Letting you enemies abort themselves

I never opposed abortion if getting an abortion would save the mother's life and not getting an abortion would result in the death of the mother.  But I supported outlawing abortions after the development of brain cells and possibly also earlier in the past.

Maybe I was wrong in opposing abortion and here is why I might have been wrong.  I am not saying I was definitely wrong but I might have been wrong.

Let's presuppose abortion is an act of killing and in some cases it is more specifically an act of murder.

Most Democratic Candidates support legalized abortion.  Now someone who votes Democrat is more likely to teach their children to vote Democrat and to have the value systems very often that go with voting Democrat including supporting abortion.

There are some exceptions of Democratic Candidates that do not support abortion

https://web.archive.org/web/20030614103243/https://www.ontheissues.org/OH/Jim_Traficant_Abortion.htm

After the Republicans took control of the House in 1995, Traficant tended to vote more often with the Republicans than with his own party. On the issue of abortion, Traficant voted with the position of the National Right to Life Committee 95% of the time in the 105th Congress, and 100% of the time in the 106th and 107th Congresses.If someone who votes democrat does not get an abortion and raised children they would not have raised if they got an abortion their children would be more likely to vote to legalize abortion

https://web.archive.org/web/20220412003322/http://en.wikipedia.org/wiki/James_Traficant

When I talk about Democrats through the rest of the article I am not talking about the rare exceptions but for people who primarily support taxpayer funding of abortion, more taxes, taxpayer funding of public schools, forced hiring policies controlling the percent of employees based on race, religion, gender identity and sexual orientation, taxing carbon dioxide emissions, internet censorship of viewpoints that do not agree with the democratic party viewpoints and forcing people who do not want to live in a communist society to be coerced to do work for other people through taxation, the right for public school teachers to persuade children under 18 years old that they are transgender without parental permission, the right to surgically remove children under 18 years old anatomical parts without parental consent if the children are persuaded by public school teachers that they are transgender, the right to fine or imprison people who do not call you by the gender pronoun you desire them to, taxing people to pay insurance benefits for monogamous homosexual married couples, arresting police who use force to try to stop black on black violence, open border immigration for people with HIV AIDS, open border immigration for people without background checks to see if they committed violent crimes, etc.

Talking Democrats out of getting abortions or outlawing abortions for Democrats would only spread abortion in the next generation

Democrats tend to support taxing people to spend money on Public Schools.  Public Schools tend to instill in people the Democratic Party value system.

The Democratic Party Value system supports war against people who should not have war waged against them and supports using violent to redistribute wealth, even if they give lip service to opposing war, by supporting tax payer funded schools that teach blind faith in government Democrats support unjust wars.

If people were made fully aware that abortion is killing or murder but not prevented from getting abortions then people who do not value human life would be more likely to choose to get abortions, but people who do value human life would be less likely to choose to get abortions.  Hopefully this would result in the next generation having a lower percentage of people that do not value human life and a higher percentage of people that do value human life.  This might not happen if those who got abortions adopted later and still raised children with their anti life value system.  Also hypothetically if someone got A abortions but still gave birth to X children and raised X children but would have given birth to and raised Y children if they did not get any abortions then if X is greater than or equal to Y then allowing them to get an abortion does not make the situation better in terms of preventing people with anti life value systems from raising children

When people with anti life value systems teach their children an anti life value system those children are more likely to grow up to become murderers or commit other violent acts against non violent people.

Allowing people to voluntarily set up a communal wealth system is not a problem and many voluntary communal societies have successfully worked when the society was allowed to reject members who would not contribute labor to help others in the community such as working to provide food for the community or provide services for the community members which the community members agree are valuable enough to let them stay without producing food in exchange for the food.

New Book: Bernie Sanders Was Kicked Off Vermont Commune for Loafing

https://web.archive.org/web/20160420123527/https://www.jewishpress.com/news/breaking-news/new-book-bernie-sanders-was-kicked-off-vermont-commune-for-loafing/2016/04/20/

Imposing communism by force has had a track record of multiple holodomores in which massive numbers of people starved.  

In 1932–1933, a famine known as the Holodomor killed 3.3–3.9 million people in the Ukrainian Soviet Socialist Republic

https://web.archive.org/web/20220429172547/https://en.wikipedia.org/wiki/Holodomor_genocide_question

https://web.archive.org/web/20220502021057/https://en.wikipedia.org/wiki/Holodomor

Democrats support policies that lead to holodomores in which massive numbers of people starve to death

If Democratic parents raise children who vote and more importantly behave like Democrats more people would be murdered if the parents did not abort the children and successfully instilled Democrat value systems in the children then the number that would be murdered if the parents aborted the children and did not give birth to or adopt any children to replace the children they murdered through abortion

Now not all children that are raised by Democratic parents choose the value system of their Democratic parents so this reasoning might not hold in practice

Although there is an unlimited amount of money since money is created by belief there is a finite amount of food mass per volume in any section of the world of a given volume.  I am not opposed to people receiving welfare if they are offered it but I am opposed to people using violence to force other people to do slave labor work to give them welfare.  Someone can choose to take food stamps while simultaneously voting against any tax that is justified with the excuse of raising funds for food stamps.  

Currently men when looked on as a group as a whole are net tax payers and women looked on as a group as a whole are net tax receivers.  Traditionally women would have children and receive net resources of food from her husband but not from other women's husbands.  The husband who provides the food for his wife's children would get to instill his value system in her children, whether they are both of their biological or adopted children or children she had from a previous marriage in the case of a widow or sometimes in the case of a divorced woman depending on custody arrangements.  

Now some single mothers are exceptions to this but the following applies to the net effect of most single mothers as a group.  Now single mothers will tax men she is not married to, to give food to them without letting that men paying the tax raise her children and teaching them their value system.  These single mothers do not do the work of raising their children because they do not earn the food to feed the children, do not baby sit their own children and do not morally educate their own children instead they send their children to public schools that babysit the children and to public schools to immorally educate the children and tax men they are not married to, to pay for their children's food.  These single mothers tend to vote Democrat and the Public schools they send their kids to tend to teach a Democrat value system.  If voting actually worked there is not way to solve this problem by voting.  The problem can not be solved by voting because single mothers tax men who are not married to them.  This means that married men who try to have as many children as they can support in order to teach them other value systems than the Democrat value system are are limited in how many children they can support because they have to pay taxes to support children of single mothers who vote Democrat, but single mothers who vote Democrat have no limit to how many children they can have and raise to vote Democrat because the more children they have the more tax they can take from men they are not married to.  This is a positive feedback loop that can only be stopped if single mothers no longer can tax men they are not married to.  This positive feedback loop of an ever increasing percent of the population of people who do not work for food taxing an ever decreasing percent of the population who work to produce food tends to lead towards mass starvation.  The only reason it has not yet reached a state of mass starvation in the United States yet is because technology improves over time so one man can potentially produce more food per time now than in the past.

Suddenly Hermes and La Barbara have returned from Spa 5. He had made the labor camp so efficient that they only needed one Australian man to perform the labor.

https://web.archive.org/web/20220503233255/https://futurama.fandom.com/wiki/How_Hermes_Requisitioned_His_Groove_Back

The only way to stop the positive feedback loop that will lead to starvation is to stop taxing men to pay for other men's children which will never happen as long as net tax receivers can vote to tax net tax payers.  This positive feedback loop could be slowed down by letting single mom's get abortions if single mom's would have less children and thus raise less children who vote to tax people to fund net tax receivers.

Democrats also support open borders which when combined with allowing net tax receivers to tax net tax payers will result in mass starvation.  Communal societies only work with border restrictions.  Forced communism plus open borders leads to mass starvation, because you can not close the borders to keep out people who will refuse to produce food but will demand to receive food through the violent imposition of communism.  When these non food producers enter the border and have children they can persuade their children to vote for the value system that will tax the net food producers leading to mass starvation.  Allowing the immigrants who want to violently force other people to produce food for them to get abortions can slow down the positive feedback loop that would lead to mass starvation if non net tax paying immigrants would have less children and thus raise less children who vote to tax people to fund net tax receivers.

Getting an abortion is still killing so I am not suggesting people who oppose the Democrats anti life value system go out and get jobs as professional abortionists.  I am suggesting maybe we should let people know abortion is the killing of a life, and let people who do not value human life get abortions without stopping them.  We should still stop forced abortions of mothers who do not want abortions and who would not die as a result of not getting an abortion.

Presuming the reader is on my team, now we should encourage people on our team to not get abortions.  But on the team that supports all the bad things I listed above that Democrats support, preventing them from getting abortions might lead to an increase in their numbers resulting in mass starvation of both or all teams in the long run and increased violence in future generations in the short run.  We can try to persuade them to change teams and then persuade them not to get an abortion if they switch to our team, but if they will not switch to our team preventing them from getting an abortion might increase the numbers of an army of evil.  

I still maintain that Paul Hill and Scott Roeder committed third party defense and not murder when they executed abortionists, but Paul Hill was executing someone from the enemies team to defend someone else who would likely be recruited to the enemies team which might have increased the number of abortions in the long run even though it decreased the number of abortions in the local geographic area in the short run.  Although Paul Hill technically committed defense it might not have been a wise decision because he may have increased the population of the anti life team by preventing a member of the anti life team from aborting potential recruits of the anti life team who have anti life parents who would try to raise them in anti life values.

Letting the antilife team completely exterminate themselves would result in less abortions in the long run then letting the antilife team procreate more members who will get future abortions.  Perhaps allowing the antilife team to grow in population relative to the prolife team by temporary forcing antilife people not to get abortions instead of allowing them to naturally exterminate themselves would allow them to grow in numbers enough to be powerful enough to not only change the law in the future and resume abortions but also to force abortions on the prolife team as has been done in China with the one child policy. 

But someone might object the Bible opposes abortion.  The Bible classifies causing a parent who should not receive an abortion to have an abortion as murder but actually has prescribed abortions for wicked people or executing the children of wicked people in some cases.

I am not saying we should enforce old testament laws or execute people based on old testament laws in a different geographical location than ancient Israel and a different time period.  I am not saying whether or not people should obey the Bible but simply explaining this for those who object to what I say on the grounds of the Bible.

Exodus 21:22-24 describes up to the death penalty for a man who injures the baby of a pregnant woman with the death penalty in the case of an abortion that results from hitting a pregnant woman but the following exceptions in the Bible in which there is no death penalty for abortion must be considered

Deuteronomy 20:10-18 

Deuteronomy 20:10-11 prescribes not to kill people who make peace with you,

Deuteronomy 20:12-14 prescribes  to execute men only and take the cattle, women and children of people who do not make peace with you 

except those people from specific groups listed in Deuteronomy 20:16-17 who you are to leave nothing alive of not even the cattle, women nor children

The groups described in Deuteronomy 20:16-17 may have committed human sacrifice, incest and bestiality in Leviticus 18 and Leviticus 20 and because of that leaving any of them alive even their offspring may have resulted in a spread of stds and genetic defects leading unto future generations, and leaving the adults alive may have spread the teachings of the practices of incest, bestiality and idol worship

Leviticus 20:20-21 prescribes the execution of people who committed a specific type of incest and for them to die childless.  They were not to be given an abortion and allowed to live but to be executed.  The execution would result indirectly in an abortion unless the execution was delayed and the woman was allowed to give birth prior to being executed.  However Leviticus 20:20-21 prescribes for them to die childless hence an indirect abortion through the execution of the mother.

Numbers 5 Prescribes giving a woman suspected of adultery drink a solution and if she has committed adultery the result of the solution will result in her having an abortion but if she has not committed adultery the solution will not result in her having an abortion.

Deuteronomy 22 Execution of an adulteress woman would result in an abortion unless the woman is required to have her execution delayed until she gives birth which is not mentioned in the text

The difference between Numbers 5 and Deuteronomy 22 is in Deuteronomy 22 understood in the context of the books of Moses a further degree of proof is required before executing the woman involving a proper court trial with witnesses but in Numbers 5 the proof is insufficient and the solution is given upon suspicion of adultery

Starting in Exodus 11 and continuing in later parts of Exodus, God warns he will slay the firstborn sons of the Egyptians who were supporting Pharaoh in enslaving the Israelites, except perhaps hypothetically for any Egyptians who changed sides to the Israelites side and performed the same passover ritual Israelites were required to perform to prevent their firstborn from being executed.  This would be post birth abortions and might potentially have included pre birth abortions of any Egyptians who were pregnant with their first son but have not yet given birth

Copyright Carl Janssen 2022 May 9

Evolutionary biologists implying birds are reptiles

If all birds are dinosaurs and all dinosaurs are reptiles then all birds are reptiles

But if all birds are not reptiles then not all dinosaurs are reptiles and or all birds are not dinosaurs

If some birds are not reptiles then not all dinosaurs are reptiles and or not all birds are dinosaurs

Copyright Carl Janssen 2022 April 15

"Modern taxonomy classifies all dinosaurs as reptiles."

http://web.archive.org/web/20210617054043/https://www.worldatlas.com/articles/were-dinosaurs-reptiles.html

"Modern classification considers all dinosaurs to be reptiles"

http://web.archive.org/web/20220415082239/https://adventuredinosaurs.com/2019/09/18/dinosaurs-were-reptiles-heres-why/

"What Category Is A Dinosaur?

Since dinosaurs have anatomical features that are similar to living reptiles, they have always been classified as reptiles.

Are Dinosaurs Not Reptiles?

The modern taxonomy classifies all dinosaurs as reptiles, not birds or mammals"

http://web.archive.org/web/20220415082458/https://www.animalpicturesarchive.com/is-dinosaur-a-reptile-or-an-amphibian/

Using more modern classification techniques, we’ve also found out that not only are dinosaurs reptiles, but birds are too.

http://web.archive.org/web/20220314141928/activewild.com/are-dinosaurs-reptiles/

"birds are reptiles"

http://web.archive.org/web/20211204145747/https://askabiologist.asu.edu/questions/birds-dinosaurs-reptiles

"In the Linnaean system, organisms are grouped by characteristics regardless of their ancestry. So a reptile is an animal that is ectothermic and has scales, and birds would not be reptiles. In the 1940's, a biologist named Willi Hennig came up with another classification system that he called phylogenetics. In this system, organisms are grouped only by their ancestry, and characteristics are only used to discover the ancestry."

http://web.archive.org/web/20211204145747/https://askabiologist.asu.edu/questions/birds-dinosaurs-reptiles

https://duckduckgo.com/?q=are+all+dinosaurs+reptiles&ia=web

"birds are literally dinosaurs"

http://web.archive.org/web/20220408070301/birdlife.org/news/2021/12/21/its-official-birds-are-literally-dinosaurs-heres-how-we-know/

https://duckduckgo.com/?q=are+all+birds+dinosaurs&ia=web

birds are considered a separate class to reptiles

http://web.archive.org/web/20220403071650/https://en.m.wikipedia.org/wiki/Reptile

https://duckduckgo.com/?q=are+birds+reptiles&ia=web

Percentage of greater values between two distributions

Importance of raw data in knowing practical or clinical significance as opposed to statistical significance

Sometimes a t test is very useless to achieving real life goals yet it is incredibly popular to publish t tests comparing two sets of data without showing the raw data in medical science.  Although it could make sense to remove some parts of raw data in order to keep patient data confidential someone could simply replace identifying data such as patient name with unidentifiable information such as id numbers from which the patient name can not be determined.  This would not be possible in all cases such as studying if there is a correlation between the latitude or longitude of primary location of residence address and health conditions but would probably have been possible in most cases that occurred in the past.

In many cases it maybe more useful to know what each of two distributions look like rather than if two distributions are statistically significantly different by a certain alpha value or if one distribution is statistically significantly greater than the other by a certain alpha value

In many cases the question of practical significance or clinical significance is more important than statistical significance.  A question of practical significance could be, what is the probability that a single specific choice will result in a value that is acceptable for my goal.  Other times a question of practical significance could be out of all the available choices which choice has the highest probability of resulting in a value acceptable for my goal.

In such a case it might make more sense to simply look at the raw data of a study and count the number of cases in which the desired value was greater than the minimum value acceptable and less than the maximum value acceptable and then divide that number by the total number of cases.

For example if someone is comparing two treatments for blood pressure someone and wants to decrease a patients blood pressure by at least 10 units but by no more than 50 units it would make more sense to figure out the frequency at which each treatment in a study resulted in a decrease of more than 10 units but less than 50 units than to use a t test.  This would be done by counting the number of cases that result in a decrease of at least 10 units but no more than 50 units then dividing by the total number of cases for each distribution.  Next the person choosing the two treatments figures out which treatment has a higher percentage of acceptable results and chooses that treatment.  

This can not be done without the raw data which is commonly removed from scientific journal articles that give the results of a t test comparing two sets of raw data but removes the raw data.  It might be possible however if the raw data was removed but both sets of raw data were given a standard deviation and mean, to use that information, to estimate the percentage or frequency of cases for each of two choices that produced a decrease of at least 10 units but no more than 50 units in the example above, by using the mean and standard deviations published to construct a distribution to represent each choice based on the assumption of a normal distribution for each of the two treatments that were used.  This however would be a very bad idea if no results for tests of having a normal distribution were presented in the scientific journal article.  I would not be surprised if it is very common never to show the results of any tests showing that the two distributions were actually normally distributed before conducting a t test.  I would like to see a study looking at the percentage of studies in which normal distribution was not checked for but a t test was performed.

Sometimes a question of practical significance might not be so delicate as to have both a upper and lower limit in desired outcomes.  For example if someone wanted a fire arm that could shoot at least a distance of 200 units but did not worry if it could shoot too great a distance.  It would make more sense to look at the raw data for each of the different firearm choices and calculate the percent frequency that exceeded a firing distance of 200 units for each firearm choice's distribution than to conduct a t test on the raw data to determine if each of two firing distribution choices available produced statistically significant different results for an alpha value or if one test produced statistically significant greater results for an alpha value

Sometimes a question of practical significance is yet another degree even less delicate than that and someone might not even care if a at least a minimal number of units were produced but only want to know which of two choices produced greater results the most often.  Someone might say, now we can finally use a t test legitimately.  And in such a case you could use a t test but it still would not be the best choice for at least two reasons.

Firstly, a t test would not be the best choice because the question was not which choice had a greater mean but which choice produced greater results than the other available choice most often.  Secondly, a t test would not be the best choice because you can not know if the results of both distributions will be normally distributed before conducting the test.

I am going to write a possibly new statistics test I thought of which may or may not have already been created by someone else under another name.  I will name this test the "Percentage of greater values between two distributions" test.

Test steps

This test works for ordinal, interval or ratio data and it does not matter if the two sets of data being compared have equal sample sizes or not or if they have odd or even sample sizes.

After collecting data from two samples order the values of the data for each sample in a list in ascendimg or descending order.

Pick one of the two lists

For each value on the chosen list count the number of values on the other list that are below that value as 1 point each, the number of data points exactly equal to that value as 0.5 points each and the number of data points higher than that value as 0 points each.  Each value on the chosen list will have a certain score or sum total of points.  If there are more than one data points on the list other than the chosen list that have that value count that data point multiple times.  Add up the total number of points for each value on the chosen list together for all the values on the chosen list and divide it by the product of the sample size of the chosen list and the sample size of the other list.  If a value on the chosen list occurs multiple times then count or use that value multiple times when adding up the points for all of the values.  You can swap lists next and get a score for each list.  The final value for each list should give you the percent of time that a value randomly selected from the population that one list was sampled from should be greater than another value randomly selected from the population the other list was sampled from.  In some cases involving data with discrete quantized values it maybe better to set the 0.5 points each values to 0 points instead as long as you do so consistently for both lists, I choose them to be 0.5 points based on the assumption of non quantized data in which it could have a 50% chance of being above and 50% chance of being below the other data point if a very small measurement difference was made such as one data point being 1.49999 and the other being 1.50001 instead of both being 1.5 when measured to two significant digits each.

Examples

I will use this possibly new test to compare two such sets of random uniform data each with a sample size of five, one between 0 and 1 and the other between 0.1 and 1.1 both to 4 decimal places from

https://www.random.org/decimal-fractions/

https://web.archive.org/web/20220402133005/https://www.random.org/decimal-fractions/ 

I will add 0.1 to the second set of numbers between 0 and 1 to get a range between 0.1 and 1.1  

( I was hoping this would increase the likelihood of the results for the two distributions looking different but unfortunately the distribution which has 0.1 added to it had a lower mean and median and the opposite of intended results were produced)

In order to compare this test with a t-test I will assume the p value for the possibly new data is one minus the percent that a randomly selected value from one list will be greater than a randomly selected value from another list, even though this does not line up the same way as a t test because a t test only compares if one mean is likely to be greater than another.  I will also look at the percent of values from one list that are less than or less than or equal to the mean and median of the other list ( four combinations choice of mean or median and choice of less than or less than or equal to. )

Here are your random numbers:

0.8349
0.3538
0.8425
0.2781
0.5241 

Timestamp: 2022-04-11 00:42:01 UTC

List A (sample A in order from least to greatest)

0.2781

0.3538

0.5241

0.8349

0.8425

Sample B before adding 0.1

Here are your random numbers:

0.1081
0.3479
0.4587
0.7225
0.3923

Timestamp: 2022-04-11 00:46:43 UTC

0.1081

0.3479

0.3923

0.4587

0.7225

List B ( sample B in order after 0.1 is added)

0.2081

0.4479

0.4923

0.5587

0.8225

Start of example for "Percentage of greater values between two distributions" test

Value B, Value A, points ( 1 if A<B, 0.5 if A=B, 0 if A>B)

0.2081, 0.2781, 0

0.2081, 0.3538, 0

0.2081, 0.5241, 0

0.2081, 0.8349, 0

0.2081, 0.8425, 0

0.4479, 0.2781, 1

0.4479, 0.3538, 1

0.4479, 0.5241, 0

0.4479, 0.8349, 0

0.4479, 0.8425, 0

0.4923, 0.2781, 1

0.4923, 0.3538, 1

0.4923, 0.5241, 0

0.4923, 0.8349, 0

0.4923, 0.8425, 0

0.5587, 0.2781, 1

0.5587, 0.3538, 1

0.5587, 0.5241, 1

0.5587, 0.8349, 0

0.5587, 0.8425, 0

0.8225, 0.2781, 1

0.8225, 0.3538, 1

0.8225, 0.5241, 1

0.8225, 0.8349, 0

0.8225, 0.8425, 0

Total points 10

Sample Size A * Sample Size B = 5 * 5 = 25

Total Points / Sample Size = 10 / 25

estimated 40% of random value from population B being greater than value from population A

one tailed P value = 1 - 0.40 = 0.60 used for comparing with one tailed t test if population B > A

100% - 40% = 60% 

estimated 60% of random value from population A being greater than value from population B

one tailed P value = 1 - 0.60 = 0.40 used for comparing with one tailed t test if population A > B

Value A, Value B, points ( 1 if B<A, 0.5 if B=A, 0 if B>A)

0.2781, 0.2081, 1

0.2781, 0.4479, 0

0.2781, 0.4923, 0

0.2781, 0.5587, 0

0.2781, 0.8225, 0

0.3538, 0.2081, 1

0.3538, 0.4479, 0

0.3538, 0.4923, 0

0.3538, 0.5587, 0

0.3538, 0.8225, 0

0.5241, 0.2081, 1

0.5241, 0.4479, 1

0.5241, 0.4923, 1

0.5241, 0.5587, 0

0.5241, 0.8225, 0

0.8349, 0.2081, 1

0.8349, 0.4479, 1

0.8349, 0.4923, 1

0.8349, 0.5587, 1

0.8349, 0.8225, 1

0.8425, 0.2081, 1

0.8425, 0.4479, 1

0.8425, 0.4923, 1

0.8425, 0.5587, 1

0.8425, 0.8225, 1

Total points 15

Sample Size A * Sample Size B = 5 * 5 = 25

Total Points / Sample Size = 15 / 25

estimated 60% of random value from population A being greater than value from population B

one tailed P value = 1 - 0.60 = 0.40 used for comparing with one tailed t test if population A > B

100% - 60% = 40% 

estimated 40% of random value from population B being greater than value from population A

one tailed P value = 1 - 0.40 = 0.60 used for comparing with one tailed t test if population B > A

End of test example for "Percentage of greater values between two distributions" test

Comparing with t - test

One tailed t-test to determine if population A > B

https://www.socscistatistics.com/tests/studentttest/default2.aspx

p-value is .351604

Comparing with percent of values above and below mean and median of data from other list

Percent of values in one list that are less than or greater than mean or median of values from other list

List B ( sample B in order after 0.1 is added)

0.2081

0.4479

0.4923

0.5587

0.8225

median = 0.4923

mean = 0.5059

list of values from sample A that are less than mean of sample B ( 0.2781, 0.3538 )

list of values from sample A that are greater than mean of sample B ( 0.5241, 0.8349, 0.8425 )

no values from sample A that are equal to the mean of sample B

list of values from sample A that are less than median of sample B ( 0.2781, 0.3538 )

list of values from sample A that are greater than median of sample B ( 0.5241, 0.8349, 0.8425 )

no values from sample A that are equal to the median of sample B

60% of values from A are greater than or equal to the mean of B

60% of values from A are greater than the mean of B

60% of values from A are greater than or equal to the median of B

60% of values from A are greater than the median of B

https://www.calculatorsoup.com/calculators/statistics/average.php

https://web.archive.org/web/20220324192741/https://www.calculatorsoup.com/calculators/statistics/average.php

List A (sample A in order from least to greatest)

0.2781

0.3538

0.5241

0.8349

0.8425

median = 0.5241

mean = 0.56668

list of values from sample B that are less than mean of sample A ( 0.2081, 0.4479, 0.4923, 0.5587 )

list of values from sample B that are greater than mean of sample A ( 0.8225 )

no values from sample B that are equal to the mean of sample A

list of values from sample B that are less than median of sample A ( 0.2081, 0.4479, 0.4923 )

list of values from sample B that are greater than median of sample A ( 0.5587, 0.8225 )

no values from sample B that are equal to the median of sample A

20% of values from B are greater than or equal to the mean of A

20% of values from B are greater than the mean of A

40% of values from B are greater than or equal to the median of A

40% of values from B are greater than the median of A

Start of example for "Percentage of greater values between two distributions" test

Sample E

0.1081

0.3479

0.4587

0.7225

0.3923

List E

0.1081

0.3479

0.3923

0.4587

0.7225

Calculating scores for list E

Value B, Value A, points ( 1 if A<B, 0.5 if A=B, 0 if A>B)

0.1081, 0.2781, 0

0.1081, 0.3538, 0

0.1081, 0.5241, 0

0.1081, 0.8349, 0

0.1081, 0.8425, 0

0.3479, 0.2781, 1

0.3479, 0.3538, 0

0.3479, 0.5241, 0

0.3479, 0.8349, 0

0.3479, 0.8425, 0

0.3923, 0.2781, 1

0.3923, 0.3538, 1

0.3923, 0.5241, 0

0.3923, 0.8349, 0

0.3923, 0.8425, 0

0.4587, 0.2781, 1

0.4587, 0.3538, 1

0.4587, 0.5241, 0

0.4587, 0.8349, 0

0.4587, 0.8425, 0

0.7225, 0.2781, 1

0.7225, 0.3538, 1

0.7225, 0.5241, 1

0.7225, 0.8349, 0

0.7225, 0.8425, 0

Total points 8

Sample Size E * Sample Size B = 5 * 5 = 25

Total Points / Sample Size = 8 / 25

estimated 32% of random value from population E being greater than value from population A

one tailed P value = 1 - 0.32 = 0.68 used for comparing with one tailed t test if population E > A

100% - 32% = 68% 

estimated 68% of random value from population A being greater than value from population E

one tailed P value = 1 - 0.68 = 0.32 used for comparing with one tailed t test if population A > E

End of example for "Percentage of greater values between two distributions" test

Comparing with other tests

one tailed t-test for mean of population A > mean of population E

P value = 0.163344

https://www.socscistatistics.com/tests/studentttest/default2.aspx

Copyright Carl Janssen 2022 April 10

Custom Distribution Statistical Hypothesis Test

This might not be mathematically accurate in terms of probability theory I am experimenting with the results of doing different things with numbers.  These assumptions I am using do contradict with reality as do all probability based statistical hypothesis tests but possibly in different ways than some others.

I am literally making up this statistical test and calling it the custom distribution statistical hypothesis test.  I do not know if someone already made a test like this before me and called it a different name

Goal :  The probability distribution model that best represents data collected from the population that corresponds to real life samples is not known before collecting the data therefore it is erroneous to assume it will be a normal distribution before analyzing the sample data.  I am trying to create a model that creates a custom model for frequency distribution to represent the population that corresponds to data collected from a sample then create a possibly new type of statistical test.  I will call this possibly new type of statistical test a, "custom distribution statistical hypothesis test."

A "custom distribution statistical hypothesis test" is similar to a replacement for two sample independent unpaired t tests only with the assumption of a "custom distribution" instead of a normal distribution.

This statistics test includes determining the probability that the median of one sample of  data would be at least the distance it is measured to be in a specific direction from the median of another sample of data based on using the "custom frequency distribution" to represent the population of the sample from the other set of data.  This is done twice once for each sample of data compared to the other one.

By similar I do not mean the mathematical definition of the word similar.  The shape of the "custom frequency distribution" is empirically determined in a custom manner for each sample of data simply by using a cumulative frequency table plus certain additional assumptions and it is assumed that the population has a similar shape to the "custom frequency distribution" determined by a table except that it is modeled as continuous instead of discrete.  

The shape of the normal distribution used in t tests however is not determined empirically by the actual sample data but presumed to represent something "close enough" to the true shape of the population's probability distribution from which a sample is collected when running a t test.  Although the standard deviation or variance and mean of a normal distribution used for a t test is determined empirically the shape is not.  For example the shape of a set of data could appear to be uniform (or any other shape than a normal distribution) based on someone rational looking at a empirical probability plot or empirical probability table for a set of data but would still be treated as a normal distribution shape for a t test.

This test should work with ordinal, interval or ratio data when there is a odd sample size for both samples.  When there is a even sample size for one or both samples one can use a mean to get the median for interval or ratio data but the test results should be less trustworthy than with a odd sample size.  When there is a even sample size for one or both samples and the data is ordinal it does not work to use a mean to estimate the median unless you are taking the mean of two identical values.  However, it might be possible in the case of an even number sample size to create a fictitious rank in between the two values that are closest to where the median would be that you would normally take the mean of to get the median with interval or ratio data and use that fictitious rank in place of the median.  For example if the median would be between "10th street" and "11th street" you could create a fictitious rank of "the street that is less than 11th street but greater than 10th street" or if the median was between "3rd degree" and "4th degree" you could create a fictitious rank of "the degree that is more than 3rd degree but less than 4th degree" but you should not use 14th street as a replacement for the median that is in between 12th street and 16th street because there might be a real 14th street that is not located at the mean of the coordinates or positions of 12th and 16th street and you should not use 7th degree to represent a median that is in between 5th degree and 9th degree because 7th degree might be a real rank that is not the same as the mean of 5th degree and 9th degree.

Comparing the medians of two different samples with the probability distributions of the other sample to estimate the probability that the median of one population is greater than the median of the other population.

Assumption 1 :  The sample which is expected to have a greater median is named sample B and the one expected to have a lower median is named sample A.

Assumption 2 : If two values collected from a sample have no collected values taken from a sample found between them then the probability of obtaining or being above a third value that is in between them when collecting a sample with a sample size of one from that population shall be inclusively between the probability of obtaining or being above each of the two values that were collected from the sample.

Assumption 3 : If two values collected from a sample have no collected values taken from a sample found between them then the probability of obtaining or being below a third value that is in between them when collecting a sample with a sample size of one from that population shall be inclusively between the probability of obtaining or being below each of the two values that were collected from the sample.

How I am defining "inclusively between"

2 <= X <= 3 in this example X is inclusively between 2 and 3

2 < X < 3  in this example X is exclusively between 2 and 3

Assumption 4 : The median of a population shall be estimated to be the median of the sample taken from that population.  Sample A is a sample taken from population A and sample B is a sample taken from population B.

Assumption 5 : If both the median of sample A is lower than the median for the population estimated from sample B and the median of sample B is higher than the median for the population estimated from sample A, both for the same alpha level, then the median of population B is higher than the median of population A for that alpha level.  If exactly one of those two conditions are met but not both then it is unclear if the median of population A is lower than the median of population B for that alpha level.  If neither of those conditions are met then the median of population A is not lower than the median of population B for that alpha level.

Null Hypothesis 1 : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis 2 : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

Null Hypothesis 3 : Median of population B <= Median of population A

Alternative Hypothesis 3 : Median of population B > Median of population A

If Null Hypotheses 1 and 2 are both rejected then null hypothesis 3 is rejected.  If exactly one of Null Hypotheses 1 and 2 are rejected but not both of them then it is unclear if Null Hypothesis 3 is rejected or not.  If Null Hypothesis 1 and 2 both fail to be rejected then then Null Hypothesis 3 fails to be rejected.

Assumption 6 : The P value of rejecting Null Hypothesis 1 shall be one minus the cumulative frequency distribution as calculated from left to right of achieving the median of Sample B on the probability distribution table for Sample A.  In the case where no value from sample A exists with the same value as the median of Sample B this shall be estimated by using the closest value above and the closest value below the median of sample B from the probability distribution table on sample A as explained in assumption 2.  In the case where a value exists on sample A which is the same as the median of sample B the cumulative frequency distribution for the value already on the chart of the cumulative frequency distribution for  sample A shall be used with the frequency greater than or equal the value instead of the greater than only option

Assumption 7 : The P value of rejecting Null Hypothesis 2 shall be one minus the cumulative frequency distribution as calculated from right to left of achieving the median of Sample A on the probability distribution table for Sample B.  In the case where no value from sample B exists with the same value as the median of Sample A this shall be estimated by using the closest value above and the closest value below the median of sample B from the probability distribution table on sample B as explained in assumption 3.  In the case where a value exists on sample B which is the same as the median of sample A the cumulative frequency distribution for the value already on the chart of the cumulative frequency distribution for  sample B shall be used with the frequency less than or equal to the value instead of the less than only option

Examples 1-4

Comparing results between t tests and custom distribution statistical hypothesis tests for uniform distributions in which both samples have equal variance and independent unpaired samples are used

Example 1

sample A = (1, 2, 3, 4, 5)

sample B = (2.5, 3.5, 4.5, 5.5, 6.5)

custom distribution statistical hypothesis test

sample A = (1, 2, 3, 4, 5), median = 3

value, frequency=value, frequency <= value, frequency < value

0.5, 0, 0, 0, 0

1, 1/5, 1/5, 0

1.5, 0, 1/5, 1/5

2, 1/5, 2/5, 1/5

2.5, 0, 2/5, 2/5

3, 1/5, 3/5, 2/5

3.5, 0, 3/5, 3/5

4, 1/5, 4/5, 3/5

median of sample B 4.5, 0, 4/5, 4/5

5, 1/5, 1, 4/5

5.5, 0, 1, 1 

1-1  <= P <= 1 - 4/5

0 <= P <= 0.2 for the median of sample B being higher than the estimated median of population A  

sample B = (2.5, 3.5, 4.5, 5.5, 6.5) median = 4.5

value, frequency=value, frequency => value, frequency > value

7, 0, 0, 0

6.5, 1/5, 1/5, 0

6, 0, 1/5, 1/5

5.5, 1/5, 2/5, 1/5

5, 0, 2/5, 2/5

4.5, 1/5, 3/5, 2/5

4, 0, 3/5, 3/5

3.5, 1/5, 4/5, 3/5

median of sample A 3, 0, 4/5, 4/5

2.5, 1/5, 1, 4/5

2, 0, 1, 1

1-1  <= P <= 1 - 4/5

0 <= P <= 0.2 for the median of sample A being lower than the estimated median of population B

for alpha > P reject the null hypothesis

for alpha < P fail to reject the null hypothesis

for one tailed alpha > 0.2 the median of sample A can be considered lower than the median of population B

and

for one tailed alpha > 0.2 the median of sample B can be considered higher than the median of population A

therefore

for one tailed alpha > 0.2 the median of population B can be considered greater than the median of population A

0 < one tailed alpha < 0.2 the median of sample A can not be considered conclusively if it is lower than the median of population B

and

0 < one tailed alpha < 0.2 the median of sample B can not be considered conclusively if it is higher than the median of population A

therefore

0 < one tailed alpha < 0.2 the median of population B can not be considered conclusively if it is greater than the median of population A

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

sample A = (1, 2, 3, 4, 5), mean = 3, n = 5

sample variance = [ ( 5 -3 ) ^ 2 + ( 4-3 ) ^ 2 + ( 3 - 3) ^2 + ( 2 - 3 ) ^2 + (1-3) ^2 ] / ( 5 - 1 )

sample variance = ( 4 + 1 + 1 + 4 ) / 4 = 10 /4 = 2.5

sample std = sample variance ^ 0.5 = 2.5 ^ 0.5 = approx 1.58113883008

sample B = (2.5, 3.5, 4.5, 5.5, 6.5), mean = 4.5, n = 5

sample v =[ ( 6.5 -4.5 ) ^ 2 + ( 5.5-4.5 ) ^ 2 + ( 4.5 - 4.5) ^2 + ( 3.5 - 4.5 ) ^2 + (2.5-4.5) ^2 ] / ( 5 - 1 )

sample variance = ( 4 + 1 + 1 + 4 ) / 4 = 10 /4 = 2.5

sample std = sample variance ^ 0.5 = 2.5 ^ 0.5 = ( 5 / 2 ) ^ 0.5

mean sample B - mean sample A = 4.5 - 3 = 1.5

in this case Sp = sample std A = sample std B because the sample sizes and variance are exactly equal

t = ( mean sample B - mean sample A ) / ( Sp *[ (1/na) +(1/nB) ] ^ 0.5 )

1/na + 1/nB = 1/5 + 1/5 = 2/5

t = 1.5 / [ (5/2) ^ 0.5 * (2/5) ^ 0.5 ] = 1.5

degrees of freedom = df = nA + nB -2 = 5 + 5 -2 = 8

one tailed p value = .086002

https://www.socscistatistics.com/pvalues/tdistribution.aspx

one tailed p value = 0.08600

https://www.statology.org/t-score-p-value-calculator/

for one tailed alpha > 0.086 the mean of population B can be considered greater than the mean of population A

for one tailed alpha < 0.086 the mean of population B can not be considered greater than the mean of population A

Example 2

sample A = (1, 2, 3, 4, 5)

sample B = (2, 3, 4, 5, 6)

sample A = (1, 2, 3, 4, 5), median = 3

value, frequency=value, frequency <= value, frequency < value

1, 1/5, 1/5, 0

2, 1/5, 2/5, 1/5

3, 1/5, 3/5, 2/5

3.5, 0, 3/5, 3/5

4, 1/5, 4/5, 3/5

median of sample B 4, 1/5, 4/5, 3/5

4.5, 0, 4/5, 4/5

5, 1/5, 1, 4/5

5.5, 0, 1, 1

P = 1 - 4/5

P = 0.2 for the median of sample B to be greater than than estimated median of population A

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean Population B

Alternative Hypothesis : mean of Population B > mean of Population A

t = 1

one tailed P = 0.173297

https://www.socscistatistics.com/tests/studentttest/default2.aspx

one tailed P = 0.17330

https://www.statology.org/t-score-p-value-calculator/

Example 3

sample A = (1, 2, 3, 4, 5, 6)

sample B = (2.5, 3.5, 4.5, 5.5, 6.5, 7.5)

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

Example 4

sample A = (1, 2, 3, 4, 5, 6) 

sample B = (2, 3, 4, 5, 6, 7) 

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

Example 5

Comparing custom distribution statistical hypothesis test with unpaired independent t test for the following triangular shaped distributions

sample A = ( 1, 2, 2, 3, 3, 3, 4, 4, 5 )

sample B = ( 2, 3, 3, 4, 4, 4, 5, 5, 6 )

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

Example 6 

custom distribution statistical hypothesis test with unequal sample sizes

sample A = ( 1, 2, 3, 4, 5, 6, 7, 8)

sample B = ( 3, 4, 5, 6, 7 )

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

Copyright Carl Janssen 2022

https://en.m.wikipedia.org/wiki/Student%27s_t-test

http://web.archive.org/web/20220307082135/https://en.m.wikipedia.org/wiki/Student's_t-test

https://duckduckgo.com/?q=independent+t+test+equal+variance+and+equal+sample+size&ia=web

https://www.real-statistics.com/students-t-distribution/two-sample-t-test-equal-variances/

http://web.archive.org/web/20200804112708/https://www.real-statistics.com/students-t-distribution/two-sample-t-test-equal-variances/

https://duckduckgo.com/?q=unpaired+t+test+equal+variance+and+equal+sample+size&ia=web

https://tungmphung.com/unpaired-two-sample-t-test-independent-t-test/

http://web.archive.org/web/20210423122739/https://tungmphung.com/unpaired-two-sample-t-test-independent-t-test/

https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-sample/a/population-and-sample-standard-deviation-review

http://web.archive.org/web/20220323223702/https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-sample/a/population-and-sample-standard-deviation-review

https://duckduckgo.com/?q=standard+deviation+sample+vs+population+formula&ia=web

https://www.statology.org/population-vs-sample-standard-deviation/

http://web.archive.org/web/20210824024007/https://www.statology.org/population-vs-sample-standard-deviation/

https://duckduckgo.com/?q=test+statistic+and+critical+value+calculator&ia=web

https://duckduckgo.com/?q=p-value+and+alpha&ia=web

https://duckduckgo.com/?q=+hypothesis+one+tail+t+test+example&ia=web

https://duckduckgo.com/?q=t+test+percentile&ia=web

https://duckduckgo.com/?q=t+test+p+value+calculator&ia=web

https://www.socscistatistics.com/pvalues/tdistribution.aspx

https://web.archive.org/web/20211011165105/https://www.socscistatistics.com/pvalues/tdistribution.aspx

https://www.socscistatistics.com/tests/studentttest/default2.aspx

https://web.archive.org/web/20211011072830/https://www.socscistatistics.com/tests/studentttest/default2.aspx

https://duckduckgo.com/?q=p+value+t+test+chart&ia=web

https://www.statology.org/how-to-calculate-a-p-value-from-a-t-test-by-hand/

https://web.archive.org/web/20211123175421/https://www.statology.org/how-to-calculate-a-p-value-from-a-t-test-by-hand/

https://www.statology.org/t-score-p-value-calculator/

https://web.archive.org/web/20210306170506/https://www.statology.org/t-score-p-value-calculator/

fat runner paradox test for special relativity

There is no acceleration the racer starts running before reaching the startline but both the racer and referee start their stopwatch at zero the exact moment the midpoint or center of the racers body crosses the startline and stop the stopwatch the moment the midpoint of the racers body crosses the finish line.  The runner does not stop running when he crosses the finish line but maintains the same speed unless blocked by a wall eliminating the issue of acceleration from the calculations.  The midpoint is measured in the direction the racer is running.  

There shall be one more line called a "percentage line."   The ( Y * 100 ) percent completion line marked whatever percent between the start line and the finish line one wants to know that fraction or percentage of the race has been complete.  Where if Y = 0 the line would be at the start line, if Y = 0.5 the line would be half way between the start line and the finish line marking 50% completion when crossed and if Y = 1 the line will be at the finish line.

There is an observer who is stationary relative to the startline, finish line, racing track and wall who measures the following 

all the following measurements are in one dimension going in the same direction and it's opposite

H is used to represent speed as a fraction times the speed of light

H and Y are unitless

0 < H < 1

0 <= Y <= 1

L, W and D are used to represent thr distances described below in units of the speed of light * time such as light years or light seconds

L, W and D have units of time

L > 0

W > 0

D > 0

If the racer stood still relative to the referee his body would have a length of 2D*c in the direction he is running, or the front of the runner's body is a distance D*c in front of his midpoint

The distance from the startline to the stopline is L*c

The distance from the finish to a wall is W*c

The racer is running at a velocity of H*c

The distance from the startline to the percentage line is Y*L*c

Is there any combination of these variables such that the runner will hit the wall at the exact moment in time when his midpoint touches the stopline from the point of view of the referee but not from the point of view of the runner or will hit the wall from the point of view of the runner but not from the point of view of the referee?

The distance L*c is not necessary to answer that question but prior to answering that question for the sake of practice the running time and running distance from start to finish from the point of view of both the runner and referee will be calculated and it will be confirmed that the speed of the wall moving toward the runner from the runners point of view is the same as the speed of the runner moving toward the wall from the referee's point of view

Even though both are observer's the referee shall be remembered by a lowercase o as in observer which can be a different symbol than the number 0 zero

The runner shall be remembered by j as in jogger because runner and referee both start with r even though running is usually considered faster than jogging

Tof= time to reach the finish line according to referee's stopwatch

Toy= time to reach the percentage line according to referee's stopwatch

Tjf= time to reach the finish line according to the runner's stopwatch

Tjy= time to reach the percentage line according to the runner's stopwatch

Sof = Distance from startline to finish line from referee's viewpoint, this is a proper or rest length

Soy = Distance from startline to percentage line from referee's viewpoint, this is a proper or rest length

Sjf = Distance from startline to start finish line from runner's viewpoint, this is not a proper nor rest length

Sjy = Distance from startline to percentage line from runner's viewpoint, this is not a proper nor rest length

Fow = Length from finish line to wall from referee's viewpoint, this is a proper or rest length

Fjw = Length from finish line to wall from runner's viewpoint, this is not a proper nor rest length

Do = Length from midpoint to front of runner's body from referee's viewpoint, this is not a proper nor rest length

Dj = Length from midpoint to front of runner's body from runner's viewpoint, this is a proper or rest length

From the point of view of the referee and according to the referee's stopwatch

The runners body would appear thinner being shorter in it's direction of movement because it is moving toward the referee

The running track would not have it's length distorted because it is stationary relative to the referee

Sof = L*c

Tof = Sof / ( H*c ) = L*c / ( H*c ) = L / H

Soy = Y*L*c

Toy = Soy / ( H*c ) = Y*L*c / (H*c) = Y * L / H

Dj = D * c

Do = Dj * (1 - [ ( H*c ) ^ 2 ] / c^2 ) ^ 0.5

Do = D * c * ( 1 - H ^ 2 ) ^ 0.5

Fow = W * c

From the point of view of the runner and according to the runners stopwatch

The runner would be stationary and the wall would be moving toward the runner and the running track, startline and finish line would be moving in the same direction as the wall

The runners body would not appear thinner because the runner is stationary relative to himself

The running track would appear shorter because it would be moving relative to the runner

Sjf = Sof * ( 1 - H ^ 2 ) ^ 0.5

Sjf = L*c * ( 1 - H ^ 2 ) ^ 0.5

Tjf = Sjf / H

Tjf = [ L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Sjy = Soy * ( 1 - H ^ 2 ) ^ 0.5

Sjy = Y*L*c * ( 1 - H ^ 2 ) ^ 0.5

Tjy = Sjy / H

Tjy = [ Y*L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Dj = W * c

Fjw = Fow * ( 1 - H ^ 2 ) ^ 0.5

Fjw = W * c * ( 1 - H ^ 2 ) ^ 0.5

Proof that special relativity can not change order of events when there is no acceleration

Percent of time complete = 100% * Tjy / TjF = 100% * Toy / Tof

Toy / Tof = ( Y * L / H ) / ( L / H ) 

Toy / Tof = Y

Tjy / Tjf =  ( [ Y*L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H ) /  ( [ L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H ) 

Tjy / Tjf = Y

The percentage of time completed is the same as the percentage of the distance completed on the race track from the point of view of both the referee and the runner.  

A% will never be completed before B% for both the referee and the runner when A is less than B

B% will never be completed before A% for both the referee and the runner when B is less than A

This proves that the order of events never changes in special relativity without acceleration, the time that the same event occurs would sometimes be different for both the referee and the runner but the order that events occur in does not change.  The order of events is the same for both the referee and the runner.

Example to help understand the proof

For both the referee and the runner these 11 events happen in the same order

First 0% completion Y = 0

Toy = 0

Tjy = 0

Second 10% completion Y = 0.1

Toy = 0.1 * L / H 

Tjy = [ 0.1 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Third 20% completion Y = 0.2

Toy = 0.2 * L / H 

Tjy = [ 0.2 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Fourth 30% completion Y = 0.3

Toy = 0.3 * L / H 

Tjy = [ 0.3 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Fifth 40% completion Y = 0.4

Toy = 0.4 * L / H 

Tjy = [ 0.4 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Sixth 50% completion Y = 0.5

Toy = 0.5 * L / H 

Tjy = [ 0.5 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Seventh 60% completion Y = 0.6

Toy = 0.6 * L / H 

Tjy = [ 0.6 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Eighth 70% completion Y = 0.7

Toy = 0.7 * L / H 

Tjy = [ 0.7 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Ninth 80% completion Y = 0.8

Toy = 0.8 * L / H 

Tjy = [ 0.8 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Tenth 90% completion Y = 0.9

Toy = 0.9 * L / H 

Tjy = [ 0.9 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Eleventh 100% completion Y = 1

Toy = L / H 

Tjy = [ L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H

Disproof of special relativity

Proof of contradiction with reality inherant in special relativity

If someone can hit the wall when their midpoint crosses the finish line from the point of view of one observer but not hit the wall when the midpoint crosses the finish line from the point of view of the other observer then special relativity can not be a true representation of reality and no excuses about diffetent orders of events from different reference frames can justify the theory of special relativity because it has already been proven above that the order of events is the same in all reference frames in cases such as this one where no acceleration is occuring

If Dj = Fjw but Do does not equal Fow for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality

or

If Do = Fow but Dj does not equal  Fjw for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality

or

If Do < Fow and simultaneously Dj > Fjw for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality

or

If Do > Fow and simultaneously Dj < Fjw for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality

Example of disproof

In the case where the proper distance between the front of the runner's body and the center of the runner's body when the runner is at rest is equal to the proper distance from the finish line to the wall when the wall is at rest

If Dj = Fow 

then

Do = Dj * ( 1 - H ^ 2 ) ^ 0.5

Do = Fow * ( 1 - H ^ 2 ) ^ 0.5 < Fow

Do < Fow      

meaning collision with wall does not occur from referee's viewpoint

Fjw = Fow * ( 1 - H ^ 2 ) ^ 0.5

Dj = Fow > Fow * ( 1 - H ^ 2 ) ^ 0.5 = Fjw

Dj > Fjw

meaning collision with wall does occur from runner's viewpoint

Copyright Carl Janssen 2022

https://wikimedia.org/api/rest_v1/media/math/render/svg/37ae2718b3d30ba8c8f9019bedde2e289f1f3b28

http://web.archive.org/web/20220312022749/https://wikimedia.org/api/rest_v1/media/math/render/svg/37ae2718b3d30ba8c8f9019bedde2e289f1f3b28

https://en.m.wikipedia.org/wiki/Length_contraction

http://web.archive.org/web/20211130084048/https://en.m.wikipedia.org/wiki/Length_contraction

The proper length[1] or rest length[2] of an object is the length of the object measured by an observer which is at rest relative to it, by applying standard measuring rods on the object. 

https://en.m.wikipedia.org/wiki/Proper_length

http://web.archive.org/web/20211126104939/https://en.m.wikipedia.org/wiki/Proper_length

Stars Red shift can be from a medium instead of a movement

1 The intensity of light should be inversely proportional to the distance between the source and the observer before considering how much intensity is lost by traveling through a medium

2 The intensity of light is lost as it travels through a medium by a different amount for each frequency or wavelength

3 The farther a light source is from an observer the more mass it will need to have as a source if made of the same material at the same temperature and density in order to have sufficient intensity of brightness to be seen by the observer and the more mass the light source has the greater gravitational red shift will occur and the greater the gravitational red shift that occurs the less energy per area per time the observer will experience from the light emitted by the source.  Light from some sources might not experience a red shift but the percent of those light sources that do not have enough mass to be visible would increase as their distance from the earth increases.  As the distance increases the minimum mass required and thus the minimal amount of red shift required for a stationary light source (of the same material, temperature, pressure and density) to be seen increases.  This is  assuming that gravitational red shifting and blue shifting really does occur in real life.

4 From a probabilistic viewpoint, the further the distance between the source and the observer the more likely at least one opaque object of a given size or greater will be between the source and the observer.  This might be similar to the relationship of the number of cracks on a section of road and the length of the segment of a road or the Poisson distribution.

Points 1 through 4 could account for red shifts from distant stars and a lack of unlimitted or infinite brightness experienced on earth by an individual in a universe that might be of unlimited or infinite volume and might have never experienced a big bang and in which some stars that were thought to be moving away from an observer due to a doppler shift might not be moving away from the observer in all cases that big bang believers have claimed them to be doing so.

Alleged shifts in light spectrums may occur from light sources that are stationary relative to the earth as the light from a stationary source traveles through the medium of outer space not necessarily through a doppler effect caused by a light source moving away from or towards the earth.

The intensity of light at one frequency or wavelength may be decreased by a different percent than the intensity at another frequency or wavelength for the same medium at the same thickness

Outer space is supposedly an imperfect vacuum which would mean it is a physical material.  If the physical material outer space is made out of reduces the intensity of blue light more strongly than it reduces the intensity of red light or absorbs blue light better than red light traveling through the same distance or thickness of material at the same temperature, pressure, chemical concentration and density then the further the distance between a stationary light source and an observer the more red shifted the light would appear to be to that observer.

By red shift in the context of the effects of light traveling through a medium, I mean a shift in the frequency and wavelength distributions of the light.  In this specific type of red shift the weighted average of frequency with respect to intensity would decrease and the weighted average of wavelength with respect to intensity would increase as the distance the light has to travel from the source through the medium to reach the observer increases.  A blue shift in this context would mean the weighted average of frequency with respect to intensity would increase and the weighted average of wavelength with respect to intensity would decrease.  The frequency of the individual photons would not change as the distance traveled through the same medium increases but the intensity would change for a given frequency as the distance traveled through the same medium increases.  The percent decrease in intensity would be different for blue light than red light since the medium the light is traveling through blocks or absorbs one wavelength or frequency a different amount than it does with another wavelength or frequency.  I mention traveling a further distance through the same medium because changing what medium a wave is in can also change it's wavelength intensity distribution and or frequency intensity distribution but that is not the source of the red shift I am talking about.  

One should also consider that if the path of a light source orbited around a observer in a perfect circular path at constant absolute value of acceleration and absolute value of velocity and maintained a constant distance from that observer what sort of doppler effect ( if any ) would happen even though the  light source is neither moving towards or away from the observer in terms of the absolute value of the distance between the source and the observer

Supposedly gravitation could also cause a shift in frequency that is separate from or in addition to the one allegedly caused by velocity.  The farther a star is from earth the more massive the star would usually have to be to be seen from earth because the intensity of light is inversely proportional to the square of the distance between the observer and the light source before intensity lost due to traveling through a medium is even considered.  This means a greater gravitational red shift would usually be experienced the farther the distance from the earth a star is observed from even if it was not moving away from the earth.

In the case of gravitational red shift I believe the claim would be that each photon actually individually increases it's wavelength and or decreases it's frequency.  It is possible for a wave to change it's frequency without changing it's wavelength or change it's wavelength without changing it's ftequency if the velocity or speed of the wave changes which can happen if it changes it's medium or if the medium changes some factor like temperature.

A universe of infinite or unlimited volume with an unlimited number of stars would not necessarily be unlimitedly or infinitely bright as viewed from the earth because objects between some of the stars and the earth would be opaque or partly opaque and block some of the light from other stars or objects in addition to light becoming more dim before it reaches or fails to reach earth through the inverse square law and the effect of traveling through a medium as well as allegedly shifting in frequency and or wavelength and reducing in energy per photon through gravitational red shifting it experiences on the way to earth from some objects near it's path exceeding any gravitational blue shifting it experiences on the way to earth from other objects.

Someone might argue that although I listed three different sources of red shifts ( something similar to Beer-Lambert Law, Doppler, Gravitation) we can still know the universe is expanding because each source of red shift effects things in a mathematically different way and we can know which one of each type contributes to how much of each and from there calculate the doppler shift and know how fast each of the stars are moving away from the earth based on the frequency distribution a star should emit based on it's chemical composition.  The problem with that is we do not know the chemical composition of stars.  Supposedly every element we have tested on earth emits a unique distribution of light frequencies or wavelengths and the distribution emitted by a star is the same as the distribution emitted by the elements or perhaps chemical compounds that make it up only shifted in a precise way such that there is only one possible combination of elements or compounds that could have emitted that light frequency or wavelength distribution with not a single one to possibly be added or removed from the list mathematically determinable for that star.  That however is simply untrue because we can only compare the distributions with distributions for materials found on earth and we have never flew a rocket to the sun and collected a sample of the matetial to know it is not made from something different, perhaps an undiscovered element that does not even fit on the periodic table with it's integer atomic numbers the way we currently understand it to work and maybe this element emits what looks like a shifted distribution of another element.  It sounds ridiculus but theoritical astronomers claim there is dark matter that is not like any material discovered on earth but somehow eliminates their massive calculation errors if you put the right amount of this dark matter in if I am being ridiculus for claiming the stars might be made of a material not discovered on earth then they are being ridiculus for claiming outer space has a material not discovered on earth that just so happens to exist in the quantities to reduce their calculation errors from the amount that disproves their theories to an amount that excuses their theories.  I am not saying the stars are made of a undiscovered or hypothetical material, I am saying they might be but to some people it is a definitive fact that 85% of the universe is made out of a hypothetical material.  Here on earth I have never known a construction worker to build a building out of a hypothetical matetial, they might build something out of a material they do not know the name of but it is not hypothetical they can actually touch it, unlike the sun which has never been touched by human hands if it is so hot you will burn up before you reach it as has been claimed and more importantly if it is so high in the sky I can not build a ladder or skyscraper or climb a mountain to reach it.  There is another problem than not knowing the material the stars are made out of and that is not knowing how much gravity they have which would mean not knowing how much of the red shift is from gravity vs how much is from doppler.  We can know how much acceleration is caused by local gravity on earth but we can not personally know how much acceleration is caused by local gravity on the moon unless we personally go to the moon which most people can not do and therefore can not personally confirm the moon data is not fake.  If the most people could go to the moon then most people could travel to the moon and take the acceleration measutements from there personally instead of going by the word of people who already have a track record of fabricating stories about dark matter.  We can not personally measure the Universal gravitational constant from the earth only the local gravitational constant because the universal gravitational constant is calculated by manipulating the position of objects in a physics laboratory and carefully measuring their masses but the person who takes the observation's mass and position is not measured but worse yet the mass and position of the walls, ceilings and floors of the building next to the objects is not measured.

We do not know

1 How much of the red shift is from gravity - because we do not know the universal gravitational constant - because they ignore the mass of the building but measure the mass of the equipment inside the building) - you can take a video camera and drop an object in front of a ruler with a stopwatch also running on video and record it and measure local acceleration due to gravity but that is different than proving a Universal Gravitational Constant even exists - And no you probably have not tested it on the moon if you are reading this

2 How much of the red shift is from traveling through a medium -  Because we do not know how outer space effects light over long distances involving something similar to the Beer-Lambert law - Because the common person can not fly up in a satelite and shoot several different types of monochromatic lasers through the medium outer space is made up of and take measurements.  Even if we could we have not taken those measurements to make sure outer space between the star and wherever the observers atmosphere becomes outer space is the same material

3 What the starting spectrum that the light frequency distribution was shifted from - Because we do not know what the spectrum of the star would have been based on it's material chemical composition - Since we do not know what material the stars are made out of since we can not assume they are made from chemicals that exist on earth because for all we know they could be 85% dark matter, why not 85% of everything else is except things we can observe on earth

4 Once we know those three things we do not know we can calculate the doppler shift of a star based on a extrapolation of other things that have never been tested in that data range  - If you do not believe in doppler you could set up a race track and take a video camera and could measure the location and time positions of the car and compare it with the doppler speed data for a wide variety of speeds less than 120 miles per hour that a commoner can afford a car to drive at but you can not drive your car at 3/4 the speed of light and take measurements.

 "The primary evidence for dark matter comes from calculations showing that many galaxies would behave quite differently if they did not contain a large amount of unseen matter"

That is not the primary evidence for dark matter that is the primary evidence of at least one of five things 

1 the "physics" assumptions that led to you doing those calculations are wrong

2 You made an expertimental error collecting the data

3 You made an error doing the calculations with the data you collected

4  It's not the theoritical astrophysisicts fault some other physicist calculated G wrong they just plugged the wrong number someone else calculated into the correct equations

Although a novice  would come to the instinctual conclusion that astronomers made a 85% error in how much mass is in the universe after further examination they would reslise it is only a negative 46 % error.  But a true expert would say there was no calculation error at all for the mass except we put in the wrong value for G which was clearly wrong because we ignored those massive walls every time we did a calculation to figure out G

We really need to multiply or perhaps divide what we thought G was by 3.4225 to get the true value of G.  Or perhaps G is another value altogether calculated a different way then how I suggested but it would not surprise me at all if G was pure fiction since g is measurable but no experiment to this day has used correct methodology to measure g that I know of taking into account the mass and position of the human being that looked into the equipment and the mass and position of any walls structures or buildings nearby.  Perhaps it could be measured out doors far away from massive buildings in a region where local g measurements are consistent at several locations near the test site to make sure there is not extra density mass in a section of the ground nearby and with no wind to shift the results.

1.85 * 1.85 = 3.4225

F = G*m1*m2 / (R^2)

3.4225*G*m1*m2  = 1.85*m1*1.85*m2

(G / 3.4225) * m1* m2= G* ( m1 / 1.85 ) * ( m2 / 1.85 )

It is theoritical that there is 85% more dark matter than expetimentally observed.

Traditional Percent Error formula based on assumption that the theory is correct and the experimental data is wrong

  experimental - theoritical / theoritical

Theoritical amount of mass in universe = 1.85 * Experimental

( E - 1.85E ) / 1.85 E= - 0.85 / 1.85 = - 0.459459459459

So I made up a theory and my observed data does not match my theory, I know reality is wrong not my theory the error is in the data not the theory

Keeping it real percent error based on that the experimental observations are correct and the theory that dark matter exists is wrong

theoritical - experimental / experimental

( 1.85E - E ) / E = 0.85

5 There was never any data and this is a practical joke and the common people can not ever look into one of these expensive telescopes to find out there never were any observations just fabricated observations used as an excuse to request tax funding for research and to brag about how smart you are but humbly still not educated enough until you get more money because there is a 85% unknown missing matter mystery that needs more funding.

Copyright Carl Janssen 2022

https://en.m.wikipedia.org/wiki/Beer%E2%80%93Lambert_law

http://web.archive.org/web/20220314215558/https://en.m.wikipedia.org/wiki/Beer%E2%80%93Lambert_law

https://en.m.wikipedia.org/wiki/Gravitational_redshift

http://web.archive.org/web/20211126104210/https://en.m.wikipedia.org/wiki/Gravitational_redshift

https://en.m.wikipedia.org/wiki/Inverse-square_law

http://web.archive.org/web/20220320133858/https://en.m.wikipedia.org/wiki/Inverse-square_law

https://en.m.wikipedia.org/wiki/Poisson_distribution

https://hubpages.com/@fatfist

http://web.archive.org/web/20220313060928/https://hubpages.com/@fatfist

https://discover.hubpages.com/education/OLBERS-PARADOX-A-Physical-Explanation-For-The-DARK-Night-Sky

http://web.archive.org/web/20210518201220/https://discover.hubpages.com/education/OLBERS-PARADOX-A-Physical-Explanation-For-The-DARK-Night-Sky

https://duckduckgo.com/?q=red+shift+not+caused+by+movement&ia=about

https://duckduckgo.com/?q=red+shift+beer+lambert&ia=web

The most absorbance is obtained when beam color is complementary to the color of solution.

https://colors-newyork.com/what-is-red-shift-what-does-it-indicate/

http://web.archive.org/web/20220323062447/https://colors-newyork.com/what-is-red-shift-what-does-it-indicate/

Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe

https://en.m.wikipedia.org/wiki/Dark_matter

http://web.archive.org/web/20220321143913/https://en.m.wikipedia.org/wiki/Dark_matter

 The primary evidence for dark matter comes from calculations showing that many galaxies would behave quite differently if they did not contain a large amount of unseen matter

http://web.archive.org/web/20220321143913/https://en.m.wikipedia.org/wiki/Dark_matter

14 out of 54 mentions of walls

That is to say, we now accept apples as having easily measurable and verifiable gravitational attractions, but we ignore the gravitational attractions of walls weighing thousands of pounds. 

http://milesmathis.com/caven.html

http://web.archive.org/web/20220130225907/http://milesmathis.com/caven.html

some scientists continue to work on models that might not require dark energy. Inhomogeneous cosmology falls into this class.

https://en.m.wikipedia.org/wiki/Inhomogeneous_cosmology

http://web.archive.org/web/20220322060158/https://en.m.wikipedia.org/wiki/Inhomogeneous_cosmology

https://en.m.wikipedia.org/wiki/Exotic_matter

http://web.archive.org/web/20220321143900/https://en.m.wikipedia.org/wiki/Exotic_matter

https://en.m.wikipedia.org/wiki/Exotic_atom

http://web.archive.org/web/20220319073945/https://en.m.wikipedia.org/wiki/Exotic_atom

Historical Origins Science is not real experimental science

 The only model consistent with science is an eternal universe not big bang or finite amount of time ago earth creation.  The assumption for the big bang is we can use input  data to extrapolate what happened in the past as an output and then put that output data in as a new input to figure out what happened even further in the past.  The only way to be consistent about it is to allow someone to extrapolate as far back in the past as they want, if you limit yourself to billions of years ago when the special event of the big bang occured instead of trillions or an unlimmitted amount of years big bangers are no better than the creationists who limit extrapolation to thousands of years in the past when the special event of creation occured or when the special event of a worldwide flood occured.  Both secular evolutionary big bang cosmology origin science and creationist origin science are not real experimental science.

Copyright Carl Janssen 2022 March 22

sine and cosine of sum of two angles

http://web.archive.org/web/20220314121223/https://upload.wikimedia.org/wikipedia/commons/thumb/f/f5/AngleAdditionDiagramSine.svg/338px-AngleAdditionDiagramSine.svg.png

http://web.archive.org/web/20201111211702/https://en.m.wikipedia.org/wiki/File:AngleAdditionDiagramSine.svg

http://web.archive.org/web/20150208110925/https://upload.wikimedia.org/wikipedia/commons/f/f5/AngleAdditionDiagramSine.svg

http://web.archive.org/web/20220319192920/https://en.m.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2013_November_24

http://web.archive.org/web/20220311205122/https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities

https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities

https://en.m.wikipedia.org/wiki/Small-angle_approximation#Angle_sum_and_difference

http://web.archive.org/web/20210827113612/https://en.m.wikipedia.org/wiki/Small-angle_approximation

https://en.m.wikipedia.org/wiki/Proofs_of_trigonometric_identities#Angle_sum_identities

http://web.archive.org/web/20210506193820/https://en.m.wikipedia.org/wiki/Proofs_of_trigonometric_identities

https://ccssmathanswers.com/trigonometrical-ratios-of-90-degree-minus-theta/

http://web.archive.org/web/20210411120031/https://ccssmathanswers.com/trigonometrical-ratios-of-90-degree-minus-theta/

https://imgflip.com/i/69a0vj

https://i.imgflip.com/69a0vj.jpg

http://web.archive.org/web/20220319200030/https://imgflip.com/i/69a0vj

http://web.archive.org/web/20220319200030im_/https://i.imgflip.com/69a0vj.jpg

Square Roots of Complex Numbers without trigonometry or exponential functions

 

M, N, D and E do not equal 0 

D and E are real numbers

i * i = - 1

- i * - i = - 1

D + E i = ( M + N i ) ^ 2 = M ^ 2 - N ^ 2 + 2 M N i

D = M ^ 2 - N ^ 2

E = 2 M N

N = E / 2 M

D = M ^ 2 - ( E / 2 M ) ^ 2

You should not multiply or divide both sides of an equation by a variable unless you exclude cases of division by zero but that has already been done in the preconditions already set

D M ^ 2 = M ^ 4 - ( E ^ 2 ) / 4

0 = 4 M ^ 4 - 4 D M ^ 2 - E ^ 2

if a x ^ 2 + b x + c = 0 then x = ( - b +- [ b ^ 2 - 4 a c ] ^ 0.5 ) / ( 2 a )

x = M ^ 2

a  = 4

b = - 4 D

c = - E ^ 2

M ^ 2 = ( 4 D +- [ ( - 4 D ) ^ 2 - 4 * 4 * (- E ^ 2) ] ^ 0.5 ) / ( 2 * 4 )

M ^ 2 = ( 4 D +- [ 16 D ^ 2 + 16 E ^ 2 ] ^ 0.5 ) / 8

M = + - [ ( 4 D +- [ 16 D ^ 2 + 16 E ^ 2 ] ^ 0.5 ) / 8 ] ^ 0.5

N = +- 0.5 E / [ ( 4 D +- [ 16 D ^ 2 + 16 E ^ 2 ] ^ 0.5 ) / 8 ] ^ 0.5

Although there are eight possible solutions for N and four possible solutions for M based on what sign is chosen based on the plus or minus signs, only certain combinations of M and N values work and there should theoritically be exactly two solutions for the square root of D + Ei and not all combinations of solutions for M and N will work so you should check your solutions

if M is a pure imaginary number then N will also be a pure imaginary number and this would not prevent a solution

if M is a real number then N will also be a real number

Example

D + E i = 1 +  i

M =  + - [ ( 4 * 1 +- [ 16 + 16 ] ^ 0.5 ) / 8 ] ^ 0.5

Real solutions for M and N

In this case when M is positive then N is positive and when M is negative then N is negative because both D and E are positive

https://duckduckgo.com/?q=(+(+4+*+1+%2B+(+16+%2B+16+)+%5E+0.5+)+%2F+8+)+%5E+0.5&ia=calculator

https://duckduckgo.com/?q=0.5+%2F+(+(+(+4+*+1+%2B+(+16+%2B+16+)+%5E+0.5+)+%2F+8+)+%5E+0.5+)&ia=calculator

M = approximately +- 1.09868411347

N = +- 0.5 / 1.09868411347 approximately

N = approximately +- 0.455089860562

M ^ 2 - N ^ 2 = 1.09868411347 ^ 2 - 0.455089860562 ^ 2 = 1.00000000001 = D = = 1 approximately

2MN = 2*1.09868411347*0.455089860562 = 1 = E approximately

https://duckduckgo.com/?q=2*1.09868411347*0.455089860562&ia=calculator

https://duckduckgo.com/?q=(+1.09868411347+%5E+2+)+-+(+0.455089860562+%5E+2+)&ia=calculator

Pure imaginary solutions for M and N

Flip Flopped Solutions for the absolute values of M and N compared to real solutions

These have the same absolute values as before except M and N are switched and M and N are pure imaginary numbers instead of real numbers.  Only two out of these four solutions work based on choosing the sign correctly.  I recommend simply solving for the real solutions for M and N because figuring out the proper sign may be easier for most people that way.

M = +- 0.455089860562 i

N = +- 1.09868411347 i

https://duckduckgo.com/?q=(+(+4+*+1+-+(+16+%2B+16+)+%5E+0.5+)+%2F+8+)+%5E+0.5&ia=calculator

https://duckduckgo.com/?q=0.5+%2F+(+(+(+4+*+1+-+(+16+%2B+16+)+%5E+0.5+)+%2F+8+)+%5E+0.5+)&ia=calculator

Copyright Carl Janssen 2022 March 18