A Practical View of Bayesian Inference

Bayes Theorem has practical applications. Use it to make real world decisions. [Updated 8 Sep 2013]

Bayes Theorem is not just an obscure artifact of the statistics of probability handed down to us from centuries ago. You can use it now to make decisions that will affect your financial well-being.

A relatively simple Excel-based tool helps you choose the right course of action in the face of uncertain probabilities and inexact test results. It is available for FREE.

[Presented to the Science-Technology Club, The Villages, FL, 9 September 2013. For a copy of my PowerPoint slide show, send an email to ira@techie.com.]

What can the Bayesian Inference Advisor Tool do for You?

I know you are probably not in the oil business (and neither am I), but the best way to understand an abstract concept is to go through a practical example. The example below has to do with oil exploration and drilling, but the Bayesian Inference Advisor can handle any problem where you know:

1) the probability of success if you take action without doing further testing,
2) the cost of further testing and the probability the test results will be reliable,
3) the cost of taking some action,
4) the financial benefit to you if the action is successful, and
5) the compensation you expect for taking the risk.

You can download the Bayesian Inference Advisor at:
https://sites.google.com/site/bigira/stuff-ira-knows/BayesianInferenceAdvisorV3.xls?attredirects=0&d=1

The Bayesian Inference Advisor will compute the most likely financial implications of your actions. What if you proceed without further testing? What if you get a positive test result and proceed? What if you get a negative test result and proceed? Several other examples in very different domains are included later in this posting, but for now, put on your hard hat and let us imagine we are in the oil business!

The Trayvon Tragedy

Having watched most of the trial on TV, and carefully considered the evidence, I firmly believe:

1. Had Trayvon Martin (TM) been white, he would most likely be alive today, and
2. The jury decision that George Zimmerman (GZ) was "not guilty" was fully justified by the available evidence.

Although the above conclusions appear to be contradictory, they are not.

DOWNLOAD MY POWERPOINT CHARTS, AS PRESENTED TO THE VILLAGES (FL) PHILOSOPHY CLUB (02 Aug 2013): https://sites.google.com/site/iraclass/my-forms/Philo%20The%20Trayvon%20Tragedy.pps?attredirects=0&d=1

I utilized http://en.wikipedia.org/wiki/Shooting_of_Trayvon_Martin as my main source for quoted testimony and forensics, but the following speculations and conclusions are my own.

There are many "ifs and buts" in this tragic case of the unnecessary death of a teenager.

• IF GZ had not profiled TM, TM would be alive today.
• IF TM, after noticing that GZ was following by car, had taken the good advice of his girlfriend and gone straight home to the townhouse at which he and his father were staying, TM would be alive today.
• IF GZ had followed the non-emergency police dispatcher's good advice not to leave his car and follow TM, TM would be alive today.
• IF TM, after noticing that GZ was following him by foot, had gone straight home, TM would be alive today.
• IF GZ had made it clear that he was a Neighborhood Watch volunteer, and if TM had accepted that information and avoided a physical confrontation, TM would be alive today.
• IF TM had not sucker-punched GZ, TM would be alive today.
• IF TM had run away after punching GZ, instead of continuing the fight and causing two lacerations on the back of GZ's head, TM would be alive today.
• IF GZ had not shot TM in the chest, TM would be alive today.
• IF GZ had not shot TM, GZ might have sustained severe bodily harm, or even death.

Much has been made of the fact that "TM did nothing illegal". Yes, TM had every right to purchase candy and a soft drink and wear a hoodie while he walked home in the light rain of the early evening through the gated community where he and his father were visiting. He had no obligation to dress differently or to run home or change his plans when he noticed he was being observed and followed, first by car and then by foot. TM had every right to be there. He had every right to verbally challenge GZ when they approached each other along the dark concrete walk behind the two rows of townhomes.

Indeed, TM did nothing illegal until he sucker-punched GZ. That is what started the physical part of the confrontation. That is what led to the injury to GM's nose and, ultimately, lacerations to the back of GZ's head. The evidence of the eye witness Jonathan Good makes it clear that TM was beating the heck out of GZ. The forensic evidence shows that all the injuries of the fight were suffered by GZ, except for two light cuts on TM's knuckles (and, sadly, the fatal gunshot wound).

On the other hand, GZ did nothing illegal either! According to available evidence, GZ had every right to profile TM and report him as a suspicious person to the non-emergency police number. He was not legally required to follow the dispatcher's good advice that "we don't need you to do that" when he said he was going to follow TM.

According to TM's friend Rachel Jeantel, who was on the phone with him at the first visual encounter, she urged him to run to the townhouse where he was staying, but TM did not follow that good advice. Furthermore, she testified that when TM and GZ came within talking distance in the dark behind the two rows of townhomes, TM verbally challenged GZ, saying "What are you following me for?" According to her account, GZ returned the challenge with "What are you doing around here?" (GZ's version of the verbal encounter also has TM challenging first, saying "You got a f---ing problem, homie?",GZ replying "No", and TM following up with "You got a problem now" and punching GZ in the nose.).

According to the closest eye witness to the physical encounter, Jonathan Good, GZ got the worst of the fight, calling for "Help" with TM on top of him.

GZ could have submitted to the beating. Had he done so, both GZ and TM would most likely be alive today. On the other hand, the way things were going, GZ might have suffered serious head injury or even death. We will never know.

But GZ did not submit to the beating. Reasonably fearing for his life (or serious bodily injury), GZ drew his handgun and shot TM in the chest. According to the forensic evidence, when the fatal shot was fired, the gun barrel was touching TM's clothing, but the clothing was two to four inches away from TM's skin, indicating that TM was on top and facing downwards, with gravity pulling the clothing down and away from his skin..

Alternative Scenario Where TM is Totally Innocent

Although I generally accept GZ's account of the incident (with some reservations about his claim that he walked past the dark area behind the two rows of houses because he was looking for a street name and an address to provide to the police dispatcher), I have searched my imagination for a scenario that fits all the available testimony and forensics and that shows TM totally innocent. I stretched my brain to come up with the following:

TM purchases candy and a soft drink and, while walking home, he notices GZ stop his car, look at him suspiciously, roll up his windows, and make a cellphone call. TM is also on his cellphone with his young lady friend and tells her that GZ looks like a "crazy ass cracker".

Although he is close to the townhome where he and his father are visiting, TM does not go directly home because he is fearful that GZ may be a sexual predator or otherwise dangerous and that he will track him there and possibly cause trouble. So, TM runs to the dark area behind the two rows of townhomes and hides there.

GZ, walking and searching in the dark area with the aid of a flashlight, slips on the rain-soaked grass, landing face-first on the concrete walk (or a hard plastic sprinkler cover or a tree branch). This accounts for the injuries to GZ's nose.

As GZ struggles to his feet, he notices TM hiding in the shadows. GZ angrily challenges TM and grabs him in a bear hug. TM cries for "help" and tries to get away. In the struggle, they fall down, with GZ striking the back of his head against the concrete walk (or other hard object). This accounts for the lacerations on the back of GZ's head and the eyewitness report of TM being on top.

TM manages to break GZ's bear hug grip and pulls himself up, preparing to run away. At that point, with TM still on top, GZ draws his gun and shoots TM in the chest, killing him.

Although the above scenario is possible, it does not appear as reasonable as the defense account. In any case, GZ had to be judged "not guilty beyond a reasonable doubt", and there are many reasonable doubts about the scenario I sketched!

Does "Stand Your Ground" Apply To This Case?

The common law version of self-defense allows a person who is challenged by another person, in their own home, to use deadly force if they reasonably fear death or great bodily harm, even if it would be safe to retreat. However, if in their vehicle or public place, there is a duty to retreat if it would be safe to do so.

The Stand Your Ground extension to the law of self-defense expands the concept to vehicles and public places. Thus, under Stand Your Ground, a person who is challenged, in their vehicle or public place, does not have a duty to retreat, even if it would be safe to do so, but may use deadly force against the person challenging them, if they reasonably fear death or great bodily harm.

Much has been made of Stand Your Ground in the Zimmerman/Martin case, but it does not seem to apply. Once the physical confrontation started, and GZ was getting the worst of it, he no longer had the option to retreat, safely or otherwise. At that point, if he reasonably feared death or great bodily harm, he had the right to use deadly force. (It is true that Zimmerman's defense team initially requested a Stand Your Ground hearing, but later decided to bypass that hearing and go to a jury trial.)

Was George Zimmerman a Racist?

There is no doubt in my mind that GZ profiled TM, using a combination of what he was doing, where he was, how he was dressed, the fact that he was a young man, and ... YES ... the fact that he was black. In other words, TM fit the profile of the young black men who had recently been observed committing burglaries and a home invasion in the gated community.

But, GZ was not any more of a racist than any of the rest of us. I think it is an undisputed fact that most of we Americans (sadly including black Americans who are more often the victims of urban crime than white Americans) are more suspicious of young black men than they would be of young white men, and more suspicious of young men of any race than they would be of older men or of women of any age.

In fact, there is reason to believe that GZ was actually less of a racist than most of we Americans. His voter registration lists him as Hispanic and a Democrat. His mother, from Peru, has both Hispanic and black ancestry. His next-door neighbor in the gated community was a black woman who praised him as a good friend. According to the local ABC TV station, "George Zimmerman accused the Sanford police department of corruption more than a year before he shot Trayvon Martin, saying at a public forum the agency covered up the beating of a black homeless man by the son of a white officer." (http://www.wjla.com/articles/2012/05/zimmerman-publicly-accused-sanford-police-of-corruption-in-2011-76322.html#ixzz2ZYfvmxDM)

 Ira Glickstein

IRS and NSA Controversies

In recent months, the Obama administration has been plagued by several serious controversies, chief among them:

• Charges of political profiling by the Internal Revenue Service (IRS) in delaying the approval of tax exemption under § 501 (c)(4) to some "patriotic" organizations, and


• Large-scale domestic snooping by the National Security Agency (NSA) according to Top Secret documents leaked by Edward Snowden.

You may download my PowerPoint presentation (Philosophy Club, The Villages, FL, 5 July 2013) here: https://sites.google.com/site/bigira/philosophy-related-pps/Philo%20IRS%20NSA%20July%202013.pptx?attredirects=0&d=1

IRS POLITICAL PROFILING CONTROVERSY

According to the May 2013 report by the US Treasury Department Inspector General (IG) for Tax Administration (.pdf available here: http://www.washingtonpost.com/blogs/wonkblog/files/2013/05/201310053fr-revised-redacted-1.pdf ), starting in 2010 and continuing through 2012 and two election cycles, "inappropriate criteria were used to identify tax-exempt applications for review".

The IG Report identified some specific inappropriate criteria including "Patriots", "Tea Party", "Issues include government spending, government debt or taxes", "Education of the public by advocacy/lobbying 'to make America a better place to live'", and "Statement in the case file criticize how the country is being run". [exact quotes, including grammatical errors]

The result was that some applications submitted by Liberal groups were approved for § 501 (c)(4) while otherwise identical applications by Conservative groups were forwarded to a team of "specialists" and thus delayed for years.

According to the IG Report:

Organizations that applied for tax-exempt status and had their applications forwarded to the team
of specialists experienced substantial delays. As of December 17, 2012, many organizations had
not received an approval or denial letter for more than two years after they submitted their
applications. Some cases have been open during two election cycles (2010 and 2012). [my bold]

On 13 May 2013, a day before the IG Report was issued, President Obama stated that the practice was "Outrageous, if true."

The next day, when it was clear that the charges were indeed true, Obama followed up stating:

"The IRS must apply the law in a fair and impartial way, and its employees must act with utmost integrity.

“This report shows that some [IRS] employees failed that test. I’ve directed Secretary Lew to hold those responsible for these failures accountable, … so that such conduct never happens again.

“But regardless of how this conduct was allowed to take place, the bottom line is, it was wrong."

The IG Report included a detailed list of some of the "unnecessary" questions asked of targeted organizations by the "specialists" to delay approval.

1 Requests the names of donors. 2 Requests a list of all issues that are important to the organization and asks that the organization indicate its position regarding such issues. 3 Requests 1) the roles and activities of the audience and participants other than members in the activity and 2) the type of conversations and discussions members and participants had during the activity. 4 Asks whether the officer, director, etc., has run or will run for public office. 5 Requests the political affiliation of the officer, director, speakers, candidates supported, etc., or otherwise refers to the relationship with identified political party–related organizations. 6 Requests information regarding employment, other than for the organization, including hours worked. 7 Requests information regarding activities of another organization – not just the relationship of the other organization to the applicant.

Were "Progressive" Organizations also Targeted?

The Democrats on the House Ways and Means Committee published what they said was evidence that "progressive" groups were also targeted (.pdf available here: http://democrats.waysandmeans.house.gov/sites/democrats.waysandmeans.house.gov/files/November%202010%20BOLO%20IRS0000001349-IRS0000001364.pdf).

Indeed, the term "Progressive" does appear on a spreadsheet utilized by the IRS reviewers, however, that line of the spreadsheet applies only to § 501 (c)(3) applications, which are very different from the 501 (c)(4) applications that are the main object of the IRS political profiling controversy.

As the IG Report makes clear, § 501 (c)(3) organizations may NOT "engage in political campaign intervention" while § 501 (c)(4) groups may do so up to 40% of their activities. Another difference is that contributions to § 501 (c)(3) groups ARE tax deductible by the donors while § 501 (c)(4) are NOT tax deductible by the donors.

The House Ways and Means Democrats include one example of a "Tea Party" group that appears on an IRS spreadsheet, but careful observation shows that that line applies to BOTH § 501 (c)(3) and § 501 (c)(4) groups. It should be obvious that tax exemption should not be allowed for donors for any "political campaign intervention", whether Liberal or Conservative.

Thus, there is no evidence that "Progressive" groups were subjected to any profiling related to § 501 (c)(4), while it is clear, even from the IRS spreadsheet example published by the Democrats, that such profiling was inappropriately applied to Conservative groups.

Should ANY "Political" Organizations Enjoy BOTH Tax-Exemption AND Anonymity for their Donors?

In reviewing this controversy, I wondered why the IRS allows MAJOR DONORS to make ANONYMOUS contributions to ANY tax-exempt organization that engages in any form of "political campaign intervention" (be it Liberal or Conservative) .

Well, it turns out that this strange rule dates from the 1958 Supreme Court decision regarding the NAACP vs Alabama (see http://en.wikipedia.org/wiki/NAACP_v._Alabama) where the Supremes ruled that disclosure of names could render private donors vulnerable to retaliation.

OK, if that is the Law of the Land, so be it, but it should be applied EQUALLY to both Liberal and Conservative groups. Don't you think?

In this case, IRS political profiling, targeting Conservative groups, over two election cycles (2010 and 2012), has almost certainly resulted in a net benefit for Liberal organizations in terms of fund-raising, because some donors will justifiably hesitate to contribute to any organization that has not been approved by the IRS for tax-exempt status.

Has this affected election results at the National level (House, Senate, Presidency), and/or local levels (Governors, State Legislators, etc.)? No one will ever know for sure, but I would think at least some close elections could have gone the other way absent IRS targeting of Conservative "political campaign intervention" groups.

NSA SNOOPING CONTROVERSY

Which brings us to the second part of this (admittedly long) topic posting.

The reason I have linked the IRS and NSA controversies should be painfully obvious:

If any Administration, whether Democrat or Republican, misuses an agency of the government for political profiling purposes, as the Democrats have clearly misused the IRS for two election cycles, how can we trust them not to similarly misuse the awesome snooping powers we now know have been entrusted to the NSA ?

We all know that Edward Snowden, an employee of an NSA contractor, went to Hong Kong (controlled by China) and released several TOP SECRET documents revealing that the NSA has engaged in large-scale domestic snooping. There is no doubt that all TOP SECRET materials contained on the laptop computers and other computer media he had with him have been downloaded by the Chinese and are now in their possession. Snowden subsequently went to Russia, and has been there long enough for the Russians to have downloaded all material he had with him. Also, there is no doubt that both the Chinese and Russians have interrogated Snowden thoroughly and extracted the critical TOP SECRET NSA information that he possessed.  

After the NSA leak was made public by Snowden, President Obama assured the American public:

“… nobody is listening to your telephone calls… 

“… you can't have 100 percent security, and also then have 100 percent privacy and zero inconvenience. We're going to have to make some choices as a society… 

"I don't welcome leaks … There's a reason these programs are classified." [my bold and italic]

Please note that I have bolded the President's word "Nobody". Does that mean no person is listening to our telephone calls (and that no person is reading our emails and other computer communications)?

For example, what if some automatic computer program was listening to our telephone calls (and emails) and searching for some combinations of words that might indicate criminal or terroristic intent? And, only if and when the computer program discovered some suspicious messages and identified the people involved, then the NSA went to the FISA court to get a warrant to have some person listen to phone calls (and emails) to and from the identified persons?

I have also bolded and italicized the word "is". As President Bill Clinton famously observed, "It depends upon what the meaning of the word 'is' is."

Is Obama assuring us that nobody is listening to our phone calls (and emails) right now? What if our phone calls (and emails) are being automatically recorded and stored away by the NSA for future use if and when subsequent analysis reveals that they may relate to suspicious activities and then the NSA gets a FISA warrant to have some person listen to them?

That said, I agree with Obama that we cannot expect "100 percent privacy and zero inconvenience" and maintain reasonable security against criminal and terrorist attacks. Like him, given this difficult choice, I come down on the side of security.

What do we know about NSA snooping?

Started as early as 2006 (under G.W. Bush), continued through present (2008-2013 under Obama).

Key members of Senate and Congress are aware of classified details of NSA programs and exercise oversight. Judicial oversight is exercised by FISA court.

MetaData is being collected on virtually ALL domestic home phone and cellphone calls (at least the Calling number, Called number, Date, Time, Duration, …) Internet data (VoIP, Emails, Chat, Photos, Videos, Files, Stored Data [“cloud”], Logins, SPECIAL REQUESTS, …)

What do I suspect about NSA snooping?

I’ve worked on classified military projects, but never NSA projects or any projects related to surveillance or data mining, so I am free to “speculate” without revealing classified information.

Based on my knowledge of electronics and computers and the Internet and “artificial intelligence” I never type anything into my computer that I would not mind seeing on the front page of tomorrow’s newspaper or TV news!

For many years I have suspected that NSA (not to mention Google :^) has metadata on all Internet activity and phone calls and that they utilize advanced data mining algorithms to associate Phone numbers, Email addresses, Blogs, Social networks, and so on.

It is also likely they use “artificial intelligence” and “key word analysis” computer techniques to “gist” voice phone calls, looking for languages and word combinations that may indicate criminal or terrorist activities as well as semantic analysis to identify individual writing styles. It is also likely they similarly “gist” Emails, Blogs, Photos and other Internet data and use facial recognition, voice prints, and other biometrics to associate multi-modal communications with particular groups of people and individuals.

Bottom Line

I (along with Obama) am appalled that Edward Snowden violated his pledge to protect classified government documents. Internal government processes (and specialized lawyers) exist for reporting abuses. Snowden should have used these before going to China and before revealing these Top Secret activities to the press. (Hong Kong is an “autonomous” region under the control of China.) We should assume China and Russia have all Snowden’s NSA data.

I generally SUPPORT all the known and most of my suspected NSA snooping activities, assuming proper oversight. As I’ve stated in presentations to The Villages Philosophy Club and my Novel and Blogs, advocates of “privacy” are fighting a phony and lost battle. If you have a home and a job and a credit card and a cellphone and a car – in other words if you are a “respectable” citizen – YOU HAVE NO “PRIVACY”. (The only person with real privacy is the guy using your stolen credit card to buy stuff!)

However, the IRS scandal has increased my distrust of the government. I worry that POLITICALLY-motivated NSA employees may abuse Phone and Internet data for partisan purposes (as some IRS employees have done).

Get the PowerPoint Presentation!

If you'd like more technical background on the "six degrees of separation" between (virtually) any two people on Earth and on the issue of privacy in the Internet age, please download the PowerPoint presentation I gave to the Philosophy Club of The Villages, FL.

Please download that PowerPoint here: https://sites.google.com/site/bigira/philosophy-related-pps/Philo%20IRS%20NSA%20July%202013.pptx?attredirects=0&d=1,

Feel free to express your opinions on this issue by posting a Comment to this Blog.


advTHANKSance

Ira Glickstein 

 

What is Time? Alan Alda's 2013 "Flame Challenge"

Time - the fourth dimension (2013 Flame Challenge) from Ira Glickstein on Vimeo.

My entry for Alan Alda's 2013 Flame Challenge was submitted last week. It is in the form of a short video  answering the deceptively simple question "What is Time?" (click above to view the video).

Alan Alda is on a mission to help youngsters become interested in science. In conjuction with the Center for Communicating Science at SUNY Stony Brook, he started the Flame Challenge in 2012 with the question "What is Flame?" They received some 800 entries.

I expect they will get even more this year with the question "What is Time?"

ABOUT MY ENTRY

I think I've come up with a unique way of viewing "Time - the fourth dimension".  Due to a strict limit on the length of the video, and the fact that it is aimed at 11-year old students, I have had to greatly simplify the material. This Blog posting includes additional material that will be useful to adult readers and science teachers who wish to know more about my way of viewing Time.

There are three big ideas here:

1. TIME is NOT a clock (any more than Space is a ruler or Heat is a thermometer), nor is it rotation of the Earth or motion or the order of events, etc.  
2. TIME is the fourth dimension, plain and simple. It appears different to us because the whole Universe is speeding along the Time axis at the speed of light.  
3. TIME slows down when we move in Space because nothing can move faster than the speed of light, so any motion in Space must take away from the speed in Time such that the vector sum of the Space and Time velocities exactly equals the speed of light.

WHAT TIME IS NOT

Time is not the tick, tick, tock of a click, click, clock, any more than Space is a ruler or Heat is  a thermometer!

 

Nor is Time the rotation of the Earth on its axis that gives us day and night divided into 24 hours. Nor is it the movement of the tilted Earth in orbit around the Sun that gives us the seasons, nor any other kind of motion. Nor is it the spontaneous decay of certain atoms that give radioactive materials a half-life. Nor is it simply the ordering of events.

WHAT TIME IS

Time, plain and simple, is the fourth dimension, very much like the first three dimensions of Space.

 

The Time dimension appears different to us because you and I and the whole Universe are hurtling along it at very nearly the speed of light as a consequence of the “Big Bang” expansion some 13.7 billion years ago, in which our Universe, along with the dimensions of Space and Time, originated.

Since Time itself originated with the "Big Bang" it may not be meaningful to even ask the question "What happened before the Big Bang?" In any case, we may never know what caused it.

 

The Universe originated as an incredibly energetic and dense point of Energy/Matter that suddenly expanded. During the initial moments of the expansion, it is not clear if there was anything like the sub-atomic and atomic particles of Matter or the radiation of Energy with which we are familiar today. However, when Matter and Energy, as we know it, formed, all particles with mass were expelled along the Time axis, or at very tiny angles with respect to that axis. You and I, along with everyone and everything else, are still moving along or near that dimension at very close to the speed of light, c, which is as fast as anything can go.

 

We do not notice our ultra-rapid travel along the Time dimension as motion because the whole Universe is moving along with us. Therefore, we notice only relative motion between ourselves and other people and between ourselves and other things.

 

For example, people on the equator are happily unaware that they are moving Eastward at about 1,000 miles per hour due to the rotation of the Earth on its axis. Unless you live in one of the polar regions, you are moving Eastward at hundreds of miles per hour. Even if you are on an airplane, travelling  "Westward" from New York to Chicago or Los Angeles at 500 miles per hour, your net velocity is Eastward, due to the rotation of the Earth! We are equally unaware that the whole Earth is speeding along at over 67,000 miles per hour on its orbit around the Sun!
 

WHY TIME CAN BE SLOWED A BIT
 

We live in four-dimensional SpaceTime where everything must move at the speed of light, c, either along the Time axis, along a Space axis, or in a combination of Time and Space at an angle, Θ, to the Time axis. If movement is totally aligned with the Time axis, Θ = 0 and we are said to be “at rest” in Space, and we move along the Time axis at the normal rate (c, about one foot per nanosecond).

 

If we are not "at rest" in Space, Θ > 0, and we move through SpaceTime in a combination of Space and Time such that the vector sum of our Space and Time velocities is exactly c. Since nothing can go faster than c, any movement in Space must slow down our movement in Time. This was recognized over 100 years ago by Lorentz, Minkowski, and Einstein, who use the terms "Dilation of Time" and "Contraction of Space". This is usually expressed in terms of the Lorentz factor:

where c is the velocity of light and v is the velocity of an object in Space.

As an engineer, I found that way of expressing relativistic effects of travel at significant fractions of the speed of light not to be "understandable" from my physical (and perhaps anal) point of view.

After knocking my head against the wall over an inordinate amount of Time, I finally realized that I could get an exactly equivalent Lorentz factor by considering the angle Θ, between the Time axis and the velocity vector of an object through SpaceTime.

[above image modified 12 April 2013]

It turns out that v (the velocity of the object in Space) divided by c is equal to the Sin Θ, and that 1/ϒ, the Lorenz factor, is equal to the Cos Θ.  

WHAT ARE DIMENSIONS?

 

This may sound like a simple question, and the answer is pretty simple, but, just to be sure we are all on the same page (see figure below):

 

0 - A POINT has ZERO dimensions

1 - Drag the point along the FIRST dimension ("x" of Space) and you get a LINE, that has ONE dimension.

2 - Drag the line along the SECOND dimension ("y" of Space) and you get a SQUARE (or rectangle) that has TWO dimensions.

3 - Drag the square along the THIRD dimenson ("z" of Space) and you get a CUBE (or rectangular solid) that has THREE dimensions.

4 - Drag the cube along the FOURTH dimension ("t" of Time) and you get a HYPER-CUBE (or hyper-rectangular solid) that has FOUR dimensions.



 

SUMMARY

When movement is a combination of Time and Space, and the velocity in Space is v, an object is moving through SpaceTime at an angle Θ, such that: v/c = SinΘ, and 1/ϒ (the Lorentz factor) = Cos Θ.

The figure below shows the situation for seven different values for the angle of travel through SpaceTime, from Θ = 0⁰ to Θ = 90⁰ .

Θ = 0⁰  [Sin Θ = 0.0000,  Cos Θ = 1.0000]   AT REST IN SPACE
For an object that is "at rest" in Space, Θ = 0⁰. Even when an object is not moving along the Space axis, it is moving along the Time axis. Since everything in SpaceTime must have a speed of c, an object "at rest" in Space must be moving at speed c in Time. Note that for this condition, v/c = 0 and the Lorentz factor ϒ = 1. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Even the fastest rockets and satellites developed so far go only a tiny, tiny fraction of c. Therefore, for all practical purposes, the angle, Θ, is ≈ 0⁰ (approximately equal to ZERO degrees). For example, the Earth is travelling around the Sun at a speed of 67,000 miles per hour, faster than any rocket, but that is only 0.001 % of the speed of light. At 67,000 miles per hour, v/c =  0.00001 and  Θ = 0.0000017⁰.

Θ = 15⁰ [Sin Θ = 0.2588, Cos Θ = 0.9659]    MOVING 26% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 15⁰. It moves through Space at 26% of c and through Time at 97% of c. Note that for this condition, v/c = 0.2588 and the Lorentz factor ϒ = 0.9659. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 30⁰ [Sin Θ = 0.5000, Cos Θ = 0.8660]   MOVING 50% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 30⁰. It moves through Space at 50% of c and through Time at 87% of c. Note that for this condition, v/c = 0.5000 and the Lorentz factor ϒ = 0.8660. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 45⁰ [Sin Θ = 0.7071, Cos Θ = 0.7071] MOVING 71% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ =45⁰. It moves through Space at 71% of c and through Time at 71% of c. Note that for this condition, v/c = 0.7071 and the Lorentz factor ϒ = 0.7071. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 60⁰ [Sin Θ = 0.8660, Cos Θ = 0.5000] MOVING 87% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 60⁰. It moves through Space at 87% of c and through Time at 50% of c. Note that for this condition, v/c = 0.8660 and the Lorentz factor ϒ = 0.5000. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 75⁰ [Sin Θ = 0.9659, Cos Θ = 0.2558]   MOVING 97% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 75⁰. It moves through Space at 97% of c and through Time at 26% of c. Note that for this condition, v/c = 0.9659 and the Lorentz factor ϒ = 0.2558. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 90⁰ [Sin Θ = 1.0000, Cos Θ = 0.0000]      TIME STANDS STILL 
Light (and other forms of electro-magnetic radiation) move through SpaceTime at an angle of Θ = 90⁰. Light moves through Space at 100% of c and, therefore, since nothing can go faster than c, Time stands still. Note that for this condition, v/c = 1.0000 and the Lorentz factor ϒ = 0.0000. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ. Anything with mass cannot achieve this speed in Space because it would take an infinite amount of energy to get it up to this speed in Space.
 
[ADDED 11 March 2013] In response to some skepticism about my contention that the whole known Universe is speeding along the Time dimension at nearly the speed of light, I did more research and found support from Brian Greene, Professor of Physics and Mathematics at Columbia U, who has been featured on the PBS Nova series. He writes:

“Special relativity declares a similar law for all motion: the combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light” [Excerpt From: Greene, Brian. “The Fabric of the Cosmos.” Vintage Books, 2007. See http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.htm for his PBS series.]

I have provided more detail in the first comment below.

Ira Glickstein

Ratchet Effect

From Joel Fox:
  The mechanical device called a "ratchet" lends its name to many phenomena that are not mechanical.  It refers to any situation in which a force in one direction causes a movement in that direction while a compensating force in the opposite direction causes a lesser movement in that direction.  The net effect is a drift in the less resistant direction.  A political example, credited to Margret Thatcher, is "When the Left gets power, she said, they drive everything Left; when the Right gets power, they slow the Leftward drive, perhaps even halt it for a spell; but nothing ever gets moved to the Right."  In the mechanical device, a part called a "pawl" jams the works and provides resistance to motion in one direction, leaving it free to move in the opposite direction.  Our intellectual objective should be to find the pawl in each situation in order to learn what causes the machine to function.

  For a while I lived in France, a country which is about as socialist as you can get.  It was a period during which a conservative government had been voted into power because of a fiscal crisis.  The new government tried to institute reforms; however, a mechanism existed which served as a pawl to prevent the reform from actually occurring.  Students and union members who would lose in the short term, took to the streets to oppose the reforms by blocking traffic and stalling the metro.  After weeks of painful disruption, the government and general public gave up on the reforms.  In other words, the student-union groups acted as a pawl to prevent the society from moving to the right, because of the benefits that accrued to them in a leftist society, despite the democratically expressed will of the people to reform.
  Another example of a ratchet effect is the well known "wage-price spiral."  In a low unemployment situation, wage increments can be demanded which are not merited by increases in productivity.  As a consequence, management must raise prices.  If the situation is widespread, inflation occurs and labor demands higher wages to make up for the loss in buying power.  The cycle starts again.  In our lifetime one has never seen a deflationary wage-price spiral. Hence, there is a ratchet effect.  The pawl which blocks the lowering of wages accompanied by deflation is simply human nature.  Not since the early unionization days has one witnessed the violence of management troops against union strikes and violence.  This causes the lack of symmetry required by a ratchet.   
   Another example of the ratchet effect was the battle between the Soviet Union and the Free World. The Soviets expressed their intention to fight "by all available means, including armed force, for the overthrow of the international bourgeoisie and for the creation of an international Soviet republic as a transition stage to the complete abolition of the State."  While the Soviets maintained a policy of moving their program forward at every opportunity, the West's posture was one of resistance.  Thus we have a classical situation of ratchet effect in which the West could  only lose in the long run unless other powerful factors intervened (which obviously happened).

Time to fiddle

 [from Joel]  Well, I've had enough.  I think that Plato was right.  There is an inevitable transformation of democracy into tyranny.  Democracy is unstable.  This last presidential election seems to have been a turning point.  Obama has had more strikes against him than any president preceding him (even Nixon), yet victory ensued.  Despite his failings in delivery on campaign promises, abuse of power, incompetence in foreign affairs, slow reaction to emergencies, lack of transparency and open-mike gafs, he pooled his 47% and party loyalists into a victory.  Republicans are unlikely in the future to find more favorable opportunity to retake the White House.  As Plato pointed out, the general population becomes corrupted by the goodies that they receive and are not likely to vote for a candidate that promises hardship and hard work.  I've opted out in the sense that I won't try to convince young people that their future is at risk.  Nor does it even make sense to follow the news.  Qué sera, sera.  I think I'll take up golf and learn to drink good wine while I play my fiddle..

Global Warming Predictions FAR Too High

The animated graphic above is based on a figure from the most recent draft Assessment Report (AR5), currently under review by the Intergovernmental Panel on Climate Change (IPCC). The AR5 draft has been leaked by a reviewer, see  http://wattsupwiththat.com/2012/12/14/the-real-ipcc-ar5-draft-bombshell-plus-a-poll/ 

The graphic is based on Figure 1-4 from the AR5 draft document and it clearly indicates something is and has been seriously wrong with the analysis methodology and computer models utilized by the IPCC researchers. It turns out that ALL FOUR IPCC reports, from 1990 to 2007 have seriously over-stated likely Global Warming, by factors of  TWO to FIVE. When actual observations made over a period of up to 22 years substantially contradict predictions based on a given climate theory, that theory must be modified or discarded completely.

The animation shows the central estimates of Global Warming from 1990 to 2012, from the First Assessment Report (FAR), the Second (SAR), the Third (TAR), and the Fourth (AR4). They are all high by a factor of two to three.

Actual Global Warming, from 1990 to 2012 (indicated by black bars in the base graphic) amounts to between 0.12 to 0.16˚C (indicated by the black arrow in the animation),  yet the central predictions from the four reports (indicated by the colored arrows in the animation) range from 0.3˚C to 0.5˚C.

The colored bands in the base IPCC graphic indicate the range of uncertainty above and below the central predictions claimed by the IPCC when they issued the assessment reports. Please note that the colored bands, wide as they are, do not go low enough to contain the actual observations for Global Temperature reported by the IPCC for 2012.

The colored bands indicating IPCC 2012 predictions extend above the 1990 Global Temperature by as much as 1.04˚C. Even the minimum range of uncertainty bands for 2012 are above 1990 by 0.51˚C, which is nearly five times the actual measured 2012 warming of 0.12 to 0.16˚C.

Thus, the IPCC predictions have errors that are multiples of what they thought they were predicting!

The final AR5 has not yet been issued, and it is uncertain if the above base graphic will make it through the final cut due to its honesty. We shall see.

Ira Glickstein