ================= Trained with Negative Sampling ====================
10. The forward calculation and backward updating are generally the same as in HS.
11. The main differences are that the connected nodes in layer1 (represented by syn1neg) are from a sampling of the whole vocabulary, instead of from the Huffman tree.
12. Accordingly, the pseduo target is are zero-one (similiar to sumvector of a traditioanl bag of words repr.). This essentially enforces that the syn0 repr will be very close to itself and 'orthgonal' to other words - kind of like a autoencoder flavor.
13. Compared to the encoding by Huffman tree, this 'bag-of-words' repr is not deep, and so it generally needs more instances in the training data.
In [6]:
class CBOW(object):
REAL_TYPE = np.float64
def __init__(self, hashed_vocab, unigram_table,
layer1_size, learn_hs, learn_negative):
"""
hashed_vocab: the vocab to build on
layer1_size: the size of layer1 of the net, effectively defines the dim of feature space
learn_hs: use hierarchical softmax learning
learn_negative: use negative sampling learning
"""
self.vocab = hashed_vocab
self.table = unigram_table
self.layer1_size = layer1_size
self.learn_hs = learn_hs
self.learn_negative = learn_negative

## initial value for learning rate, will decrease along learning
self.starting_alpha = 0.025
## a sentence is a bulk of words from train file
self.sentence_len = 1000
## downsampling rate to select words into a sentence
self.sampling = 1e-4
## window defines the neighborhood of a word in the sentence for hs learning
self.window = 5
## negative defines the neighborhood of a word for negative learning
self.negative = 5

## network weights
## syn0 - feature representations of words (leaf nodes) in Huffman tree
## shape = vocab_size x layer1_size
self.syn0 = None
## syn1 - feature representations of internal nodes (non-leaf) in Huffman tree
## shape = vocab_size x layer1_size
self.syn1 = None ## hidden layer for hs learning
## syn1neg - feature representations of negative-sampled words
## shape = vocab_size x layer1_size
self.syn1neg = None ## hidden layer for negative learning
def init_net(self):
"""
"""
vocab_size = len(self.vocab)
self.syn0 = np.random.uniform(low = -.5 / self.layer1_size,
high = .5 / self.layer1_size,
size = (vocab_size, self.layer1_size)).astype(CBOW.REAL_TYPE)
if self.learn_hs:
self.syn1 = np.zeros((vocab_size, self.layer1_size), dtype=CBOW.REAL_TYPE)
if self.learn_negative:
self.syn1neg = np.zeros((vocab_size, self.layer1_size), dtype = CBOW.REAL_TYPE)
def fit(self, train_words):
"""
train_words: list of training words
"""
## initialize net structure
self.init_net()
ntotal = len(train_words)
## initialize learning parameters
alpha = self.starting_alpha
next_random = 0

## read and process words sentence by sentence
## from the train_words
nprocessed = 0
while nprocessed < ntotal:
## adjust learning rate based on how many words have
## been trained on
alpha = max(self.starting_alpha * (1-nprocessed/(ntotal+1.)),
self.starting_alpha * 0.0001)
## refill the sentence
sentence = []
while nprocessed < ntotal and len(sentence) < self.sentence_len:
## sampling down the infrequent words
word = train_words[nprocessed]
word_index = self.vocab.index_of(word)
nprocessed += 1
if word_index == -1: continue
word_count = self.vocab[word_index]['count']
if self.sampling > 0:
ran = ( (math.sqrt(word_count / (self.sampling * ntotal)) + 1)
* (self.sampling * ntotal) / word_count )
next_random = next_random * 25214903917 + 11
## down sampling based on word frequency
if ran < (next_random & 0xFFFF) / 65536: continue
sentence.append(word_index)
## for each word in the preloaded sentence
## pivot is the vocab index of current word to be trained on
## ipivot is the index in the current setence
for ipivot, pivot in enumerate(sentence):
next_random = next_random * 25214903917 + 11
## window-b defines the length of the window
## which is the neighborhood size for the current
## word in the sentence
b = next_random % self.window
## initialize temp variable
## neu1: the sum of neigbhor vectors in the setence
## neu1e: the gradient vector wrt syn0
## see the explaination above the code
neu1 = np.zeros(self.layer1_size, dtype = self.REAL_TYPE)
neu1e = np.zeros(self.layer1_size, dtype = self.REAL_TYPE)
## accumulate sum of neighbor words into neu1
## neighbors are defined as [ipivot-(window-b), ipivot+(window-b)]
left = max(0, ipivot - (self.window-b))
right = min(len(sentence)-1, ipivot+self.window-b)
## all neighborhood index should >= 0 (in vocab) as otherwise
## it won't go into the sentence in the first place
neighborhood = [sentence[n] for n in range(left, right+1)
if sentence[n] >= 0]
neu1 = np.sum(self.syn0[neighborhood,:], axis = 0)
## hierarchical softmax learning
if self.learn_hs:
## for each output node in layer1
## which are parent nodes of pivot in Huffman tree
## notice the last element of 'path' is the word itself,
## so exclude it here
for parent_index, parent_code in zip(self.vocab[pivot]['path'][:-1],
self.vocab[pivot]['code']):
## F is the logistic transformation of dot product
## between neu1 and each parent repr in syn1
f = np.dot(neu1, self.syn1[parent_index, :])
## output out of range
if f <= - MAX_EXP or f >= MAX_EXP:
continue
## logistic function transformation
else:
f = EXP_TABLE[int((f + MAX_EXP) * (EXP_TABLE_SIZE / MAX_EXP / 2))]
## pseduo target is 1 - parent_code
g = (1 - parent_code - f) * alpha
## accumulate neu1 to update syn0 later
neu1e += g * self.syn1[parent_index]
## update syn1 of current parent
self.syn1[parent_index] += g * neu1
## negative sampling learning
## select one positive and several negative samples
if self.learn_negative:
for d in range(self.negative + 1):
## make sure to select the current word
## as positive sample
if d == 0:
target = pivot
label = 1
## select some 'negative' samples randomly
else:
next_random = next_random * 25214903917 + 11
target = self.table[(next_random >> 16) % self.table.TABLE_SIZE]
if (target == pivot): continue ## ignore if it is still positive
label = 0
## this time f is dot product of neu1 with
## syn1neg
f = np.dot(neu1, self.syn1neg[target, :])
## pseudo target is label
## NOTE the differece between hs and negative-sampling
## when dealing with f out of [-MAX_EXP, MAX_EXP]
if f > MAX_EXP:
g = (label - 1) * alpha
elif f < - MAX_EXP:
g = (label - 0) * alpha
else:
g = alpha * (label -
EXP_TABLE[int((f + MAX_EXP)
* (EXP_TABLE_SIZE / MAX_EXP / 2))])
## accumulate changes to syn0 to neu1e again
neu1e += g * self.syn1neg[target]
## update syn0 after hs and/or negative-sampling learning
self.syn0[neighborhood, :] += neu1e
In [9]:
## test cbow
hashed_vocab = HashedVocab().fit(HashedVocab.file2ws('data/first50k.txt'))
unigram_table = UnigramTable(hashed_vocab)
train_words = list(HashedVocab.file2ws('data/first50k.txt'))
In [10]:
cbow_model = CBOW(hashed_vocab, unigram_table,
layer1_size = 50,
learn_hs = True, learn_negative = True)
cbow_model.fit(train_words)
In [29]:
from numpy import linalg
Xnorm = np.apply_along_axis(linalg.norm, 1, cbow_model.syn0)
#X = cbow_model.syn0 / Xnorm[:, np.newaxis]
X = cbow_model.syn0
word = cbow_model.vocab.index_of('one')
word_vec = X[word]
#closest_words = np.dot(X, guess).argsort()[::-1]
closest_words = np.sum((X - word_vec)**2, axis = 1).argsort()
for i in closest_words[:5]:
print cbow_model.vocab[i]['word']
one
eight
three
four
seven

In [ ]:

In [ ]:


text:
# Pełna lista cytatów

Od jakiegoś czasu gromadzę pracowicie cytaty pojawiające się losowo na marginesie tego bloga. Trochę się tego nazbierało. Dziś postanowiłem udostępnić Czytelnikom pełną listę – a nuż ktoś znajdzie coś fajnego dla siebie?

Większość z nich to teksty sarkastyczno-dowcipne. Ale nie wszystkie, są też cytaty głębsze, poważne lub smutne. Ale te da się policzyć na palcach.

Uwaga: nie udało mi się tutaj wyświetlić autorów poszczególnych cytatów (pokazują się oni w „pojedynczej” wersji na marginesie bloga). Do wyświetlenia poniższej listy posłużyłem się wtyczką W4 Post List – nie udało mi się jeszcze wykombinować jak za jej pomocą wyświetlić również autorów. Może, kiedyś…

Bez dalszych wstępów, oto pełna lista:

I don’t think the girls at my college appreciate how handsome my mom thinks I am.
The number of eagles who can pick up a bull, you can count then on the fingers of one head.
The Golden Gate Bridge should have a long bungee cord for people who aren’t quite ready to commit suicide but want to get in a little practice.
Iron Man is actually fe-male.
I wonder if life gives dyslexic people melons instead of lemons?…
A house is just a place to keep your stuff while you go out and get more stuff.
Paying for contact lenses every month is essentially paying a monthly subscription to see life in HD.
Amazon really needs a “I have £20 to spend and no idea what I want, show me cool things” button.
The hardest thing I ever attempted to do was to come up with a new letter of the alphabet without it sounding like the 26 that already existed
If I know someone can take a joke/insult without being offended, then I don’t mind if they insult me. But if it is someone who gets offended easily who insults me, I find that offensive.
What if we are part of a procedurally generated universe in a shitty video game created by another species that no one plays anymore.
Smoking is good for the environment as it kills humans.
Books are dead trees with tattoos.
Gówno i kapusta zawsze w parze idą. Jedno popędza drugie. Perpetuum mobile.
My dog on Halloween: “Why do my humans dress in weird clothes on the Night of the Thousand Doorbells?”
“Can I help you?” is about the nicest way to say “What the fuck are you doing here?”
Someone who doesn’t want to date you because your astrological signs aren’t compatible is probably doing you a favour
I hope I’m never in a situation in life where Tom Hanks will be cast as me in the movie.
Initially, we used to pay to listen to songs. Now we pay to skip them.
My wife’s going for a sonogram soon. Or a daughterogram. We’re not sure yet…
The Empire has built 3 deaths stars, each to be the most powerful weapon in the galaxy. They have all been destroyed by x-wings. The Empire needs to invest in x-wings.
If you’re the mother of only sons, you’ve broken a chain of having daughters that goes all the way back to the very beginning of time.
If a shaved guinea pig looks like a tiny hippopotamus. A hippopotamus with hair would probably look like a giant guinea pig.
You don’t need a parachute to skydive. You only need a parachute to skydive twice.
We humans have set up a society in which we require a minimum number of laps around the sun for a person to drink fermented plant juice.
The very existence of flamethrowers proves that sometime, somewhere, someone said to themselves, “You know, I want to set those people over there on fire, but I’m just not close enough to get the job done.”
There will come a time in your life when the amount of times you have masturbated will outnumber the amount of times you will masturbate
Certain privileges become available to you based on the amount of laps you’ve done around the Sun.
If you really want to save the planet, stop having kids.
Atheism is a non-prophet organization.
Volleyball is a intense version of don’t let the balloon hit the floor.
Spiders are just web developers that are happy to find bugs.
I have no idea how much I’ve forgotten.
Brother Preptil, the master of music, had described Brutha’s voice as putting him in mind of a dissapointed vulture arriving too late at a dead donkey.
You are not, “stuck in traffic.” You are traffic.
The gods of the Disc have never bothered much about judging the souls of the dead, and so people only go to hell if that's where they believe, in their deepest heart, that they deserve to go. Which they won't do if they don't know about it. This explains why it is so important to shoot missionaries on sight
I think the biggest difference between atheists and religious people is that atheist would change their minds if god proved real, believers would not if god proved inexistent.
I wonder if I already own any of the clothes I’m going to die in
We don’t pronounce the “k” in knowledge until we acknowledge it.
Tam gdzie dziś piętrzą się góry, będą kiedyś morza, tam gdzie dziś pełnią się morza, będą kiedyś pustynie. A głupota pozostanie głupotą.
When Math teachers used to tell us “you won’t always have a calculator with you” they couldn’t have been more wrong.
A kid napping is an incredible relief while a kidnapping is quite the opposite.
At age 30, you’ve spent a month having birthdays.
I am so happy I live in a world with Facebook. Before that, it would have taken weeks, even months, before finding out someone was an idiot.
A ja myślę, że całe zło tego świata bierze się z myślenia. Zwłaszcza w wykonaniu ludzi całkiem ku temu nie mających predyspozycji.
Alcohol makes more people than it kills.
When you take a cigarette out of a pack, the pack becomes a cigarette lighter!
Restaurants should hang their dessert menus on the inside of the bathroom stalls and at the top have it read, “since you’re making more room..”
Science progresses by proving itself wrong. Religions progress by eliminating non-believers.
All models are wrong. Some models are useful.
If you live for people’s acceptance.you will die from their rejection.
There are more people offended by people being offended by everything than people who are offended by everything.
When we want someone else’s thoughts, we say “penny for your thoughts.” When we offer our own, we say “putting my two cents in.” We value our own opinions twice as much.
Humans are 75% water. Basically cucumbers with anxiety.
If I eat my meal from the frying pan at a restaurant, it’s sophisticated and a sign of quality. If I do it at home, I’m lazy and disgusting.
After clearing browser history, there should be an option to fill up history with “normal” websites instead of it just being empty.
Opera happens because a large number of things amazingly fail to go wrong.
They should really make couples pass a parent course before being allowed to have a child.
I’ve been overwhelmed. I’ve been underwhelmed… Have I ever been whelmed?
Becoming an atheist isn’t really becoming anything - it’s returning to your default state.
If you have experience as a kamikaze pilot, you are a shitty kamikaze pilot.
What if Gods test for us is how gullible we are and only the atheists go to heaven?
English is a hard language, but It can be understood through tough thorough thought though.
Your bed is a shelf for your body when you’re not using it.
I can see atoms but only if there’s a bunch of them together.
Alicia Keys stops wearing make-up and everyone gives her props for being a beautiful, proud independent woman. I stop wearing make-up and people ask if I’ve slept this year.
Do twins ever realize that one of them was not planned?
The word “parallel” has a visual representation of its definition within itself.
When keyless ignition in cars becomes a standard feature, survival rates in horror movies will go up 30%
Its hard to win an argument with a smart person, but it is damn near impossible to win an argument with a stupid person.
I know every digit of pi. Just not the order they go in.
Noses are in the middle of our faces because it’s the scenter.
People are very divided over what happens after death, but not over what happens before birth, even though they are essentially the same state of nonexistence.
It’s more accurate to say “deaths were postponed” than “lives were saved”
The first person to be scientifically made to be immortal will probably be killed by religious extremists.
Most people work just hard enough not to get fired and get paid just enough money not to quit.
It’s weird how couples trying to have a baby always seem to take a while to get pregnant, but the ONE time my condom breaks I got a little “miracle” on the way.
- What is it that a man may call the greatest things in life? - Hot water, good dentishtry and shoft lavatory paper.
„So,” it said, „before unbelievers get burned alive… do you sing to them first?” „No!” „Ah. A merciful death.”
Trees are farming us. They give us oxygen so we grow nice and big, them we finally die, decompose and make food for them.
We never realize how many people we dislike until it comes to naming our child.
Nothing ensures the survival of a species like being tasty to humans.
He moved in a way that suggested he was attempting the world speed record for the nonchalant walk.
Dying of old age is basically saying death by survival.
It’s its when it isn’t it is.
One day I want to be rich enough to need a cart when shopping at Best Buy.
If I lost at Russian Roulette I wouldn’t even know.
- Why are redneck murder cases the hardest to solve? - Because all the DNA matches and there are no dental records
Toilet paper should be free and have advertising printed on it.
65 million light years away, alien telescopes would be seeing dinosaurs on our planet.
Push up bra is like a bag of chips. Contents may seem full but when you open it, it’s half empty and you are disappointed.
Although bishops are not allowed to be gay, Bishops are the only pieces in chess who won’t go straight.
The word Fat just looks like someone took a bite out of the first letter of the word Eat.
Thou shalt keep thy religion to thyself.
My goals in life have very good goalies.
Christians are just bible nerds. They love to make their children cosplay the main character’s origin story, and go to conventions every week!
I fully expect first contact with another alien race to be like meeting new friends freshman year of college. Everyone is unrealistically ultra nice, and both sides are scared shitless the other will eventually find out how fucked up their home lives are.
The rotation of the Earth really makes my day
I rarely drink alcohol to the point of puking, but I always drink coffee to the point of pooping.
Nothing says “I’m rich” like sorting your search results from highest to lowest price while you shop
How fast a car can go from 100-0 is probably more important than how fast it can get from 0-100.
We use tables to keep food off the floor, tablecloths to keep food off the table, place mats to keep food off the tablecloth, and plates to keep food off of the place mats. I wish I had that kind of support in my life.
Every single decision you have ever taken has led to you reading this sentence.
No one knows what’s next, but everybody does it.
Walking around without a case on my phone is a lot like having sex with girls without a condom. It feels good and looks cool, but I know eventually an expensive accident is gonna happen.
You have to be odd to be number one.
The Matrix would be a hell of a lot harder to get out of today with the lack of landlines available.
Set your WIFI password to 2444666668888888, when your friend ask just tell him it’s 12345678.
Odległy musi być czas, w którym kandydatów na najwyższe stanowiska jakichkolwiek państw będzie się kierowało na egzaminacyjne filtry, ażeby umysłowości wielostronnie marne bez wszelkiego miłosierdzia kierować do robót publicznych.
Google should have named their virtual reality headset Googley Eyes.
No enemies had ever taken Ankh-Morpock. Well technically they had, quite often; the city welcomed free-spending barbarian invaders, but somehow the puzzled raiders found, after a few days, that they didn't own their horses any more, and within a couple of months they were just another minority group with its own graffiti and food shops.
Jesteśmy jak na krze, która jest unoszona prądami technologii. Nie panujemy nad nią, nie wiemy dokąd nas niesie, nie wiemy jak nią sterować.
Technically you are always starving to death, and eating resets the timer
There are truck drivers who deliver bananas. Driving people bananas is literally their job.
In 1968, civil unrest fueled the media. In 2016, the media fuels the civil unrest.
The most average person on earth is a 24.3 year old Christian Chinese Man making $9,733 a year with 2.333 children and will eventually die from heart disease. History teaches us that mankind doesn’t learn from history. On the internet you can choose to be anything you want. It’s strange that so many people choose to be stupid. Dragons would think its cool that we create water in our mouths. Horror movies used to fuel my nightmares, I miss that, now it just takes watching the news I have more respect for someone with opposing views but an open mind than someone with the same views and a closed mind. Everyone was born with a limited amount of fucks to give. During your teenage years you give a ton and slowly give less and less from there. If you take a woman to bed and her bra and panties match, I’m sorry to tell you she’s the one who planned everything. Christmas is the only day when you get presents on someone else’s birthday. If you treat sick animals, you may be considered a veterinarian. If you fought for Germany in WWII, you may be considered a veteran Aryan. Time is the only currency you absolutely will run out of, spend it wisely. Don’t spend it on hating people for disagreeing with you. The pen is mightier than the sword if the sword is very short, and the pen is very sharp. - "What're quantum mechanics?" - "I don't know. People who repair quantums, I suppose." The best way to not lose you wireless headphones is with a Y shaped string between your headphones and your phone. He did of course sometimes have people horribly tortured to death, but this was considered to be perfectly acceptable behaviour for a civic ruler and generally approved of by the overhelming majority of citizens. (* The overhelming majority of citizens being defined in this case as everyone not currently hanging upside down over a scorpion pit) Watching Christmas movies about families celebrating Christmas has become more traditional than actually celebrating a traditional Christmas. If someone made special scissors for cutting paper made of stone, they’d be rock paper scissors. Remember when Trinity uses fast learning in the Matrix to fly a B212 helicopter? That’s how I feel when Google shows me how to fix a leaky toilet shutoff valve. If you don’t lie to the doctor about how much you drink, you’re not drinking enough. In 1916, the average person owned a horse and was considered “rich” if they owned a car. In 2016, it’s the other way around. Birth is the #1 cause of deaths. “Survived a shark attack” sounds a lot cooler than “Almost killed by a fish”. On April Fools Day, Brazzers should make a video where a hot male plumber goes to a sorority house and fixes the toilet and leaves normally. You can always tell when they use fake dinosaurs in movies. What our ancestors would really be thinking, if they were alive today, is: "Why is it so dark in here?" You give a man a plane ride and he'll fly for a day. You push a man out of a plane and he'll fly for the rest of his life. Cars can drive themselves, phones are voice activated, and I can pay for groceries with my phone– but elevators still don’t have a “cancel” button. Life is like tetris. Your accomplishments disappear and your mistakes add up. My computer freezes when it overheats. One day you’ll either wake up and never go back to sleep, or go to sleep and never wake up again. On internet people don’t want to hear your opinion. They just want to hear you saying their opinion. “When Will Jesus Bring the Pork Chops?” This title offends all three major religions, and even vegetarians! The best sign of a healthy relationship is no sign of it on Facebook. The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it. "Meat pies! Hot sausages! Inna bun! So fresh the pig h'an't noticed they're gone!" At some point in your life, your parents go from hoping that you aren’t having sex, to hoping that you are. Horses went from pulling the cart to getting towed around in trailers. That’s a pretty good deal. Once Time Travel Becomes Possible, It Always Has Been. When a woman is giving birth, is she literally kidding? You cook bacon and bake cookies. After five movies, I’m pretty sure we can start calling them Highly Unlikely, Yet Doable Missions. If I touch my phone in the right places a pizza will arrive at my door. Kids wanna be teenagers, adults wanna be teenagers again. Everybody wants to be a teenager, except teenagers. In the beginning there was nothing, which exploded. Rather than give candy to kids who don’t need it, what if we gave food to the homeless once a year. If I linked enough watches together to make a belt, it would be a complete waist of time. When people say they love the smell of autumn, they’re basically saying they love the smell of dying plants, leaf rot and mold. Lawyers carry a briefcase in hopes that it will be a brief case. Reach for the stars, because even if you miss, you’ll be miles away from me with your motivational bullshit. My life is a series of increasingly difficult obstacles that I need to overcome in order to play video games at the end of the day. We’ve become so advanced that we spend at least the first 20 or so years of our lives getting caught up on the basics of what we’ve figured out so far. Maybe plants are farming us, giving us oxygen to breathe so we can die and turn into mulch for them. Being offended doesn’t make you right. Rozdaj wszystko, a uczyni to twą duszę szlachetną. A mieszek i kałdun pustymi. I hope my dog never realizes that I’m full of bones. Doctors say each piece of bacon you eat takes 9 minutes off your life. Based on that math I should have died in 1732. If I run a red light my picture is taken in HD but someone robs a bank and the video looks like footage from minecraft. In order to fall asleep, we have to pretend to be asleep My TI-83 Plus calculator is almost 15 years old and works just as well as it did on the first day. Its outlasted every other piece of technology I’ve ever purchased for a similar price or greater. One day an iPhone is going to explode, and Android people are going to be like, “Samsung has had this feature for years”. Gdyby ludzie od jaskiniowej epoki robili tylko to, co wyglądało na możliwe, do dzisiaj siedzieliby w jaskiniach. At any given time, the urge to sing “The Lion Sleeps Tonight” is just a whim away, a whim away, a whim away, a whim away. A physicist is a collection of particles trying to understand themselves. Before smart phones we knew a lot more about our shampoo. If I wrote a book titled “How to fail” and it never sold a single copy, it would be a success. If dentists make their money from looking after our unhealthy teeth then why would I trust a toothpaste 4/5 of them recommend? If you had$1 for every year the universe has existed (approximately 13.8 billion years). You wouldn’t even make the top 50 on the Forbes list.
As a pregnant woman, my body contains eight limbs, and therefore this is the closest I’ll ever be to being a spider…
If there are capital letters, why aren’t there capital numbers. I want to be able to yell statistics at people.
Farting is just shitting yourself on a molecular scale.
Onions are the only vegetable I know that try to prevent you from eating it through emotional manipulation.
They should make a show where they give contestants ikea furniture without instructions and see who builds it the fastest and most accurately.
Pacman is about a dude who has to take drugs to fight the demons chasing him.
Maybe it’s not that you lost a sock in the drier, but that you actually gained an extra sock.
Guinness World Records holds the world record for keeping track of the most world records
A pizza is basically a real-time pie chart of how much pizza is left.
The sooner you fall behind, the more time you have to catch up.
Brushing your teeth is the only time you get to clean your skeleton.
If Sesame Street and Star Wars joined, there would be Cookie Wookies.
“Go to sleep, you’ll feel better in the morning” is the human equivalent of someone saying “Did you turn it off and turn it on again?”
I don’t believe in Mrs. Claus. I think she was invented because people couldn’t handle the idea of an unmarried elderly man watching children all year long then giving them presents based on his own deluded judgement of naughty and nice.
Isn’t it a bit unnerving that doctors call what they do “practice”?
As a 40yo, babies born today will be the future paramedics coming to help me when I’ve fallen and can’t get up
Gdyby wziąć wszystkie ziemskie słonie i poustawiać je jeden na drugim aż do Księżyca, to wszystkie te słonie by umarły.
I was much happier before the Internet because I was unaware of how shitty the world really is.
There are two hard things in computer science: cache invalidation, naming things, and off-by-one errors.
Everything in the universe is either a potato or not a potato.
The best part about Apple’s changes to iPhone 7 is reading about it on my Android device.
Every time the Guinness Book Of World Records adds a new kind of world record to the book, it breaks the world record for having the most world records compiled into a single book.
I’m very punk rock when I charge my laptop, phone, and headphones. I always use the same three power cords.
Of all the things that taste like chicken, surprisingly, eggs is not one of them.
Reddit is the opposite of Facebook. Reddit is people you don’t know posting things you care about. Facebook is people you know posting things you don’t care about.
Think of how stupid the average person is, and realize half of them are stupider than that.
When I die, I want to be cremated and put into an hourglass so I can still spend time with my family.
If a zombie apocalypse happens in Vegas, does it stay in Vegas?
Adam and Eve were the first people to accept Apple’s terms and conditions without reading them…
people aren’t getting dumber, it’s just that stupid people get their voice heard easier now.
If old people realized how little time the had left on earth, maybe they’d drive a little faster.
Though, through, and tough don’t rhyme.
Babies are like random alarm clocks with really complicated snooze buttons.
There’s more planes in the ocean than there ever will be submarines in the air.
Here is a list of top 10 binary numbers: 1, 0
The invention of the shovel was groundbreaking.
I would never want to be a member of a group whose symbol was a man nailed to two pieces of wood.
My dog probably thinks that I’m walking around the block alone for 12 hours while I’m at work.
I wish I could turn my nose inside out to clean everything off of it instead of picking it.
If you ever feel mad that you missed out on something cool, just remember that Michael Collins flew all the way to the moon on Apollo 11, just to stay in orbit while Neil Armstrong and Buzz Aldrin became the first humans to walk on the moon.
Apartments are really togetherments.
If I put something in the refrigerator the first time am I just frigerating it?
You can tell someone doesn’t read much if they keep trying to talk to you while you’re reading a book
The “It’s an older meme, but it checks out” meme is now an older meme, but it checks out.
Church is just the world’s biggest book club.
Samsung just announced a series of water resistant phones. Just what you want in a phone that sets itself on fire - to be water resistant.
If 72 virgins is the reward for blowing yourself in a crowd of innocent people, someone should start a peaceful religion that awards 73 virgins for just being cool.
Ateistą jestem z powodów moralnych. Uważam, że twórcę rozpoznajemy poprzez jego dzieło. W moim odczuciu świat jest skonstruowany tak fatalnie, że wolę wierzyć, iż nikt go nie stworzył!
Does anyone feel 100% confident correctly pronouncing the word “Worcestershire”?
If you buy a used prosthetic hand, you bought your third hand, second hand.
Clint Eastwood is a anagram for Old West Action.
if you rob a bank you won’t need to worry about bills for the next 10 years, successful or not
Instead of warning pregnant women not to drink, I think female alcoholics ought to be told not to fuck.
I know I drive a worthless car when my worries about it being stolen depend on whether the fuel tank is full or not.
I bet dogs would be really disappointed to know we really don’t know what the heck is going on either.
99.99…% of the Universe will kill you instantly. The rest will take a little while to get the job done.
Thomas Edison got an idea that was so great, that it ended up being the universal symbol of a bright idea.
If you step on someone’s foot, they open their mouth, just like a bin does.
What if Mike was short for Micycle?
We put clocks in our mobile phones, so we didn’t need to look at watches. Now we put mobile phones in our watches so we don’t need to look at our mobile phones.
Two eyebrows are just enough, one eyebrow is way too much!
When your gas tank is empty it is full of gas.
If you’re no longer covered by your parent’s health insurance, your manufacturer’s warranty is over.
You can’t save anyone’s life, only postpone their death
An upside of Amnesia would be watching all your favorite movies again for the first time.
The world would probably be a better place if people thought “Is it ethical?” instead of “Is it legal?” more often.
We say that is wrong to take children to LGBT support events as they are too young to make their own choices, yet taking them to church and christening them is considered a good thing.
If you’re raised by a gay couple, but your parents divorce and marry other people, you’re going to have four moms. Or four dads.
I wonder if any prostitutes ever finish a transaction and tell their clients, “it was a business doing pleasure with you.”
My phone’s response to a low battery is to vibrate, turn the screen on, show a visual warning & chime loudly. This seems counter-productive.
I’m pretty sure the urinal was invented when a tall dude walked by a sink and thought “why not?”.
My 15 year old self would be appalled to hear how many times I’ve chosen sleep over sex
If shaving commercials want to impress me then they should shave a bison, not hairless legs.
Puberty is basically when the thought of your crush seeing you naked goes from worst case scenario to best case scenario.
We will be the last generation to have witnessed life without the Internet.
Jak się nie obrócisz, tak rzyć z tyłu.
They should make little sticks that sit behind your steering wheel to help people communicate with others on the road when they want to make a turn or merge into others lane.
At Night, I Can’t find one comfortable position to sleep. In the Morning, every position is comfortable to sleep
All dwarfs have beards and wear up to twelve layers of clothing. Gender is more or less optional.
My dog understand several human words. I don’t understand any dog barks. He may be smarter than me.
Our bodies are 70% water. We didn’t leave the ocean, we learned to take it with us.
I wish my bed was as comfy when I’m trying to fall asleep as it is when my alarm goes off.
When your phone is on vibrate you get a text massage.
The history on my calculator is far more embarrassing than the history on my web browser.
By and large, language is a tool for concealing the truth.
Most teenagers pull their phones out of their pockets to check the time. We are reverting to the era of pocket watches.
If you dig a trench beneath miners in order to sabotage them, you are mining under miners to undermine them
You know when two people kiss, they form a continuous tube with a butthole on each end.
I can’t decide if people who wear pyjamas in public have given up on life or are living it to the fullest.
I wonder how child custody battles would be different if the kid got to live in the same house full time and the parents had to move in/out every week.
Maybe plants are really farming us, giving us oxygen until we eventually expire and turn into mulch which they can consume.
Any machine can be a smoke machine if you use it wrong enough.
In fact, no gods anywhere play chess. They prefer simple, vicious games, where you Do Not Achieve Transcendence but Go Straight to Oblivion; a key to the understanding of all religion is that a god's idea of amusement is Snakes and Ladders with greased rungs.
A czymże jest prawdziwa męskość, jeśli nie wymieszanymi w odpowiednich proporcjach klasą i szaleństwem?
Do you realise, it will only take one human to be immortal to make the average human lifespan infinite.
If you rip a hole in a fish net, there are fewer holes in it.
Humans being the only sentient life in the whole entire universe is scarier than the idea that other intelligent/sentient life exist too.
We use “pass” in a lot of ways to make things more polite. Like saying “passed away” “passed gas” and “I’ll pass” instead of “They died” “I farted” and “Fuck off.”
Don’t hate people for what they look like on the outside, hate them for the horrible pieces of shit they are on the inside.
There's no sense in being precise when you don't even know what you're talking about.
If Bruce Willis dies from Viagra overdose, the headline will read “Bruce Willis Dies Hard.”
Just when I discovered the meaning of life, they changed it.
If Jesus had been stoned to death, Christians would all wear little rocks around their necks
Calling your Dad a motherfucker is a 100% accurate statement
Beethoven was so hard of hearing, he thought he was a painter.
Toasters were the first pop-up notification.
If you leave milk & cookies out for Santa on Christmas Eve, and you put heavy sedatives in the milk, he’ll fall asleep and you can take everybody’s presents.
There’s 2 kinds of people in this world, those who brake immediately upon seeing brake lights in front of them, and those who take their foot off the gas and think “let’s see how this goes”.
Theme parks can snap a crystal clear picture of you on a roller coaster at 70 mph, but bank cameras can’t get a clear shot of a robber standing still.
Poglądy są jak dupa, każdy jakieś ma, ale po co od razu pokazywać...
Ever since I started using adblocker nobody wants to date me anymore
The singular of sheep should be shoop.
I think I am, therefore, I am. I think.
The problem is not people being uneducated; The problem is that they are educated just enough to believe what they’ve been taught. And not educated enough to question what they’ve been taught.
The first 18 years of your life are like a free trial and the rest is pay to play.
Alcohol and drugs are like happiness banks; you take out a loan and pay it back later, with interest.
I mean, I wouldn't pay more than a couple of quid to see me, and I'm me.
“Getting stoned” is either really good or really bad depending on what part of the world you live in.
- Moją ogromną przywarą - wyjaśnił - jest niepohamowana dobroć. Ja po prostu muszę czynić dobro. Jestem jednak rozsądnym krasnoludem i wiem, że wszystkim wyświadczyć dobra nie zdołam. Gdybym próbował być dobry dla wszystkich, dla całego świata i wszystkich zamieszkujących go istot, byłaby to kropelka pitnej wody w słonym morzu, innymi słowy: stracony wysiłek. Postanowiłem zatem czynić dobro konkretne, takie, które nie idzie na marne. Jestem dobry dla siebie i dla mego bezpośredniego otoczenia.
Alcohol free and free alcohol are the polar opposites of fun.
Modern medicine is stunting human evolution by extending the lifespans of the weak and stupid and allowing them to procreate.
If two people on opposite sides of the world each drop a piece of bread, the Earth briefly becomes a sandwich.
I sit at work in front of a computer all day just to afford to sit at home in front of a computer all night.
Z publikacjami w internecie jest jak z dziećmi, te, które się nie udają - usuwamy.
Being born is the first time I did something for the last time and dying will be the last time I do something for the first time.
The scientific field with the most groundbreaking discoveries is geology.
The older you get the more Christmas becomes a game of survival to return to normal life unscathed from people you don’t see often.
Being born is a death sentence.
Swimming in lava is a once in a lifetime experience.
You know how you can tap on YouTube videos to see how much time is left? I wish I could do that when some people talk.
If Katniss and Peeta from “Hunger Games” were Hollywood celebrities, their supercouple nickname would either be Katpee or Peeniss.
I will not rest until I find a cure for my insomnia
We talk about Ancient Romans like they were basically all the same, but the civilization lasted almost 1000 years. That’s like saying people in 2016 and 1016 are basically the same.
We want restaurant quality food when we cook at home, but we also want home cooked quality food when we go to a restaurant.
How funny would it be if flatulating was as infectious as yawning.
This is the 21st century, where deleting history is more important than creating history.
There’s religious people going door to door to convince atheists to become religious. Imagine how much controversy there would be if the roles were switched.
In 2008, I bought an iPhone because it was the only phone with a 3.5mm jack. Now it’s the only phone without a 3.5mm jack.
The antonym of synonym is antonym.
There should be a “Toilet Paper Sampler” that sends me one roll of each major brand/type in a package, labeled with which one is which, so I can try them side by side and decide which one I like best.
"There must be a hundred silver dollars in here," moaned Boggis, waving a purse. "I mean, that's not my league. That's not my class. I can't handle that sort of money. You've got to be in the Guild of Lawyers or something to steal that much."
The teenagers that made fun of me in school for being nerd and playing a musical instrument are now adults who want their kids to perform like I did in school.
Paying for contact lenses every month is essentially paying a monthly subscription to see life in HD.
Not once in my life have I stepped into somebody’s house and thought, “I sure hope I get an apology for ‘the mess’.”
Wet socks are the worst first world problem. We are literally complaining about having both water and socks.
Mars is set to be colonized in the next decade yet I still can’t get a paper towel to rip along the perforated line with any sort of consistency.
If you have a problem with an entire generation you shouldn’t blame them. You should blame the generation that raised them.
Nigdy nie ma się drugiej okazji, żeby zrobić pierwsze wrażenie.
If pigs could fly, their wings would be delicious.
The idea that I can just take something out of my ass and put it inside someone’s lungs is really disturbing on some levels.
If I throw around large amounts of shredded bread on public property, my proximity to pigeons determines whether or not I’m littering.
If there were no sentient beings in the universe, would it really exist?
Global Warming is just the planet getting a fever to try to kill of its infection
Ludzie dzielą się na trzy kategorie: na tych co potrafią liczyć i na tych co nie potrafią.
Hanging around is another thing tortoises are very good at. They’re practically world champions.
“Meow” means “woof” in cat.
If you’ve had sex with less than 12 people, people that have had sex with you belong to a more exclusive club than those who have walked on the moon.
It’s interesting to watch kids learning to lie. They really suck at it to begin with. Then gradually get better. Then suddenly they just stop lying.
Just as potential employers can ask for references from past employers, potential employees should be able to ask for references from past employees.
It would be pretty shitty if the zombie apocalypse started on a Halloween night.
Google is like a cool landlord who lets you stay rent free, but you know that when you’re gone he goes in your room and sniffs your panties.
Real friends are those who shit on your face and praise you behind your back.
Honesty may be the best policy, but it’s important to remember that apparently, by elimination, dishonesty is the second-best policy.
You can go the rest of your life without breathing
Religion has convinced people that there’s an invisible man…living in the sky, who watches everything you do every minute of every day. And the invisible man has a list of ten specific things he doesn’t want you to do. And if you do any of these things, he will send you to a special place, of burning and fire and smoke and torture and anguish for you to live forever, and suffer and burn and scream until the end of time. But he loves you. He loves you and he needs money.
Smartphones have probably caused a large decrease in the amount of bathroom stall graffiti.
I would be more excited to see an Olympics with fully doped, drugged, and modified athletes.
What if Pi is just the random seed for our universe.
The internet uses many terms relating to water. I can surf the web, stream a video, or wait until my computer freezes.
There should be signs telling you when drug free school zones end so you know when it’s OK to do drugs again.
As an avid camper, I have spent a lot of money pretending that I don’t have a house.
When the person who invented the usb dies, they better put the coffin in the ground, bring it back out, flip it over and put it back in.
If I had a pound for every time I got suspicious… I’d wonder who the fuck was paying me, and why?
If anti-vaxxers really believed in their cause, they would band together to show lower rates of autism in their children over time.
I feel like 90% of being good with nunchucks is just not reacting when you hit yourself.
When someone says they’ve lost 2 or 3 pounds in a short amount of time, I picture them taking a giant dump and then stepping on the scale in victory.
Time is a drug. Too much of it kills you.
Live like you’re broke, and you won’t be. Live like you’re rich, and you won’t be.
Tetris taught me when you fit in you disappear.
No one ever eats the donuts at the morning meeting but they disappear immediately when moved to the lunchroom after the meeting is over. I never see anyone eating them. Apparently, I work with a bunch of donut ninjas.
Religious people that haven’t read their Holy books are basically clicking “Agree” without reading the Terms and Conditions.
People don’t like it when you share your opinion. They only like when you share their opinion.
“up” is “dn”, upside down
Have you ever noticed that their stuff is shit and your shit is stuff?
If your house doesn’t have house numbers on it, you need to address that situation.
Contractions are the ultimate push notifications.
Nie zaczyna się zdania od 'Nie'.
He was a slave: at word he went and came; His iron collar cut him to the bone. Then Liberty erased his owner’s name, Tightened the rivets and inscribed his own.
The skydiving business exists only because of surviviors bias. Its a bit hard to leave a bad review.
Może nie zrobimy więcej niż jesteśmy w stanie, ale postarajmy się, żeby to nie było dużo mniej.
Nie ma snów śnionych wspólnie.
In all the movies, Santa never goes to the house directly next door. He always gets in his sleigh & fucks off like 20 miles east.
You know what’s more fun than traveling with small children? Anything. Literally anything…
Suicide is literally the last thing I would ever do.
According to our brain, the brain is the most important organ in our body.
Weather forecast for tonight: Dark. Continued dark overnight, with widely scattered light by morning.
If you’re deaf, every fart is a gamble.
There should be a reality show where people track down and expose people who’ve posted horrible and vile comments on the internet.
The IQ and the life expectancy of the average American recently passed each other in opposite directions.
With 7 billion people on Earth, every single day (24 hour period) there is over 19 million years of human experience that occurs.
Life is like eating your favorite meal. At first your excited to eat it so you go through it fast. Then you slowly realize there is less and less of it and you should have taken your time with it. You try to slow it down, but eventually there is no more left.
I don’t know if I am actually intelligent or just dumb enough to think I am
If my wife would get dressed as fast as she used to when her parents came home early, we would never be late to dinner.
The sentence “I never said she stole my bike” can be read with seven different meanings, depending on which word you emphasize.
So far, this is the oldest I’ve been.
Growing up, everyone tells you to chase your dreams, but once you do, they tell you to be realistic.
I’m almost 150 lbs and just ate a burrito that was about a pound and a half. I’m 1% burrito.
I wonder what all of the people who type “U” instead of “you” do with all of that extra free time?
Gods don’t like people not doing much work. People who aren’t busy all the time might start to think.
Hardware is just software which has crystallized early.
If you say grace before you eat leftovers, I bet God is like, “Dude, I JUST blessed this chicken not even 24 hours ago, give it a rest.”
Postęp jest jak stado świń. I tak należy na ów postęp patrzeć, tak go należy go oceniać. Jak stado świń łażących po gumnie i obejściu, Z faktu istnienia tego stada wypływają rozliczne korzyści. Jest golonka. Jest kiełbasa, jest słonina, są nóżki w galarecie. Słowem, są korzyści! Nie ma co tedy nosem kręcić, że wszędzie nasrane.
Hiccups never truly go away. They just get further apart.
Murphy's Law is recursive.  Washing your car to make it rain doesn't work.
If they put a Pokestop on the moon we’d get back there within 6 months.
If your buttcrack was horizontal it would clap whenever you go down the stairs.
The planet is fine. The people are fucked.
If you are waiting for the waiter, aren’t you the waiter?
Once upon a time, history was written by the winners. Then the losers discovered the internet.
Conversation, n.: A vocal competition in which the one who is catching his breath is called the listener.
In just a few short years, my body has gone from saying “you don’t need to drink to have fun”, to “you don’t need to be having fun to drink”
Are trees made out of wood, or is wood made out of trees?
It sucks when I read read as read and not read, so I have to re-read read as read so I can read read correctly and it can make sense…
The most blessed people are those who sneeze the most.
By this point, i bet celebrities are offended if South Park still hasn’t made fun of them.
The reason why there are so many dumb people in the world is cause only the smart ones choose to use condoms.
On the internet I can easily find a video of a snake being swallowed by a giant frog while attacking a cat but I can’t seem to find the right drivers for my laptop.
Cinderella must have a hard time shopping for shoes if literally no one else in the kingdom had her size
Spoons are just tiny bowls on sticks.
The news is basically just someone saying good evening and then giving you a list of reasons it’s not.
Sneezing while pooping is an efficient way to clear two passages at once.
Everybody knows that Jesus drove a Honda, but he didn’t like to talk about it? From John 12:49 ‘For I do not speak of my own Accord…’
Farming is just a really long recipe to make poo taste better.
The fact that we have a universally recognized hand sign for “fuck you” and not one for “I’m sorry” should really tell us something.
“Head, shoulders, knees, and toes” is just a song about what’s gonna hurt when you’re 50.
If you’re skydiving and your parachute breaks you have the rest of your life to fix it.
Naming Iceland Iceland and Greenland Greenland is one of the biggest trolls of all time.
Learning English is difficult, but it can be taught through tough thorough thought though.
I’d be more terrified by the absence of aliens rather than the presence of them.
If God took the seventh day off to rest, shouldn’t Christians not pray on Sunday and let him enjoy his day off.
Remember that every corpse on Everest was once a highly motivated person.
I am glad that farts aren’t contagious as yawns
If you dye your hair red, then you are trans-gingered.
No matter when you read this, someone just died.
A fine is a tax for doing wrong. A tax is a fine for doing well.
Everyone wants a partner that is a great lover, but no one wants to consider how much practice that it took.
We celebrate someone’s birthday by having them blow their germs all over a cake, then serving that to everyone around.
If Jesus was well known for turning water into wine, why would the Romans crucify him rather than keeping him as a wine-manufacturing slave, and profit immensely?
With the PS4 Neo, Project Morpheus, and now the Nintendo Switch, we have a Trinity of new gaming platforms named after Matrix characters.
All vehicles should be equipped with two horns, one happy and one angry
"'E's fighting in there!" he stuttered, grabbing the captain's arm. "All by himself?" said the captain. "No, with everyone!" shouted Nobby, hopping from one foot to the other.
Myspace is so outdated that jokes about it being outdated has become outdated.
Of course, Ankh-Morpork's citizens had always claimed that the river water was incredibly pure. Any water that had passed through so many kidneys, they reasoned, had to be very pure indeed.
Maybe the reason you’re single is that your soulmate got stuck in a condom.
What year did Jesus think it was?
Screaming and yelling at customer service is like punching a monitor when your CPU fucks up
With an average of 7 lbs of feces inside them, 536 people have been to space. It costs ~10k per pound for a trip to space. We’ve spent around \$32.5 million shipping literal shit into space.
To find a needle in a haystack all you have to do is burn down the haystack.
Let’s give the top 100 richest people in the world cancer and see how long it takes to be cured.
I wonder if anyone has ever killed themselves solely because they were SUPER CURIOUS to see what happens afterwards and didn’t feel like waiting 60 more years dicking around on Earth
“Look, mom. No hands!” would be a great slogan for a unicycle shop, but a terrible slogan for a fireworks stand.
If Mary had baby Jesus, and Jesus is the lamb of God…. Then Mary really did have a little lamb.
“Go to bed, you’ll feel better in the morning” is just the human version of “Did you turn off and back on again?”
Bywają okazje, gdy zwyczajnie nie można się nie napić.
May the forces of evil become confused on the way to your house.
Czekajcie, klienty! Wnet wam pójdzie w pięty! Rozleci się ten burdel Aż po fundamenty!
Saying “I lost the stylus for my tablet” would’ve still made sense over 2000 years ago.
The person who coined the phrase “coined the phrase” coined the phrase.
I always thought reality shows were stupid but then I remembered that in reality people are stupid.
You live longer when you work out, but that additional time is spent in working out.
There are more stars in the known universe than there are grains of sand. But in a single grain of sand there are more atoms than there are stars in the known universe.
Człowiek to rzeczownik, a rzeczownikiem rządzą przypadki.
After all the years of being asked in job interviews what my greatest weakness is, I have come to realize that my greatest weakness is the complete inability to think of a good answer to that question.
Po studiach humanistycznych można zostać tylko nauczycielem albo urzędowym gryzipiórkiem, czyli kimś, kogo skrót rozszyfrowuje się jako Dobry Urzędnik Państwowej Administracji.
I go to work so I can afford food to eat. I eat so I can have energy to go to work. It’s a trap.
Gyms should offer a membership package where you pay for every day that you don’t go.
Exceptio probat regulam.
If Tom Cruise put his car into cruise control, is it no longer cruise control?
All dwarfs are by nature dutiful, serious, literate, obedient and thoughtful people whose only minor failing is a tendency, after one drink, to rush at enemies screaming "Arrrrrrgh!" and axing their legs off at the knee.
All men like to think they’re marrying nymphomaniacs. The problem is, after few years the nympho leaves and the maniac stays.
Lepiej zaliczać się do niektórych niż do wszystkich.
The amount of battery life I have left when I leave work is a good indication of how productive my day was.
I wish my toilet had a scale measuring the contents of the bowl. You could link it to your fitbit data, challenge your friends, the possibilities are endless really.
Mick Jagger, 72, is having a kid, his 8th, with his 29 year old girlfriend, who is 16 years younger than his oldest child, which is 45. But two moms or two dads is too difficult to explain to a seven year old.
So I say, “Live and let live.” That’s my motto. “Live and let live.” Anyone who can’t go along with that, take him outside and shoot the motherfucker. It’s a simple philosophy, but it’s always worked in our family.
Been calling to the British football abuse Hotline, but apparently it's only for victims...
There’s nothing more suspicious than a clear browser history.
The use of birth control by responsible people is slowly replacing the human race with irresponsible people who get pregnant unintentionally.
The difference between stupidity and genius is that genius has its limits.
Since taking my smartphone to the toilet, I know much less about my shampoo ingredients.
The person who prays for God to change things thinks God has arranged matters wrong, and also thinks they can instruct God on how they should be put right.
Before the internet, there were people who wiped while sitting and people who wiped while standing and they didn’t know that the other existed.

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text:
Chapter 6 : Velocity in Mechanisms(Instantaneous Centre Method)¶

Example 6.1 Page No : 126¶

In [2]:
import math

# Variables:
NAB = 100. 			#rpm
AB = 300./1000
BC = 360./1000
CD = BC 			#m

#Solution:
#Refer Fig. 6.9
#Calculating the angular speed of link AB
#Calculating the velocity of point B on link AB
vB = omegaAB*AB 			#m/s
#Calculating the angular velocity of link BC
#By measurement from instantaneous centre diagram  Fig. 6.10

I13B = 500./1000 			#m

#Results:
print " The angular velocity of the link BC omegaBC  =  %.3f rad/s."%(omegaBC)

 The angular velocity of the link BC omegaBC  =  6.283 rad/s.

Example 6.2 Page No : 128¶

In [4]:
import math

# Variables:
OB = 100/1000. 			#m

#Solution:
#Refer Fig. 6.12
#Calculating the velocity of the crank OB
vOB = omegaOB*OB 			#m/s
vB = vOB
#By measurement from the instantaneous cemtre diagram  Fig. 6.13

I13A = 460./1000
I13B = 560./1000 			#m
#Calculating the velocity of slider A
vA = vB/I13B*I13A
#Calculating the angular velocity of the connecting rod AB

#Results:
print "The velocity of slider A vA  =  %.2f m/s."%(vA)
print "The angular velocity of connecting rod AB omegaAB  =  %.2f rad/s."%(omegaAB)

The velocity of slider A vA  =  0.82 m/s.
The angular velocity of connecting rod AB omegaAB  =  1.79 rad/s.

Example 6.3 Page No : 130¶

In [5]:
import math

# Variables:
NOA = 120. 			#rpm
OA = 200./1000 			#m/s

#Results:
#Refer Fig. 6.15
#Calculating the angular velocity of the crank OA
#Calculating the velocity of crank OA
vOA = omegaOA*OA 			#m/s
vA = vOA
#By measurement from the instantaneous cemtre diagram Fig. 6.16

I13A = 840./1000
I13B = 1070./1000
I14B = 400./1000
I14C = 200./1000
I15C = 740./1000
I15D = 500./1000 			#m

#Calculating the velocity of point B
vB = vA/I13A*I13B 			#m/s
#Calculating the velocity of point C
vC = vB/I14B*I14C 			#m/s
#Calculating the velocity of point B
vD = vC/I15C*I15D 			#m/s
#Calculating the angular velocity of the link AB
#Calculating the angular velocity of the link BC
#Calculating the angular velocity of the link CD

#Results:
print " The velocity of point B vB  =  %.1f m/s."%(vB)
print " The velocity of point C vC  =  %.1f m/s."%(vC)
print " The velocity of point D vD  =  %.2f m/s."%(vD)
print " The angular velocity of the link AB omegaAB  =  %.2f rad/s."%(omegaAB)
print " The angular velocity of the link BC omegaBC  =  %d rad/s."%(omegaBC)
print " The angular velocity of the link CD omegaCD  =  %.2f rad/s."%(omegaCD)

 The velocity of point B vB  =  3.2 m/s.
The velocity of point C vC  =  1.6 m/s.
The velocity of point D vD  =  1.08 m/s.

Example 6.4 Page No : 133¶

In [6]:
import math

# Variables:
O1A = 100/1000. 			#m

#Solution:
#Refer Fig. 6.18
#Calculating the linear velocity of crank O1A
vO1A = omegaO1A*O1A 			#m/s
vA = vO1A
#By measurement from the instantaneous cemtre diagram Fig. 6.19
I13A = 910./1000
I13B = 820./1000
I15B = 130./1000
I15D = 50./1000
I16D = 200./1000
I16E = 400./1000 			#m
#Calculating the velocity of point B
vB = vA/I13A*I13B 			#m/s
#Calculating the velocity of point D
vD = vB/I15B*I15D 			#m/s
#Calculating the velocity of point E
vE = vD/I16D*I16E 			#m/s

#Results:
print " The velocity of point B vB  =  %.2f m/s."%(vB)
print " The velocity of point D vD  =  %.2f m/s."%(vD)
print " The velocity of point E vE  =  %.2f m/s."%(vE)

 The velocity of point B vB  =  9.01 m/s.
The velocity of point D vD  =  3.47 m/s.
The velocity of point E vE  =  6.93 m/s.

Example 6.5 Page No : 135¶

In [7]:
import math

# Variables:
NO1A = 400. 			#rpm
O1A = 16./1000 			#m

#Solution:
#Refer Fig. 6.21
#Calculating the angular velocity of the crank O1A
#Calculating the linear velocity of the crank O1A
vO1A = omegaO1A*O1A 			#m/s
vA = vO1A
#By measurement from the instantaneous cemtre diagram Fig. 6.22
I13A = 41./1000
I13B = 50./1000
I14B = 23./1000
I14C = 28./1000
I15C = 65./1000
I15D = 62./1000 			#m
#Calculating the velocity of point B
vB = vA/I13A*I13B 			#m/s
#Calculating the velocity of point C
vC = vB/I14B*I14C 			#m/s
#Calculating the velocity of of the needle at D
vD = vC/I15C*I15D 			#m/s

#Results:
print "The velocity of the needle at D vD  =  %.2f m/s."%(vD)

The velocity of the needle at D vD  =  0.95 m/s.

Example 6.6 Page No : 137¶

In [1]:
import math

# Variables:
NOA = 120. 			#rpm
#Solution:
#Refer Fig. 6.24
#Calculating the angular speed of crank OA

 The velocity of ram, vD  =  0.817 m/s.