## Cygwin has come a long way … A story in animated GIFs

First of all, let me say that there is some currency to what the title and pictures imply.

Cygwin/X really has come a long way.  10 years ago, the only viable way to run Cygwin was through a DOS-style UNIX shell. The windows system Cygwin/X provided, such as it was, was  mostly TWM, a primitive window manager which  I used to use, which ran the core programs in the X-Windows distribution. Most  of what came with Cygwin,  such as Gnome or KDE, never worked for me, making me an FVWM2 fan for a long time. Along the way, I appreciated  that while FVWM2 was very stripped-down, it made up for it in flexibility and configurability. Even now, FVWM2 is quite liveable.

I decided yesterday to upgrade Cygwin on one of my older computers,  and after working past some glitches in installation, found that:

1. If you have your guard down, you may still install packages you hadn’t intended, particularly the TeX language packs for languages and alphabet systems that you know you will never use. Minutes can turn to hours with postinstall scripts running trying to configure these redundant packages.
2. Mate is recent addition to Cygwin, and actually works on my slow system in 2016. In fact, I am using the Midori web browser to edit this blog under Mate in Cygwin/X.

3. GIMP was once a graphics program you had to compile; now it is intallable for Cygwin as its own package.
4. When moving my old

distribution to another drive, I found a ton of permision problems which were caused by compiling the source for various downloaded code  as another user – not the owner of the directory.

5. I now have a good system, with much more functionality than ever before. Cygwin has gone from a system that was “mostly broken” to “mostly working” in the space of 10 or so years.

## Junk science: The 5-second rule

You remember this. It’s where a child says that if you drop food on the floor and pick it up in less than five seconds, you can safely eat it again. Many adults believe it too. It is hard to know where these ideas come from.

There was a V-Sauce video on the 5-second rule made back in Noveber of 2012, that debunks it with everyday science. V-Sauce mentions, however, that your immune system protects you from a good deal of the bacteria that are sure to come from the floor. There is a MythBusters episode on TV that debunked the 5-second rule also. But away from popular science, there is also a 2007 article in The Journal of Applied Microbiology that not only do microbes adhere to food pretty much on contact, but further that, on an otherwise clean, dry tile floor, Salmonella typhimurium can survive for over a month in large enough numbers to pose a human health problem (40 days, according to the journal). S. typhimurium is a bacteria known to cause typhoid fever in humans.

In scientific terms, “clean” is taken to mean “free of dirt and debris”. Only “sterile” can mean “free of all bacteria and other single-celled organisms”. The floor in this case would be clean but not sterile, just like a floor would be in any average well-kept home.

Well, that was back in 2007, and there has since been another journal article released two days ago by researchers at Rutgers University (who published in the journal Applied and Environmental Microbiology), with what appears to be bigger samples with more surfaces and more measurements than ever before. The lesson, however, is still the same: if food falls on the floor, the safest way to deal with the food is to just throw it out.

Sterility is too lofty a goal for an average home, requiring the inside of the home to be sealed off and air-tight, and for the people entering the home to cover their clothes with a sterile outer suit (since they are contaminated from being outside), and to put on shoe and hair coverings before entering the house.

###### Eating in a sterile environment

Eating and getting rid of bodily wastes would require, as the easiest solution, to do all that outside the house. Once food is brought into the home, any hope of sterility is gone. Growing food in the home does not absolve you from microbes, since most plants and animals need bacteria to grow. And you don’t just need the individual microbes, you need the whole ecosystem they belong in. Past attempts at building artificial ecosystems isolated from the rest of the world had all ended in failure. To get rid of bodily wastes, you would need to build an outhouse — one with running water, if you like to be fancy. None of these are the most comfortable solution to everyday needs which we take for granted.

## Wait! What? Chomsky is wrong about something?

I am a Chomsky enthusiast, admittedly. I have read several of his articles and books, and have viewed countless videos. I am no expert in Linguistics, but would sit through a video of his lectures on it.

So, when Tom Wolfe wrote in Harper’s magazine, an article entitled The Origins of Speech, I learned about the fallability of one of the “most important intellectuals alive”. Not that this is tragic. After all, who cares if an intellectual makes a mistake or not? It would be beyond naive to think that Chomsky’s pronouncements on any topic are flawless, and I am sure that Chomsky would subscribe to that admission, although much has been made on the part of others about his legendary rhetorical skills, which had served him well in live public debates and his countless speeches.

Tom Wolfe mentioned Chomsky’s insistence that Linguistics be seen as a science. As a science, it is unique, as Wolfe states, in that it requires zero field study. Linguistics is the only “science” that does this. Rather than be seen as, say, another Linus Pauling or Frederick Banting, it would be better to see him as an ancient Greek philosopher like Democritus. Democritus asked the question about the essential nature of matter and came up with “atoms” without all the bother of needing to observe samples under a scanning tunnelling microscope, for which he would have had to wait 2500 years for such a microscope to be invented.

Similarly, Chomsky asked the question about the essential nature of language acquisition as a philosopher. He asked the question of how children first acquire language from truly degenerate and imperfect samples found in the environment around him. The child is a toddler, perhaps age 2, so there is no way for the child to look up words somewhere on Google; no way to get perfect grammar samples; no way to know the parts of speech. The child’s cognitive skills are not up to a sufficient level, nor his motor skills, nor his reasoning skills. In addition, toddlers acquire language in very adverse situations, where the parent’s education and vocabulary are not great, and the growing environment is not the best. So, Chomsky reasoned, acquisition of language must be innate to our species. We chat up a storm just as surely as beavers build dams and birds build nests. Therefore, language acquisition must be tied to neurological processes more than it is tied to processes outside of the language learner. So, maybe there is a “language centre” in the brain, and maybe a universal grammar … ?

That’s a lot of reasoning, and a true scientist would demand “real-world” evidence, such as those obtained from field study, but as Wolfe points out, Chomsky himself downplayed that. That still doesn’t fault Chomsky, since that could still be for others to do, and I am sure a great deal of this has been done over the past 60 years that Chomskyan Linguistics has been around, if only by detractors of Chomsky’s theories and would try to knock it down somehow.

There has, and any linguistics based on samples and statistics have been treated as a separate paradigm of thought. While these would be dismissed by Chomsky and his followers, it did give us Google Translate. Google Translate, invented by Google research director Peter Norvig, is a unique beast. Google Translate knows nothing about any language, relying only on statistical occurrences of actual use of specific words and phrases in documents on the Internet. It uses what linguists call “corpus” linguistics: the study of language as it is actually used and observed to be used by people in the real world. And it does it with a significant degree of success. I have used it extensively, and can attest to its usefulness. Corpus linguistics would be dismissed by Chomsky as one dismisses a paradigm that is outside of one’s own.

Chomsky and those invested in his paradigm would have not been able to create Google Translate from universal grammar (UG) theory. UG is touted to exist, but such a UG is not fully realized, at least not to the point where a translating engine could auto-detect your language and translate it to another one for you the way Google Translate does. Corpus Linguistics appears to do the real work manifest in our techhnologies and education systems, while UG is that shiny new theory, 60 years old but largely still on the drawing board, attractive but too new to be applied to existing technologies right now. UG is like the wave mechanical model in physics, where you are better off with high school physics most of the time. Einstein may have been right and Newton may have been wrong, but you can still build bridges and skyscrapers with Newtonian physics.

Wolfe does not go into any of this stuff about paradigmatic differences, by the way. While there is effectively a schism between modern linguists, Wolfe chose to attack Chomsky in ways that border on ad hominem. Wolfe has been criticized for misinterpreting actions of Chomsky to fill out a particular narrative. He was painted, for example, as a kind of defensive person, unresponsive to criticism. This is laughable, since he is famous for responding to email from just about anybody. I had even corresponded with him in the past, and to this day I have never met him in person. His correspondence with me had always been thoughtful and helpful, and far from defensive or unresponsive.

There has been barrels of ink, moles of electrons, and weeks of nighttime talk shows used up over notion that over the past 30 to 40 years, we were all duped. Flossing does nothing for your teeth. All that guilt about not doing it, wasted over nothing. But let’s be precise here. The FDA is citing “lack of strong evidence”, not that it had no effect.

Journalists, with a BS in something that is not a Bachelor of Science, take it to mean that there was some kind of propaganda conspiracy to get us to floss un-necessarily. It is amazing that journalists think we are that stupid. I get stuff in my teeth that I can’t get with my toothbrush, and journalists are leading me to believe that the FDA is telling me that it’s OK to leave it there?

“No evidence” was cited, since, according to the FDA, no one did a serious study. It could have been that the FDA thought that the benefits are self-evident. Do people really need evidence that getting stuff out from between their teeth is better for their oral health than leaving the food stuck in there? The FDA probably thought, rightly, that tax money could be better spent elsewhere.

## Programmatic Mathematica XVI: Patterns in Highly Composite Numbers

This article was inspired by a vlog from Numberphile, on the discussion of “5040: an anti-prime number”, or some title like that.

A contributor to the OEIS named Jean-François Alcover came up with a short bit of Mathematica code that I modified slightly:

Reap[
For[
record = 0; n = 1, n <= 110880, n = If[n < 60, n + 1, n + 60], tau = DivisorSigma[0, n];
If[tau > record, record = tau; Print[n, "\t\t", tau];
Sow[tau]]]][[2, 1]]


This generates a list of a set of numbers with an unusually high amount of factors called “highly composite numbers” up to 110,880. The second column of the output are the number of factors.

1      1
2       2
4       3
6       4
12      6
24      8
36      9
48      10
60      12
120     16
180     18
240     20
360     24
720     30
840     32
1260        36
1680        40
2520        48
5040        60
7560        64
10080       72
15120       80
20160       84
25200       90
27720       96
45360       100
50400       108
55440       120
83160       128
110880      144


For a number like 110,880, there is no number before it that has more than 144 factors.

Highly composite numbers (HCNs) are loosely defined as a natural number which has more factors than any others that came before it. 12 is such a number, with 6 factors, as is 6 itself with 4. The number 5040 has 60 factors, and is also considered highly composite.

5040=24×32×5×7
This works out to 60, because with 24, for example, we get the factors 2, 4, 8, and 16. With 24×32, we get 2, 3, 4, 6, 8, 9, 16, 18, 36, 72, and 144, all which evenly divide 5040. The total number of factors including 1 and 5040 itself can be had from adding 1 to each exponent and multiplying: (4+1)(2+1)(1+1)(1+1)=5×3×2×2=60.

Initially, facotorization of HCNs was done in Maple using the “ifactor()” command. But there is a publication circulating the Internet referring to a table created by Ramanujan that has these factors. A partial list of these are summarized in a table below. The top row headers are the prime numbers that can be the prime factors, from 2 to 17. The first column is the number to factorize. The numbers in the same columns below these prime numbers are the exponents on the primes, such as: 10,080=25×32×51×71. The last column are the total number of factors on these HCNs. So, by adding 1 to each exponent in the row and multiplying, we find that 10,080 has 6×3×2×2=72 factors.

###### NUMBER PATTERNS OBSERVED

As a number of factors (underneath the “# facotrs” column), We get overlapping patterns starting from 60. One of them would be the sequence: 120, 240, 360, 480, 600, and 720. But the lack of an 840 breaks that pattern. But then we get 960, then 1080 is skipped, but then we get 1200.

For numbers of factors that are powers of 2, it seems to go right off the end of the table and beyond: 64, 128, 256, 512, 1024, 2048, 4096, 8192, … . Before 5040, the pattern is completed, since 2 has 2 factors, 6 has 4 factors, 24 has 8 factors, 120 has 16 factors, and 840 has 32 factors. The HCN with 8192 factors is 3,212,537,328,000. We have to go beyond that to see if there is a number with 16,384 factors.

Multiples of 12 make their appearance as numbers of factors: 12, 24, 36, 48, 60 (which are the numbers of factors of 5040), 72, 84, 96, 108, 120, but a lack of a 132 breaks that pattern. But then we see: 144, 288, 432, 576, 720, 864, 1008, 1152, and the pattern ends with the lack of a 1296.

We also observe short runs of numbers of factors in the sequence 100, 200, 400, 800, until we reach the end of this table. But the pattern continues with the number 2,095,133,040, which has 1600 factors. Then, 3200 is skipped.

There are also multiples of 200: 200, 400, 600, 800, but the lack of a 1000 breaks that pattern. But when seen as multiples of 400, we get: 400, 800, 1200, 1600, but then 2000 is skipped.

There are also peculiarities in the HCNs themselves. Going from 5040 to as high as 41,902,660,800, only 4 of the 60 HCNs were not multiples of 5040. The rest had the remainder 2520, which is one-half of 5040.

Also beginning from the HCN 720,720, we observe a run of numbers containing 3-digit repeats: 1081080, 1441440, 2162160, 2882880, 3603600, 4324320, 6486480, 7207200, 8648640, 10810800, and 14414400.

Number 2   3   5   7   11  13  17  # of
factors
-----------------------------------------------------------------------
5040    4   2   1   1               60
7560    3   3   1   1               64
10080   5   2   1   1               72
15120   4   3   1   1               80
20160   6   2   1   1               84
25200   4   2   2   1               90
27720   3   2   1   1   1           96
45360   4   4   1   1               100
50400   5   2   2   1               108
55440   4   2   1   1   1           120
83160   3   3   1   1   1           128
110880  5   2   1   1   1           144
166320  4   3   1   1   1           160
221760  6   2   1   1   1           168
332640  5   3   1   1   1           192
498960  4   4   1   1   1           200
554400  5   2   2   1   1           216
665280  6   3   1   1   1           224
720720  4   2   1   1   1   1       240
1081080 3   3   1   1   1   1       256
1441440 5   2   1   1   1   1       288
2162160 4   3   1   1   1   1       320
2882880 6   2   1   1   1   1       336
3603600 4   2   2   1   1   1       360
4324320 5   3   1   1   1   1       384
6486480 4   4   1   1   1   1       400
7207200 5   2   2   1   1   1       432
8648640 6   3   1   1   1   1       448
10810800    4   3   2   1   1   1       480
14414400    6   2   2   1   1   1       504
17297280    7   3   1   1   1   1       512
21621600    5   3   2   1   1   1       576
32432400    4   4   2   1   1   1       600
61261200    4   2   2   1   1   1   1   720
73513440    5   3   1   1   1   1   1   768
110270160   4   4   1   1   1   1   1   800
122522400   5   2   2   1   1   1   1   864
147026880   6   3   1   1   1   1   1   896
183783600   4   3   2   1   1   1   1   960
245044800   6   2   2   1   1   1   1   1008
294053760   7   3   1   1   1   1   1   1024
367567200   5   3   2   1   1   1   1   1152
551350800   4   4   2   1   1   1   1   1200


After that run, we see a 4-digit overlapping repeat. The digits of the HCN 17297280 could be thought of as an overlap of 1728 and 1728 to make 1729728 as part of that number. The 3-digit run continues with: 21621600, 32432400, 61261200, and after that the pattern is broken.

## Programmatic Mathematica XV: Lucas Numbers

The Lucas sequence follows the same rules for its generation as the Fibonacci sequence, except that the Lucas sequence begins with t1 = 2 and t2 =1.

Lucas numbers are found in the petal counts of flowing plants and pinecone spirals much the same as the Fibonnaci numbers. Also, like the Fibonacci numbers, successive pairs of Lucas numbers can be divided to make the Golden Ratio, $\phi$. The Mathematica version (10) which I am using has a way of  highlighting certain numbers that meet certain conditions. One of them is the Framed[] function, which draws a box around numbers. Framed[] can be placed into If[] statements so that an array of numbers can be fed into it (using a Table[] command).

For example, let’s frame all Lucas numbers that are prime:

In[1]:= If[PrimeQ[#], Framed[#], #] & /@ Table[L[n], {n, 0, 30}]

The If[] statement is best described as:

If[Condition[#], do_if_true[#], do_if_false[#]]

The crosshatch # is a positional parameter upon which some condition is placed by some function we are calling Condition[]. This boolean function returns True or False. In the statement we are using above, the function PrimeQ will return true if the number in the positional parameter is prime; false if 1 or composite.

The positional parameters require a source of numbers by which to make computations, so for this source, we shall look to a sequence of Lucas numbers generated by the Table command. The function which generates the numbers is a user-defined function L[n_]:

In[2]:= L[0] := 2 In[3]:= L[1] := 1 In[4]:= L[n_] := L[n-2] + L[n-1]

With that, I can generate an array with the Table[] command to get the first 31 Lucas numbers:

In[5]:= Table[L[n], {n, 0, 30}] {2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, \ 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, \ 271443, 439204, 710647, 1149851, 1860498}

This list (or “table”) of numbers is passed through the If[] statement thusly:

In[6]:= If[PrimeQ[#], Framed[#], #] & /@ Table[L[n], {n, 0, 30}]

to produce the following output:

In[7]:=

Note that this one was an actual screenshot, to get the effect of the boxes. So, these are the first 31 Lucas numbers, with boxes around the prime numbers. The Table[] command appears to feed the Lucas numbers into the positional parameters represented by #.

There was a sequence I created. Maybe it’s already famous; I have no idea. On the other hand, maybe no one cares. But I wanted to show that with any made-up sequence that is recursive in the same way Fibonacci and Lucas numbers were, that I could show, for example, that as the numbers grow, neighbouring numbers can get closer to the Golden Ratio. The Golden Ratio is $\phi = \frac{1 + \sqrt{5}}{2}$. I want to show that this is not really anything special that would be attributed to Fibonacci or François Lucas. It can be shown that, for any recursive sequence involving the next term being the sum of the previous two terms, sooner or later, you will always approach the Golden Ratio in the same way. It doesn’t matter what your starting numbers are. In Lucas’s sequence, the numbers don’t even have to begin in order. So let’s say I have:

K[0] := 2 K[1] := 5
K[n_] := K[n-2] + K[n-1]

So, just for kicks, I’ll show the first 31 terms:

Table[K[n], {n, 0, 30}] {2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 898, 1453, 2351, \ 3804, 6155, 9959, 16114, 26073, 42187, 68260, 110447, 178707, 289154, \ 467861, 757015, 1224876, 1981891, 3206767, 5188658}

Now, let’s output the Golden Ratio to 15 decimals as a reference:

N[GoldenRatio, 15] 1.61803398874989

Now, let’s take the ratio of the last two numbers in my 31-member sequence:

N[K[30]/K[29], 15] 1.61803398874942

You may say that the last two digits are off, but trying against the Fibonacci sequence, the ratio of the 30th and 31st numbers yields merely: 1.61803398874820, off by 3 digits.

For Lucas: 1.61803398875159, off by 4 digits — even worse.

So, my made-up sequence is more accurate for $\phi$ than either Lucas or Fibonacci. I have tried other made-up sequences. Some are more, and some are less accurate. If it depends on the starting numbers, I think some combinations work better, and you won’t necessarily get greater accuracy by starting and ending with larger numbers.

## More junk science: the 90-day Accu-weather forecast

Weather forecasting is a black art at the best of times. You can look at the existing weather pattern today, then using probability models based on those weather patterns, forecast tomorrow’s weather. We all know that this only works sometimes over a 5-day period. But now there are people who want to sell services for pinpointing weather conditions on  a daily basis for a 90 day period.

A private company known as AccuWeather is offering the waiting public a 90-day weather forecast, selling to consumers the feeling of control over the distant future. There is not much anyone can say about weather in the long term except that “winter is cold” and “summer is hot”. The rest is all the stuff of farmer’s almanacs and crystal ball gazers. AccuWeather is not telling anyone (at least not yet) how they are able to forecast specific weather conditions on specific days over a 90-day period. But this is what they are doing. So apparently, you can know how to pack your suitcase for that trip to New York 60 days from now, since you will know that on that day there will be 1.5 inches of rain.

This is not that new. AccuWeather already has had a 45-day forecast, and so, according to their press release from April 11, 2016, they are providing a 90-day forecast, driven to “greater challenges” such as this by consumer demand. They claim to be able to forecast on this scale with Superior Accuracy™. (Yes, that phrase is trademarked by AccuWeather).

This forecasting is not endorsed by any existing government weather service, college meteorology department, or university professor that knows anything about forecasting the weather. But I am sure that there are enough gullible people that want that feeling of control who find things like “truth” (the truth that weather is chaotic, and too influenced by “the butterfly effect” to be knowable on this scale) to be inconvenient. AccuWeather probably knows that no one will take this seriously except a small group that just wants that feeling of predictability and control in their lives. And that is what AccuWeather is really selling: your feelings.

## Happy π day, 2016!

It seems that there are a lot of videos celebrating π. Here is one of a person setting up a domino spiral with π in the center of it.

## The HP 35s Calculator: a revised review

A while ago, I wrote a blog article on a different blog regarding the HP 35s programmable calculator. Depending on where you buy it, it could cost anywhere from $55 to$98 to buy.

I have heard in other places about the plastic used to make this calculator. It is indeed cheap plastic. It certainly feels hollow when you hold it. It belies the amount of memory and the increased calculating power that lies inside. The calculator has two calculation modes: ALG mode (algebraic mode) to resemble conventional calculators, and RPN mode (reverse-Polish notation), which, for those who do long calculations, provides a way to avoid parentheses, but requires getting used to stacks.

As far as RPN mode goes, only four numbers can be pushed on to the stack at maximum for this calculator. I have read other reviews for other HP calculators where the stack can be much larger. The numbers push to the bottom of the stack as you enter new numbers, and as you enter them, the “bottom” of the stack actually moves “up” on the display. It makes it difficult to discuss how it implements this data structure because the numbers scroll in the opposite direction. The theory goes that you “push” data to the top of the stack, and you “pop” data off the top of the stack. This is a LIFO data structure (LIFO = “last in, first out”). To see the HP25s implementation, you apparently “push” data to the bottom of the stack, numbers “above” it move upward, and then you “pop” data off the bottom of the stack. It actually amounts to the same thing in the end. It is still a LIFO data structure. Pushing a fifth number on to the stack will cause the first number to disappear, so you can only work with four numbers at a time.

So, let’s say that you have the following stack:

a: 8
b: 7
c: 6
d: 5

The last two numbers entered are the numbers “6” and “5” in memory locations “c” and “d” respectively. Operations will be done on the last two numbers entered. So, if I now press the operator “+”, it will add 6 to 5 and pop both of these numbers off of the stack.

a: 0 (empty)
b: 8
c: 7
d: 11

The stack rotates down, the “bottom” (location “a”) of the stack becomes empty, and the “11”, the result of the calculation replaces both 6 and 5.

Some operators are unary, so pressing the square root will perform an operation on only the last number (location “d”), and replace the result back into location “d”, eliminating the number 11.

a: 0 (empty)
b: 8
c: 7
d: 3.31662479036

Well, there is also the programmability of the calculator. There are many commands available, and one pet peeve is how you are only allowed to assign a single letter to name a program.

## I don’t often talk about politics, …

If government was always seen as the shadow cast by big business, I guess someone must have felt it was time for big business to be directly at the controls of power.

I feel the need to comment on the Trump rout of the Republican party. I can see that he has resonated with a lot of normally disenfranchised voters: the poor, people of color, religious people, and so on. He was thought of as a clown doing what Sarah Palin used to do, which was pretty much the same thing. Problem is that Trump does it much better than Palin ever did. And by doing so, he lays a blow to the solar plexus of the Republican Party.

But what really intrigues me is that the other candidates are so shocked, simply shocked (to borrow a line from Casablanca), to find that voters are gravitating to a candidate who embodies all of the most misogynist, ignorant, and racist elements of the country. Indeed, Trump’s campaign is also so full of self-contradictions that on a close look, it is difficult to know what he stands for, except it is against whatever traditional Republicans stand for. Even searches for “Donald Drumpf”, his original family name according to HBO’s This Week Tonight is getting more Google searches than any of the competing Republican candidates.

American society has been ripe for just the kind of candidate Trump is. It’s just that no one wants to admit it. I read in The New York Times that Republicans were critical of Trump supporters for not caring about the “traditions” of the Republican party. But in the way that politics has adopted business terminology, the voters, like consumers, are attracted to the Trump “brand”. If we are on the level of “branding” names of people like soap or cars, then voters hardly need to remember the traditions or history of anything. Like their favourite toothpaste, they have a favourite candidate, with no need to go deeper than that. Trump understands this viscerally. He is a billionaire businessman, after all. He just needs to sell himself. The art of persuation wins over functional literacy and discourse of the facts. Propagandists have always known this. Selling himself is something Trump is indeed good at, though critics may pick away at the fact that this-or-that Trump business venture failed, but that misses the point. Trump knows about consumers, about mindless consumption, and about tapping into that mindset.

I predict that Trump is the new face of the Republican Party. And it is no surprise, since he is at the end of a continuum beginning with Ronald Regan, proceeding to George W. Bush, who all preyed on ignorance. From here on in, I predict that the Republicans will need to be more like Trump, not the other way around. It is also difficult to say if Trump will respect the traditions of Deomcracy, or will he just unilaterally fire or imprison anyone who gets in his way.

What gets me is that none of the other candidates in the Republican party are “taking one for the team” and joining another candidate to defeat Trump if they are so shocked by Trump’s victories. It is as if the vote against Trump is being split on purpose as a coronation of Trump. Naw, can’t be. There is too much press, in nearly all news sources, going against that theory. What would anyone high up in the Republican establishment want with a billionaire businessman possibly running the Oval Office, anyway?