principiascientificinternational--2020-03-13--‘MEDIA BIAS/FACT CHECK’ Site Fails Fact Check

Discredited self-styled ‘ fact checker ’ website is served with a ‘ cease and desist ’ legal notice today for publishing unsubstantiated and defamatory claims against Principia Scientific International ( PSI ) .
MEDIA BIAS FACT CHECK site owner admits he is unqualified and misrepresented himself as a seasoned journalist .
According to MEDIA BIAS FACT CHECK Principia Scientific International CIC is : “ CONSPIRACY-PSEUDOSCIENCE Sources in the Conspiracy-Pseudoscience category may publish unverifiable information that is not always supported by evidence .
These [ … ] ” So , who is fact-checking the ‘ fact checkers ’ ?
Today , @ @ @ @ @ @ @ MB/FC ) site owner , Dave Van Zandt with a pre-action legal notice to take down the defamatory and false smear .
Ironically , the self-styled ‘ MEDIA BIAS/ FACT CHECK ‘ ( MB/FC ) which negatively fact-checked PSI admits it relies on subjective bias to decide how biased others are .
In other words MB/FC is a pseudoscientific fact checker !
Apart from unlawfully smearing PSI Mr Van Zandt has smeared other websites that publish scientific articles critical of man-made global warming claims .
Among the unfairly smeared are : Below we @ @ @ @ @ @ @ fact checker .
We put Dave Van Zandt the faceless fact checker under the microscope and discovered the following : • None Van Zandt cites no scientific qualifications at all • None Van Zandt was exposed by WND as a fraud and a liar • None Van Zandt ’ s website ( MB/FC ) does not apply any objective scientific method • None Van Zandt relies on unverifiable subjectivity ( own bias ) to make judgments In a 2017 WND Exclusive ‘ Phony baloney : The 9 fakest fake-news checkers ’ Chelsea Schilling @ @ @ @ @ @ @ systemic faker .
She wrote : “ WND was unable to locate a single article with Van Zandt ’ s byline .
Ironically , the “ fact checker ” fails to establish his own credibility by disclosing his qualifications and training in evaluating news sources .
Asked for information concerning his expertise in the field of journalism and evaluating news sources , Van Zandt told WND : “ I am not a journalist and just a person who is interested in how media bias impacts politics .
You will find zero claims of @ @ @ @ @ @ @ purported “ 25+ years ” of experience writing for print and web media , he said : “ I am not sure why the 25+ years is still on the website.
” With the increasing scourge of fake news reports , especially on matters of wider scientific interest , Principia Scientific International ( PSI ) has become a recognised source of highly-qualified scientific opinion .
That scoundrels like Mr Van Zandt get such traction with his bogus ‘ fact checking ’ website is testimony for the need for more diligence and push back @ @ @ @ @ @ @ endless scientific fraud and misinformation .
Below we share with readers the take down letter issued today to Mr Van Zandt : Please accept this communication as a Cease and Desist Notice prior to legal action under 28 U.S. Code § 4101 ( 1 ) .
It has been drawn to our attention that your business , MEDIA BIAS FACT CHECK is libeling our business , Principia Scientific International ( PSI ) by posting the following ( recorded on March 13 , 2020 ) On your site at : https : //mediabiasfactcheck.com/methodology/ you @ @ @ @ @ @ @ for sources that publish unverifiable information that relates to known conspiracies such as the New World Order , Illuminati , False Flags , Aliens , etc .
Pseudoscience is determined by publishing unverified health and scientific claims .
In order to be classified in this group the central theme of the source must revolve around conspiracies or pseudoscience.
” On the same webpage you add the following disclaimer : “ Disclaimer : The methodology used by Media Bias Fact Check is our own .
It is not a tested scientific method .
It @ @ @ @ @ @ @ people to get an idea of a source ’ s bias .
Media Bias Fact Check will always review and change any factual errors when brought to our attention .
We make every effort to be as factual as possible .
Our goal is to have MBFC rated as least biased by our own criteria.
” According to Merriam-Webster online dictionary the term ‘ pseudoscience ’ is defined as : “ a system of theories , assumptions , and methods erroneously regarded as scientific.
” You thus taint our scientific organisation as unscientific @ @ @ @ @ @ @ court of law .
It is our belief you have made the above published statement with intention of causing damage to the reputation of our legally regulated UK non-profit scientific association which is scrupulously regulated under law as a community interest company ( CiC ) .
By law a CIC is prohibited from political bias i.e .
it can not advocate for any political point of view .
To engage in such action would render us likely to be struck off the register or be prosecuted .
Contrary to the false impression you @ @ @ @ @ @ @ international body of 5,500+ members , many of whom are credentialed science professionals , engineers and STEM academics , including award-winning scientists , government experts , etc .
Our published work is not pseudoscience but premised on established scientific methods .
A select list of some of our distinguished member is here : A Selection Of Member Biographies .
[ 1 ] In conclusion , not only do you admit your own methodology is unscientific , but because you also fail to cite which specific PSI posts are pseudoscience , you condemn all @ @ @ @ @ @ @ bias .
As per 28 U.S. Code § 4101 ( 1 ) we regard the words below civilly actionable and demand removal of them within 28 days : “ CONSPIRACY-PSEUDOSCIENCE Sources in the Conspiracy-Pseudoscience category may publish unverifiable information that is not always supported by evidence .
These [ … ] ” If you persist in maintaining this false assertion against us to jeopardize our legal standing , I hereby require you to provide substantiation of your accusation .
You may do so by providing us a selection of hyperlinks from published material @ @ @ @ @ @ @ you claim are ‘ conspiracy-pseudoscience.
’ Such evidence may then be considered for submission to a court of law for adjudication of the veracity of your claims .
If you are unwilling/unable to provide us the evidence you rely on to make your claims then you are hereby required to remove your false statement .
Principia Scientific International CIC ( No : 10824140 ) Fully incorporated in the UK for charitable purposes .
https : //principia-scientific.org/ PRINCIPIA SCIENTIFIC INTERNATIONAL , legally registered in the UK as a company incorporated for charitable purposes .
@ @ @ @ @ @ @ , London WC1N 3AX .
Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method .

‘MEDIA BIAS/FACT CHECK’ Site Fails Fact Check
Written by John O'Sullivan
Discredited self-styled ‘fact checker’ website is served with a ‘cease and desist’ legal notice today for publishing unsubstantiated and defamatory claims against Principia Scientific International (PSI).
MEDIA BIAS FACT CHECK site owner admits he is unqualified and misrepresented himself as a seasoned journalist.
According to MEDIA BIAS FACT CHECK Principia Scientific International CIC is:
“CONSPIRACY-PSEUDOSCIENCE Sources in the Conspiracy-Pseudoscience category may publish unverifiable information that is not always supported by evidence. These […]”
https://mediabiasfactcheck.com/?s=principia+scientific+international
So, who is fact-checking the ‘fact checkers’?
Today, PSI has issued Media Bias/Fact Check (MB/FC) site owner, Dave Van Zandt with a pre-action legal notice to take down the defamatory and false smear.
Ironically, the self-styled ‘MEDIA BIAS/ FACT CHECK‘ (MB/FC) which negatively fact-checked PSI admits it relies on subjective bias to decide how biased others are. In other words MB/FC is a pseudoscientific fact checker!
Apart from unlawfully smearing PSI Mr Van Zandt has smeared other websites that publish scientific articles critical of man-made global warming claims. Among the unfairly smeared are:
Below we help readers to fact check the pseudo fact checker. We put Dave Van Zandt the faceless fact checker under the microscope and discovered the following:
Van Zandt cites no scientific qualifications at all
Van Zandt was exposed by WND as a fraud and a liar
Van Zandt’s website (MB/FC) does not apply any objective scientific method
Van Zandt relies on unverifiable subjectivity (own bias) to make judgments
In a 2017 WND Exclusive ‘Phony baloney: The 9 fakest fake-news checkers’ Chelsea Schilling uncovered that Van Zandt was a seasoned systemic faker. She wrote:
“WND was unable to locate a single article with Van Zandt’s byline. Ironically, the “fact checker” fails to establish his own credibility by disclosing his qualifications and training in evaluating news sources. Asked for information concerning his expertise in the field of journalism and evaluating news sources, Van Zandt told WND: “I am not a journalist and just a person who is interested in how media bias impacts politics. You will find zero claims of expertise on the website.” Concerning his purported “25+ years” of experience writing for print and web media, he said: “I am not sure why the 25+ years is still on the website.”
With the increasing scourge of fake news reports, especially on matters of wider scientific interest, Principia Scientific International (PSI) has become a recognised source of highly-qualified scientific opinion. That scoundrels like Mr Van Zandt get such traction with his bogus ‘fact checking’ website is testimony for the need for more diligence and push back from honest scientists and citizens sickened by endless scientific fraud and misinformation.
Below we share with readers the take down letter issued today to Mr Van Zandt:
Mr Dave Van Zandt Media Bias/Fact Check (mediabiasfactcheck.com) Greensboro, NC Editor@Mediabiasfactcheck.com Dear Mr Dave Van Zandt, Re: Notice to Cease & Desist Libelous Conduct Please accept this communication as a Cease and Desist Notice prior to legal action under 28 U.S. Code § 4101(1). It has been drawn to our attention that your business, MEDIA BIAS FACT CHECK is libeling our business, Principia Scientific International(PSI) by posting the following (recorded on March 13, 2020) On your site at: https://mediabiasfactcheck.com/methodology/ you state: “Conspiracy/Pseudoscience The Conspiracy/Pseudoscience designation is reserved for sources that publish unverifiable information that relates to known conspiracies such as the New World Order, Illuminati, False Flags, Aliens, etc. Pseudoscience is determined by publishing unverified health and scientific claims. In order to be classified in this group the central theme of the source must revolve around conspiracies or pseudoscience.” On the same webpage you add the following disclaimer: “Disclaimer: The methodology used by Media Bias Fact Check is our own. It is not a tested scientific method. It is meant as a simple guide for people to get an idea of a source’s bias. Media Bias Fact Check will always review and change any factual errors when brought to our attention. We make every effort to be as factual as possible. Our goal is to have MBFC rated as least biased by our own criteria.” According to Merriam-Webster online dictionary the term ‘pseudoscience’ is defined as: “a system of theories, assumptions, and methods erroneously regarded as scientific.” You thus taint our scientific organisation as unscientific – a palpable lie provable in a court of law. It is our belief you have made the above published statement with intention of causing damage to the reputation of our legally regulated UK non-profit scientific association which is scrupulously regulated under law as a community interest company (CiC). By law a CIC is prohibited from political bias i.e. it cannot advocate for any political point of view. To engage in such action would render us likely to be struck off the register or be prosecuted. Contrary to the false impression you give your readers, we are an international body of 5,500+ members, many of whom are credentialed science professionals, engineers and STEM academics, including award-winning scientists, government experts, etc. Our published work is not pseudoscience but premised on established scientific methods. A select list of some of our distinguished member is here: A Selection Of Member Biographies. [1] In conclusion, not only do you admit your own methodology is unscientific, but because you also fail to cite which specific PSI posts are pseudoscience, you condemn all our members, which compounds your own bias. As per 28 U.S. Code § 4101(1) we regard the words below civilly actionable and demand removal of them within 28 days: “CONSPIRACY-PSEUDOSCIENCE Sources in the Conspiracy-Pseudoscience category may publish unverifiable information that is not always supported by evidence. These […]” https://mediabiasfactcheck.com/?s=principia+scientific+international If you persist in maintaining this false assertion against us to jeopardize our legal standing, I hereby require you to provide substantiation of your accusation. You may do so by providing us a selection of hyperlinks from published material on our website(s) which you claim are ‘conspiracy-pseudoscience.’ Such evidence may then be considered for submission to a court of law for adjudication of the veracity of your claims. If you are unwilling/unable to provide us the evidence you rely on to make your claims then you are hereby required to remove your false statement. [1] https://principia-scientific.com/why-psi-is-proposed-as-a-cic/ I await your reply. Sincerely, John O’Sullivan CEO Principia Scientific International CIC (No: 10824140) Fully incorporated in the UK for charitable purposes. http://principia-scientific.org/ **** PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX. Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method.
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principiascientificinternational--2020-03-12--Top Biologist: Corona Virus is ‘one of biggest frauds in history’

Top Biologist : Corona Virus is ‘ one of biggest frauds in history ’ MIT biologist and the man who claims to have invented email , Dr. Shiva Ayyadurai , does research almost every day into the immune system .
He says the fear-mongering by the Deep State will go down in history as one of the biggest frauds to manipulate economies , suppress dissent , & push MANDATED Medicine !
” He linked to a tweet by President Trump which reads , The Fake News Media and their partner , the Democrat Party , is doing everything within its @ @ @ @ @ @ @ greater ! )
to inflame the CoronaVirus situation , far beyond what the facts would warrant .
Surgeon General , “ The risk is low to the average American.
” One does have to wonder what the truth is .
It is seriously negatively impacting capitalism .
It ’ s a bad virus but we can ’ t shut down the entire world every time there is a pandemic .
Congress just closed to visitors , the NBA closed down after a player contracted the virus , travel from Europe , China , @ @ @ @ @ @ @ closing , the Stock Market is crashing although it ’ s partly due to the oil war , and there is more .
All this will seriously harm the capitalist economies .
Having lived through Swine flu , H1N1 and the constant threat of cases of flu ( I had Swine flu and have a compromised immune system ) , I have never seen such an extreme reaction .
We can ’ t do this every flu season .
The President has been put under tremendous pressure .
The press needs to ease @ @ @ @ @ @ @ had 60.8 million cases ( range : 43.3-89.3 million ) , 274,304 hospitalizations ( 195,086-402,719 ) , and 12,469 deaths ( 8868-18,306 ) .
Where was the panic then ?
PRINCIPIA SCIENTIFIC INTERNATIONAL , legally registered in the UK as a company incorporated for charitable purposes .
Head Office : 27 Old Gloucester Street , London WC1N 3AX .
Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method .

Top Biologist: Corona Virus is ‘one of biggest frauds in history’
Written by M. Dowling
MIT biologist and the man who claims to have invented email, Dr. Shiva Ayyadurai, does research almost every day into the immune system. He says the fear-mongering by the Deep State will go down in history as one of the biggest frauds to manipulate economies, suppress dissent, & push MANDATED Medicine!”
Dr.SHIVA Ayyadurai, MIT PhD. Inventor of Email ✔@va_shiva As an MIT PhD in Biological Engineering who studies & does research nearly every day on the Immune System, the #coronavirus fear mongering by the Deep State will go down in history as one of the biggest fraud to manipulate economies, suppress dissent, & push MANDATED Medicine! https://twitter.com/realdonaldtrump/status/1236975196642390022 … Donald J. Trump ✔@realDonaldTrump The Fake News Media and their partner, the Democrat Party, is doing everything within its semi-considerable power (it used to be greater!) to inflame the CoronaVirus situation, far beyond what the facts would warrant. Surgeon General, “The risk is low to the average American.” 15.7K Twitter Ads info and privacy 11.4K people are talking about this
He linked to a tweet by President Trump which reads,
The Fake News Media and their partner, the Democrat Party, is doing everything within its semi-considerable power (it used to be greater!) to inflame the CoronaVirus situation, far beyond what the facts would warrant. Surgeon General, “The risk is low to the average American.”
One does have to wonder what the truth is. It is seriously negatively impacting capitalism. It’s a bad virus but we can’t shut down the entire world every time there is a pandemic. Congress just closed to visitors, the NBA closed down after a player contracted the virus, travel from Europe, China, and Iran is banned, schools are closing, the Stock Market is crashing although it’s partly due to the oil war, and there is more. All this will seriously harm the capitalist economies.
Having lived through Swine flu, H1N1 and the constant threat of cases of flu (I had Swine flu and have a compromised immune system), I have never seen such an extreme reaction. We can’t do this every flu season. The President has been put under tremendous pressure. The press needs to ease up.
Read more at www.independentsentinel.com
PSI Editor’s Note:
Recall the 2009 H1N1 virus (swine Flu) see: https://www.cdc.gov/h1n1flu/estimates_2009_h1n1.htm
During that outbreak the U.S. had 60.8 million cases (range: 43.3-89.3 million), 274,304 hospitalizations (195,086-402,719), and 12,469 deaths (8868-18,306). Where was the panic then?
PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX.
Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method.
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principiascientificinternational--2020-03-12--Coronavirus: What can we learn from the Spanish flu?

Coronavirus : What can we learn from the Spanish flu ?
The unsanitary conditions – especially in the trenches along the French border – helped it incubate and then spread .
The war ended in November 1918 , but as the soldiers returned home , bringing the virus with them , an even greater loss of life was just around the corner ; between 50 million and 100 million people are thought to have died .
The world has suffered many pandemics in the years since – at least three serious flu outbreaks among them – but no pandemic has @ @ @ @ @ @ @ .
As the world reacts to a headline-grabbing – yet far , far less deadly – outbreak of Covid-19 , caused by a new coronavirus , BBC Future looks back to our 2018 special marking the 100th anniversary of Spanish Flu to see what we learned from one of the most devastating diseases in recent history .
Pneumonia is often the killer Many of the people dying from Covid-19 are succumbing to a form of pneumonia , which takes hold as the immune system is weakened from fighting the virus .
This is @ @ @ @ @ @ @ – though it must be said that the death rate from Covid-19 is many times lower than that of Spanish flu .
Older people and those with compromised immune systems – who make up the majority of those who have been killed by the disease so far – are more susceptible to infections that cause pneumonia .
Air travel was in its infancy when Spanish flu struck .
But there are few places on Earth that escaped its horrific effects .
Its passage across the world was slower , carried by railway and @ @ @ @ @ @ @ places held out for months , or even years , before the flu arrived and wreaked its terrible toll .

Coronavirus: What can we learn from the Spanish flu?
Written by Stephen Dowling
One hundred years ago, a world recovering from a global war that had killed some 20 million people suddenly had to contend with something even more deadly: a flu outbreak. The pandemic, which became known as Spanish flu, is thought to have begun in cramped and crowded army training camps on the Western Front.
The unsanitary conditions – especially in the trenches along the French border – helped it incubate and then spread. The war ended in November 1918, but as the soldiers returned home, bringing the virus with them, an even greater loss of life was just around the corner; between 50 million and 100 million people are thought to have died.
The world has suffered many pandemics in the years since – at least three serious flu outbreaks among them – but no pandemic has been as deadly, nor as far-reaching.
As the world reacts to a headline-grabbing – yet far, far less deadly – outbreak of Covid-19, caused by a new coronavirus, BBC Future looks back to our 2018 special marking the 100th anniversary of Spanish Flu to see what we learned from one of the most devastating diseases in recent history.
Pneumonia is often the killer
Many of the people dying from Covid-19 are succumbing to a form of pneumonia, which takes hold as the immune system is weakened from fighting the virus.
This is something that it shares with Spanish flu – though it must be said that the death rate from Covid-19 is many times lower than that of Spanish flu. Older people and those with compromised immune systems – who make up the majority of those who have been killed by the disease so far – are more susceptible to infections that cause pneumonia.
Few places escaped
Air travel was in its infancy when Spanish flu struck. But there are few places on Earth that escaped its horrific effects. Its passage across the world was slower, carried by railway and passenger steamer rather by airliners. Some places held out for months, or even years, before the flu arrived and wreaked its terrible toll.
The coronavirus, though capturing public attention, is significantly less lethal than Spanish Flu (Credit: Getty Images)
But some places did manage to keep the flu at bay, often by using basic techniques that are still being used 100 years later. In Alaska, one community on Bristol Bay escaped the flu almost unscathed. They closed schools, banned public gatherings, and shut off access to the village from the main road. It was a low-tech version of the travel restrictions that have been used in some areas today, such as China’s Hubei province and northern Italy, in an effort to stop the coronavirus spreading. Different viruses target different populations Doctors have described the Spanish flu as the “greatest medical holocaust in history”. It was not just the fact it killed so many, it was that so many of its victims were young and healthy. Normally, a healthy immune system can deal reasonably well with flu, but this version struck so quickly that it overwhelmed the immune system, causing a massive over-reaction known as a cytokine storm, flooding the lungs with fluid which became the perfect reservoir for secondary infections. Older people, interestingly, were not as susceptible, perhaps because they had survived a very similar strain of flu which had started to spread through human populations in the 1830s.
The flu spurred the development of public health systems across the developed world, as scientists and governments realised pandemics would spread more quickly
With the new coronavirus, the elderly and people with pre-existing illnesses are considered to be most at risk. Although still low, deaths have been highest in those aged above 80 years old. Public health is the best defence The Spanish flu broke out in a world which had just come out of a global war, with vital public resources diverted to military efforts. The idea of a public health system was its infancy – in many places, only the middle class or the rich could afford to visit a doctor. The flu killed many in slums and other poor urban areas, among populations with poor nutrition and sanitation, and often those with underlying health conditions. The flu spurred the development of public health systems across the developed world, as scientists and governments realised pandemics would spread more quickly than they had in the past.
Masks were in high demand during the Spanish Flu outbreak as well (Credit: Getty Images)
Treating people on a case-by-case basis would not be enough – to deal with pandemics in urban settings, governments would have to mobilise resources as if they were at war, quarantining those showing signs of the disease, keeping minor cases separate to those suffering more serious illness, and limiting people’s movements so the disease would burn itself out. The public health measures we see being enacted today across the world as efforts to contain the spread of coronavirus are one of the Spanish flu’s most enduring effects. Read more at www.bbc.com **** PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX. Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method.
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principiascientificinternational--2020-03-12--‘Is God A Mathematician’ by Mario Livio

‘Is God A Mathematician’ by Mario Livio

After hearing about Eugene Wigner ’ s article , “ The Unreasonable Effectiveness of Mathematics in the Natural Sciences , ” for many years , I recently decided to read and digest the article for myself .
( If you ’ re so inclined , you can read about the results here . )
Continuing this exploration of the philosophy of mathematics led me to Mario Livio ’ s intriguing book , Is God a Mathematician ?
, selected by the Washington Post as one of the best books of 2009 .
Here , I present a summary of that @ @ @ @ @ @ @ in turn led me to Livio ’ s Scientific American article , “ Why Math Works , ” an interview with Krista Tippett , and a Nova special that features him prominently .
I encourage you to explore these sources as well as the book itself .
Livio does not intend the title as a theological question .
He is instead referring to two questions concerning the mysterious effectiveness of mathematics in the physical world .
The first question is “ Does mathematics have an existence independent of the human mind ?
” @ @ @ @ @ @ @ discovered , extant in an abstract realm , independent of the world we perceive with our senses , or is it an invention , that is , a creation by the human mind ?
Those who belong to the “ discovered ” camp are known as “ Platonists , ” and include ( or have included ) such notables as G. H. Hardy , Roger Pendrose , Kurt Gödel , and Martin Gardner .
On the “ formalist ” side of the argument lies Albert Einstein , David Hilbert , Georg Cantor , @ @ @ @ @ @ @ The second question is : “ Why do mathematical concepts have applicability far beyond the context in which they have originally been developed ?
” This is the question that Eugene Wigner asked .
As he put it , “ It is difficult to avoid the impression that a miracle confronts us here , comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions.
” Livio clarifies and focuses this second question by making a distinction between active and passive @ @ @ @ @ @ @ means mathematics that was created as a tool for a purpose .
Although no one is surprised that active mathematics is effective — it was developed specifically for the purpose , and the theories were tailored to fit the observations — it may be surprising just how effective it can be .
For instance , the theoretical calculation of the magnetic moment of an electron in quantum electrodynamics matches the actual value to within a few parts per trillion .
Passive applicability is more surprising .
“ Passive ” in this context refers @ @ @ @ @ @ @ of the original theory .
For instance , entire subfields of mathematics are created with no physical application in mind , “ math for math ’ s sake , ” but then decades or even centuries later , these theories fit real world situations with astounding exactitude .
For instance , group theory was developed in the early 1800s by Évariste Galois to study the solvability of polynomial equations , yet worked beautifully in the 20th century to categorize elementary particles .
As another example , so-called “ non-Euclidean geometries , ” which @ @ @ @ @ @ @ geometry ( more below ) , came as a shock to the mathematical community in the mid-1800s and were even derided by many as not being “ true ” mathematics .
Yet Einstein formulated his general theory of relativity on Riemannian geometry .
The first few chapters of the book concentrate on some famous early names in mathematics : Pythagoras , Plato , Archimedes , Galileo , Descartes , and Newton .
These men helped to simultaneously formalize mathematics and effect its role as the language of science .
Each of these mathematicians @ @ @ @ @ @ @ pre-existing , either from some mysterious realm of thought , or as arising from the mind of God .
While their predecessors were primarily interested in mathematics as a practical tool , for instance , for measuring out land , or predicting flood cycles , the followers of Pythagoras were the first “ pure mathematicians , ” interested in mathematics for its own sake .
As such , they pioneered the use of rigorous proof , the practice of starting with self evident postulates and utilizing logic to prove conclusions from them .
@ @ @ @ @ @ @ was discovered or invented , they fell firmly into the discovered camp .
Livio says it this way : “ On the question of whether mathematics was discovered or invented , Pythagoras and the Pythagoreans had no doubt — mathematics was real , immutable , omnipresent , and more sublime than anything that could conceivably emerge from the feeble human mind .
The Pythagoreans literally embedded the universe into mathematics .
In fact , to the Pythagoreans , God was not a mathematician — mathematics was God !
” They also set the @ @ @ @ @ @ @ of the Pythagorean philosophy lies not only in its actual , intrinsic value .
By setting the stage , and to some extent the agenda , for the next generation of philosophers — Plato in particular — the Pythagoreans established a commanding position in Western thought.
” Although today Archimedes is mostly known for his clever engineering inventions , famously including the hydraulic screw for raising water and various engines of war , his primary interest was in pure mathematics .
In geometry , he presented general methods for areas and volumes of @ @ @ @ @ @ @ theory , he approximated lower and upper bounds of π as 3 10/71 and 3 1/7 , respectively .
He also invented a system to denote and manipulate numbers of any magnitude .
Legend has it that he died because he wouldn ’ t move from a mathematical diagram during a battle , and a Roman soldier killed him .
Alfred North Whitehead wrote , “ The death of Archimedes at the hands of a Roman soldier is symbolical of a world change of the first magnitude .
The Romans were a great @ @ @ @ @ @ @ the sterility which waits upon practicality .
They were not dreamers enough to arrive at new points of view , which could give more fundamental control over the forces of nature .
No Roman lost his life because he was absorbed in the contemplation of a mathematical diagram.
” Although Plato was not a mathematician per se , he was a great philosopher of mathematics , influencing the field for the following millennia .
To Plato , mathematical truths did not refer to geometric figures represented on papyrus or marked in the sand @ @ @ @ @ @ @ in an idealized non-physical world of true forms .
This view that mathematics is extant in an abstract realm independent of the world of our senses became known as “ Platonism.
” Galileo enrolled in the faculty of arts of the University of Pisa to study medicine but changed to mathematics .
He became a huge fan of Archimedes .
He said , “ Those who read his works realize only too clearly how inferior are all other minds compared with Archimedes ’ and what small hope is left of ever discovering things @ @ @ @ @ @ @ Galileo is , of course , known for his challenges to the geocentric model .
Although he did not invent the telescope , he greatly improved it , and made many discoveries that supported the heliocentric view of the universe .
This view , the scientifically correct one , resulting in his eventually being tried by the inquisition and subjected to house arrest for the rest of his days .
More importantly for our purposes is the impact he brought to science .
Livo says , “ The philosopher of science Alexandre Koyré @ @ @ @ @ @ @ ’ s revolution in scientific thinking can be distilled to one essential element : the discovery that mathematics is the grammar of science .
While the Aristotelians were happy with a qualitative description of nature , and even for that they appealed to Aristotle ’ s authority , Galileo insisted that scientists should listen to nature itself , and that the keys to deciphering the universe ’ s parlance were mathematical relations and geometrical models… Centuries before the question of why mathematics was so effective in explaining nature was even asked , Galileo @ @ @ @ @ @ @ To him , mathematics was simply the language of the universe .
To understand the universe , he argued , one must speak this language .
God is indeed a mathematician.
” Descartes , of “ cogito , ergo sum ” fame , introduced several mathematically revolutionary concepts .
In particular , he developed the use of functions in mathematics .
Such a function encodes a “ rule ” that a physical phenomena follows .
For instance , Newton ’ s gravitation states that the gravitational attraction between two masses is proportional to @ @ @ @ @ @ @ square of the distance between them .
He also proposed the Cartesian coordinate system , which married the fields of algebra and geometry into a new field , analytic geometry .
Descartes also argued that the natural world is best described through mathematics , and not through the our often misleading perceptions .
“ I recognize no matter in corporeal things apart from that which the geometers call quantity , and take as the object of their demonstrations…And since all natural phenomena can be explained in this way , I do not think @ @ @ @ @ @ @ or desirable in physics.
” He went even further , suggesting that nearly all of human knowledge could follow from systematic application of mathematics .
Newton , undoubtedly one of the greatest mathematicians of all time , took Descartes ’ idea that the cosmos can be described in terms of mathematics and made it reality .
He formulated the fundamental laws of mechanics , deciphered the laws describing planetary motion , and erected the theoretical basis for the phenomena of light and color .
All of these ideas were written in the language @ @ @ @ @ @ @ course , developed differential and integral calculus .
Thus far , we would be forgiven for either concluding that the Platonist view is the obvious perspective or that the whole debate is a moot point .
However , in the mid-1800s , the mathematical world was in for a shock .
This bombshell came in the form of so-called “ non-Euclidean ” geometries .
Until the beginning of the 19th century , Euclidean geometry was considered the epitome of truth and certainty .
The Platonic ideals of Euclidean geometry were considered to be @ @ @ @ @ @ @ Kant , who in his Critique of Pure Reason asserted that we know what we know by sensory perception processed by the brain , made an exception for geometry , stating , “ Space is not an empirical concept which has been derived from external experience… Space is a necessary representation a priori , forming the very foundation of all external intuitions… ” Or put more simply , it was taken more or less as a given that absolute truths about the universe exist .
Non-Euclidean geometries were about to challenge this view @ @ @ @ @ @ @ must first understand what is meant by Euclidean geometry .
Circa 300 BC , Euclid laid out geometry in his thirteen volume work The Elements .
He started with ten axioms assumed to be self-evidently true and constructed geometry through logic applied to these postulates .
The first four axioms , such as the first one , which states that a straight line may be drawn through any two points , are obvious .
The fifth postulate , the so-called “ parallel postulate ” read as follows .
“ If two lines lying @ @ @ @ @ @ @ in such a way that the sum of the internal angles on one side is less than the two right angles , then the two lines inevitably will intersect each other if extended sufficiently on that side.
” So if angles α and β together are less than 180 degrees , the lines must cross .
The fifth postulate seems convoluted and artificial .
For centuries , attempts had been made to “ clean up ” Euclid ’ s geometry by proving the fifth postulate as a consequence of the other four postulates @ @ @ @ @ @ @ , it was shown that one could create a new kind of geometry by choosing a different axiom than the fifth postulate .
Furthermore , the resulting geometries described space just as accurately as Euclidean geometry .
This is the key turning point in our story .
The implication is that mathematics is not a preordained truth , but determined by choices that one makes .
This is why the questions we ’ re talking about even make sense to discuss .
Up until now , no one looked at mathematics in this @ @ @ @ @ @ @ given .
Livio says , “ Let me pause here for a moment to allow for the meaning of the word “ choosing ” to sink in .
For millennia , Euclidean geometry had been regarded as unique and inevitable — the sole true description of space .
The fact that one could choose the axioms and obtain an equally valid description turned the entire concept on its ear .
The certain , carefully constructed deductive scheme suddenly became more similar to a game , in which the axioms simply played the role @ @ @ @ @ @ @ the axioms and play a different game .
The impact of this realization on the understanding of the nature of mathematics can not be overemphasized.
” The stage for alternate geometries was set by Girolamo Saccheri , who investigated the consequences of replacing the fifth postulate by another statement , and Georg Klügel and Johann Heinrich Lambert , who realized that alternative geometries could exist .
Three mathematicians in particular created non-Euclidean geometries , once and for all showing that Euclidean geometry was not the only representation of space : Nikolai Ivanovich Lobachevsky @ @ @ @ @ @ @ Gauss , who presented what is now known as hyperbolic geometry .
Bernhard Riemann furthered the field of non-Euclidean geometry with “ elliptical geometry.
” These developments led Henri Poincaré to declare that Kant was wrong .
Space is not intrinsically Euclidean before we perceive it , but rather is a learned framework .
In his words , “ …to conclude that the axioms of geometry are ‘ neither synthetic a priori intuitions nor experimental facts .
They are conventions .
Our choice among all possible conventions is guided by experimental facts , @ @ @ @ @ @ @ geometries would follow , such as projective and differential geometry .
The reactions to non-Euclidean geometries were varied .
Many mathematicians did not consider these alternative geometries to be legitimate types of mathematics .
One objection was consistency .
Would these geometries ultimately lead to self contradictions ?
By the 1870s , Eugenio Beltrami and Felix Klein had shown that if Euclidean geometry is consistent , then so are the non-Euclidean geometries .
Some mathematicians turned to arithmetic ( number theory ) , connecting geometry with numbers in the spirit of Descartes analytic @ @ @ @ @ @ @ arithmetic is consistent , then so is geometry .
This observation doesn ’ t really answer the question though , but only pushes it downstream .
Another objection was relevance .
Initially , the non-Euclidean geometries were seen as curiosities , with no connection to the three dimensional space of the real world that we live in .
Many mathematicians , including Gerolamo Cardano and John Wallis , refused to consider any mathematics that dimensions higher than three .
Jean D ’ Alembert and Joseph Lagrance considered 4D mathematics , with only with @ @ @ @ @ @ @ Grüssman explored geometries in any number of dimensions , which originated the branch of mathematics we now call linear algebra .
To him , mathematics was an abstract creation of the mind that does not necessarily have any application to the real world .
At this point , mathematics was no longer restrained to describing the three dimensional observable world .
In the 1700s , Euler had declared , “ mathematics , in general , is the science of quantity ; or , the science that investigates the means of measuring quantity.
” @ @ @ @ @ @ @ along with the notion of infinity , had distorted the meaning of “ measurement ” or “ quantity ” beyond recognition .
In addition , mathematics had become the study of abstractions , far removed from physical reality .
Georg Cantor characterized the new spirit of mathematics by a “ declaration of independence ” : “ Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other and also stand in exact relationships , ordered by definitions , to @ @ @ @ @ @ @ and are already at hand and established.
” Dedekind added , “ I consider the number concept entirely independent of the notions or intuitions of space and time…Numbers are free creations of the human mind.
” Cantor continued , saying “ The essence of mathematics lies entirely in its freedom.
” By the close of the 1800s , most mathematicians considered mathematics to not be about the explanation of the physical world , but rather as the logical consequences of given axioms .
Non-Euclidean geometries and their aftermath led mathematicians to seriously investigate @ @ @ @ @ @ @ was pursued via logic .
Logicism is the point of view that mathematics can be reduced to logic .
Bertrand Russell explained it this way .
“ Mathematics and logic , historically speaking , have been entirely distinct studies .
Mathematics has been connected with science , logic with Greek .
But both have developed in modern times : logic has become more mathematical and mathematics has become more logical .
The consequence is that it has now [ in 1919 ] become wholly impossible to draw a line between the two ; @ @ @ @ @ @ @ They differ as boy and man : logic is the youth of mathematics and mathematics is the manhood of logic.
” Both camps , formalists and Platonists , embraced logicism .
Formalists were happy to see the “ games ” of mathematics coalesce into one übergame , whereas Platonists hoped that logic would eventually reveal a single metaphysical origin to mathematics .
Logic has long concerned itself with concepts and propositions , and by making valid inferences from the relationships between propositions .
For example , a syllogism is a form a reasoning @ @ @ @ @ @ @ two given premises of a certain form .
For instance , all cats are mammals , all mammals have four legs , therefore all cats have four legs is a syllogism .
Symbolically , this line of reasoning can be denoted as “ every X is a Y ; every Y is a Z ; therefore , all Xs are Zs.
” One can not help but notice the parallels between symbolic logic and mathematics .
In the 1700s , Gottfried Wilhelm Leibniz , famous for formulating calculus independently of Newton , and @ @ @ @ @ @ @ envisioned a characteristica universalis , which was a system to compute the truth or falsity of any statement symbolically .
However , his formulation had issues — the vagueness of what might constitute an “ alphabet of thought ” and the difficulty of determining when thoughts are “ equal ” — that doomed this experiment to never really get off the ground .
In the mid-1800s , Augustus DeMorgan began to make strides with the algebraization of logic , including quantifying the predicate .
George Boole , who corresponded with DeMorgan since 1842 @ @ @ @ @ @ @ Mathematical Analysis of Logic , and The Laws of Thought , which together transformed logic into a type of algebra .
Friedrich Frege wrote two more notable books , the Begriffsschrift and the Grundgesetze der Arithmetic , in which he set out to prove the truths of arithmetic from a few axioms of logic .
He wanted to show that even the natural numbers could be reduced to logical constructs , and build from these concepts to show the truth of arithmetic .
Although it was a brilliant idea to prove arithmetic from @ @ @ @ @ @ @ flawed — one of his axioms , known as Basic Law V , was shown by Bertrand Russell to lead to a contradiction .
Despite this flaw , Russell believed that deriving arithmetic from logic was the correct approach .
He wrote , along with Alfred North Whitehead , the Principia Mathematica , still considered as one of the most influential books in the history of logic .
Russell indeed successfully fixed Basic Law V , but in a highly artificial and convoluted way .
Eventually the paradoxes were more elegantly eliminated by @ @ @ @ @ @ @ set theory in a self-consistent way .
This seemed to give mathematics a kind of objective certainty , giving the Platonists a long sought after victory .
However , once again , one of the axioms , this time the so-called axiom of choice , proved to be problematic .
The axiom of choice states that if X is a collection of nonempty sets , then we can choose one element in each set in X to form a new set Y .
There is no controversy when considering finite sets since one @ @ @ @ @ @ @ that for a hundred boxes , each containing at least one marble , one can take one marble from each box to form a new set of a hundred marbles .
Extending this notion , we can see that the axiom must be true even for countably infinite sets .
However , in the case of uncountably infinite sets , we can not even define how such a choice could be made .
Similar to the days of Euclid ’ s fifth axiom , mathematicians attempted to either prove or refute the axiom @ @ @ @ @ @ @ In the 1930s , Kurt Gödel showed that the axiom of choice can neither be proved nor disproved from the other Z-F axioms .
The next phase of the debate was initiated by David Hilbert , the Formalist , who believed mathematics was no more than a collection of meaningless formulae .
His ambitious program was to show the correctness of mathematics using mathematical methods ( so-called “ metamathematics ” ) .
As he said , “ My investigations in the new grounding of mathematics have as their goal nothing less than this @ @ @ @ @ @ @ all , the general doubt about the reliability of mathematical inference…Everything that previously made up mathematics is to be rigorously formalized , so that mathematics proper or mathematics in the strict sense becomes a stock of formulae…In addition to this formalized mathematics proper , we have a mathematics that is to some extent new : a metamathematics that is necessary for securing mathematics , and in which — in contrast to the purely formal modes of inference in mathematics proper — one applies contextual inference , but only to prove the consistency of @ @ @ @ @ @ @ as a whole takes place in two ways that constantly alternate : on the one hand we derive provable formulae from the axioms by formal inference ; on the other , we adjoin new axioms and prove their consistency by contextual inference.
” Once again , enter Gödel .
As a teenager , he had become fascinated by Russell and Whitehead ’ s Principia Mathematica and by Hilbert ’ s program .
For his dissertation , he chose to determine whether Hilbert ’ s formal approach was sufficient to produce mathematics .
A @ @ @ @ @ @ @ he dropped the bomb in the form of Gödel ’ s “ Incompleteness Theorem.
” From Livio : “ …the incompleteness theorems proved that Hilbert ’ s formalist program was essentially doomed from the start .
Gödel showed that any formal system that is powerful enough to be of any interest is inherently either incomplete or inconsistent .
That is , in the best case , there will always be assertions that the formal system can neither prove nor disprove .
In the worst , the system would yield contradictions.
” For a @ @ @ @ @ @ @ Incompleteness Theorem , please refer to this article by Jørgen Veisdal .
One suspects that most professional mathematicians go about their daily work without becoming mired in philosophical meta-discussions of their favorite subject .
As Philip Davis and Reuben Hersch say in The Mathematical Experience , “ the typical mathematician is a Platonist on weekdays and a formalist on Sundays.
” Some twentieth century mathematicians did indeed have strong views in one camp or the other .
For instance , G. H. Hardy gives a strong Platonist persective in his A Mathematician ’ @ @ @ @ @ @ @ James Newman describe the opposite Formalist view in Mathematics and the Imagination .
On the Platonist side , some people believe that mathematics exists not in some kind of metaphysical realm , but is baked into the physical world .
For instance , Max Tegmark , the MIT astrophysicist , takes the view that “ our universe is not just described by mathematics — it is mathematics.
” He argues that external physical reality exists independently of humans , then examines what the nature of the “ theory of everything ” of such @ @ @ @ @ @ @ description must be free of any human “ baggage ” ( such as language ) , then concludes that such a final theory can not consist of any human constructs , and therefore the only possible description of the cosmos is one that only involves abstract concepts and their relations , i.e.
, mathematics .
Livio fails to be impressed by this chain of reasoning , claiming that Tegmark in effect assumes his conclusion .
Livio also mentions a number of neuroscientists , such as Jean-Pierre Changeux , and Lakoff and Núñez , @ @ @ @ @ @ @ a human construction of the human brain .
So what does the author think ?
Livio concludes the book by stating that the question of whether mathematics is invented or discovered is misleading , since it implies that mathematics must be either one or the other .
His view is that mathematics is both invented and discovered .
The mathematical concepts and definitions are invented , whereas the logical consequences of these concepts are discovered .
In this article , I ’ ve necessarily given you only the highlights of the book .
@ @ @ @ @ @ @ biographical material and the more technical aspects of the debates , which are well worth delving into .
I encourage you to read it for yourself .
Enjoy !
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Head Office : 27 Old Gloucester Street , London WC1N 3AX .
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‘Is God A Mathematician’ by Mario Livio
Written by Mark Pedigo
After hearing about Eugene Wigner’s article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” for many years, I recently decided to read and digest the article for myself. (If you’re so inclined, you can read about the results here.)
Continuing this exploration of the philosophy of mathematics led me to Mario Livio’s intriguing book, Is God a Mathematician?, selected by the Washington Post as one of the best books of 2009. Here, I present a summary of that book.
My research on this book in turn led me to Livio’s Scientific American article, “Why Math Works,” an interview with Krista Tippett, and a Nova special that features him prominently. I encourage you to explore these sources as well as the book itself.
Themes
Livio does not intend the title as a theological question. He is instead referring to two questions concerning the mysterious effectiveness of mathematics in the physical world.
The first question is “Does mathematics have an existence independent of the human mind?” or put another way, is mathematics discovered, extant in an abstract realm, independent of the world we perceive with our senses, or is it an invention, that is, a creation by the human mind? Those who belong to the “discovered” camp are known as “Platonists,” and include (or have included) such notables as G. H. Hardy, Roger Pendrose, Kurt Gödel, and Martin Gardner. On the “formalist” side of the argument lies Albert Einstein, David Hilbert, Georg Cantor, the Bourbaki group, and others.
The second question is: “Why do mathematical concepts have applicability far beyond the context in which they have originally been developed?” This is the question that Eugene Wigner asked. As he put it, “It is difficult to avoid the impression that a miracle confronts us here, comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions.”
Livio clarifies and focuses this second question by making a distinction between active and passive applicability. By active applicability, he means mathematics that was created as a tool for a purpose. Although no one is surprised that active mathematics is effective — it was developed specifically for the purpose, and the theories were tailored to fit the observations — it may be surprising just how effective it can be. For instance, the theoretical calculation of the magnetic moment of an electron in quantum electrodynamics matches the actual value to within a few parts per trillion. Passive applicability is more surprising. “Passive” in this context refers to applicability of mathematics beyond the intent of the original theory. For instance, entire subfields of mathematics are created with no physical application in mind, “math for math’s sake,” but then decades or even centuries later, these theories fit real world situations with astounding exactitude. For instance, group theory was developed in the early 1800s by Évariste Galois to study the solvability of polynomial equations, yet worked beautifully in the 20th century to categorize elementary particles. As another example, so-called “non-Euclidean geometries,” which defy the parallel postulate of traditional Euclidean geometry (more below), came as a shock to the mathematical community in the mid-1800s and were even derided by many as not being “true” mathematics. Yet Einstein formulated his general theory of relativity on Riemannian geometry.
Early Platonists
The first few chapters of the book concentrate on some famous early names in mathematics: Pythagoras, Plato, Archimedes, Galileo, Descartes, and Newton. These men helped to simultaneously formalize mathematics and effect its role as the language of science. Each of these mathematicians were Platonists, who viewed mathematics as pre-existing, either from some mysterious realm of thought, or as arising from the mind of God.
The Pythagoreans
While their predecessors were primarily interested in mathematics as a practical tool, for instance, for measuring out land, or predicting flood cycles, the followers of Pythagoras were the first “pure mathematicians,” interested in mathematics for its own sake. As such, they pioneered the use of rigorous proof, the practice of starting with self evident postulates and utilizing logic to prove conclusions from them. As to the question of whether mathematics was discovered or invented, they fell firmly into the discovered camp. Livio says it this way: “On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt — mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the feeble human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician — mathematics was God!”
They also set the stage for Plato. “The importance of the Pythagorean philosophy lies not only in its actual, intrinsic value. By setting the stage, and to some extent the agenda, for the next generation of philosophers — Plato in particular — the Pythagoreans established a commanding position in Western thought.”
Archimedes
Although today Archimedes is mostly known for his clever engineering inventions, famously including the hydraulic screw for raising water and various engines of war, his primary interest was in pure mathematics. In geometry, he presented general methods for areas and volumes of a variety of figures, in number theory, he approximated lower and upper bounds of π as 3 10/71 and 3 1/7, respectively. He also invented a system to denote and manipulate numbers of any magnitude.
Legend has it that he died because he wouldn’t move from a mathematical diagram during a battle, and a Roman soldier killed him. Alfred North Whitehead wrote, “The death of Archimedes at the hands of a Roman soldier is symbolical of a world change of the first magnitude. The Romans were a great race, but they were cursed by the sterility which waits upon practicality. They were not dreamers enough to arrive at new points of view, which could give more fundamental control over the forces of nature. No Roman lost his life because he was absorbed in the contemplation of a mathematical diagram.”
Plato
Although Plato was not a mathematician per se, he was a great philosopher of mathematics, influencing the field for the following millennia. To Plato, mathematical truths did not refer to geometric figures represented on papyrus or marked in the sand, but to abstract objects that exist in an idealized non-physical world of true forms. This view that mathematics is extant in an abstract realm independent of the world of our senses became known as “Platonism.”
Galileo
Galileo enrolled in the faculty of arts of the University of Pisa to study medicine but changed to mathematics. He became a huge fan of Archimedes. He said, “Those who read his works realize only too clearly how inferior are all other minds compared with Archimedes’ and what small hope is left of ever discovering things similar to the ones he discovered.”
Galileo is, of course, known for his challenges to the geocentric model. Although he did not invent the telescope, he greatly improved it, and made many discoveries that supported the heliocentric view of the universe. This view, the scientifically correct one, resulting in his eventually being tried by the inquisition and subjected to house arrest for the rest of his days.
More importantly for our purposes is the impact he brought to science. Livo says, “The philosopher of science Alexandre Koyré (1892–1964) remarked once that Galileo’s revolution in scientific thinking can be distilled to one essential element: the discovery that mathematics is the grammar of science. While the Aristotelians were happy with a qualitative description of nature, and even for that they appealed to Aristotle’s authority, Galileo insisted that scientists should listen to nature itself, and that the keys to deciphering the universe’s parlance were mathematical relations and geometrical models… Centuries before the question of why mathematics was so effective in explaining nature was even asked, Galileo thought he already knew the answer! To him, mathematics was simply the language of the universe. To understand the universe, he argued, one must speak this language. God is indeed a mathematician.”
Descartes
Descartes, of “cogito, ergo sum” fame, introduced several mathematically revolutionary concepts. In particular, he developed the use of functions in mathematics. Such a function encodes a “rule” that a physical phenomena follows. For instance, Newton’s gravitation states that the gravitational attraction between two masses is proportional to their masses and inversely proportional to the square of the distance between them. He also proposed the Cartesian coordinate system, which married the fields of algebra and geometry into a new field, analytic geometry.
Descartes also argued that the natural world is best described through mathematics, and not through the our often misleading perceptions. “I recognize no matter in corporeal things apart from that which the geometers call quantity, and take as the object of their demonstrations…And since all natural phenomena can be explained in this way, I do not think that any other principles are either admissible or desirable in physics.” He went even further, suggesting that nearly all of human knowledge could follow from systematic application of mathematics.
Newton
Newton, undoubtedly one of the greatest mathematicians of all time, took Descartes’ idea that the cosmos can be described in terms of mathematics and made it reality. He formulated the fundamental laws of mechanics, deciphered the laws describing planetary motion, and erected the theoretical basis for the phenomena of light and color. All of these ideas were written in the language of mathematics. He also, of course, developed differential and integral calculus.
Non-Euclidean Geometry
Thus far, we would be forgiven for either concluding that the Platonist view is the obvious perspective or that the whole debate is a moot point. However, in the mid-1800s, the mathematical world was in for a shock. This bombshell came in the form of so-called “non-Euclidean” geometries.
Euclidean geometry
Until the beginning of the 19th century, Euclidean geometry was considered the epitome of truth and certainty. The Platonic ideals of Euclidean geometry were considered to be abstractions of their real-world counterparts. Even Kant, who in his Critique of Pure Reason asserted that we know what we know by sensory perception processed by the brain, made an exception for geometry, stating, “Space is not an empirical concept which has been derived from external experience… Space is a necessary representation a priori, forming the very foundation of all external intuitions…” Or put more simply, it was taken more or less as a given that absolute truths about the universe exist. Non-Euclidean geometries were about to challenge this view.
To understand non-Euclidean geometries, we must first understand what is meant by Euclidean geometry.
Circa 300 BC, Euclid laid out geometry in his thirteen volume work The Elements. He started with ten axioms assumed to be self-evidently true and constructed geometry through logic applied to these postulates. The first four axioms, such as the first one, which states that a straight line may be drawn through any two points, are obvious. The fifth postulate, the so-called “parallel postulate” read as follows. “If two lines lying in a plane intersect a third line in such a way that the sum of the internal angles on one side is less than the two right angles, then the two lines inevitably will intersect each other if extended sufficiently on that side.”
Image from Wikipedia: By 6054 — Edit of http://pl.wikipedia.org/wiki/Grafika:Parallel_postulate.svg by User:Harkonnen2, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=4559984
So if angles α and β together are less than 180 degrees, the lines must cross.
Non-Euclidean Geometry
The fifth postulate seems convoluted and artificial. For centuries, attempts had been made to “clean up” Euclid’s geometry by proving the fifth postulate as a consequence of the other four postulates with no success.
In the mid-1800s, it was shown that one could create a new kind of geometry by choosing a different axiom than the fifth postulate. Furthermore, the resulting geometries described space just as accurately as Euclidean geometry. This is the key turning point in our story. The implication is that mathematics is not a preordained truth, but determined by choices that one makes. This is why the questions we’re talking about even make sense to discuss. Up until now, no one looked at mathematics in this way — it was taken as a given.
Livio says, “Let me pause here for a moment to allow for the meaning of the word “choosing” to sink in. For millennia, Euclidean geometry had been regarded as unique and inevitable — the sole true description of space. The fact that one could choose the axioms and obtain an equally valid description turned the entire concept on its ear. The certain, carefully constructed deductive scheme suddenly became more similar to a game, in which the axioms simply played the role of the rules. You could change the axioms and play a different game. The impact of this realization on the understanding of the nature of mathematics cannot be overemphasized.”
The stage for alternate geometries was set by Girolamo Saccheri, who investigated the consequences of replacing the fifth postulate by another statement, and Georg Klügel and Johann Heinrich Lambert, who realized that alternative geometries could exist. Three mathematicians in particular created non-Euclidean geometries, once and for all showing that Euclidean geometry was not the only representation of space: Nikolai Ivanovich Lobachevsky, János Bolyai, and Carl Friedrich Gauss, who presented what is now known as hyperbolic geometry. Bernhard Riemann furthered the field of non-Euclidean geometry with “elliptical geometry.” These developments led Henri Poincaré to declare that Kant was wrong. Space is not intrinsically Euclidean before we perceive it, but rather is a learned framework. In his words, “…to conclude that the axioms of geometry are ‘neither synthetic a priori intuitions nor experimental facts. They are conventions. Our choice among all possible conventions is guided by experimental facts, but it remains free.” Even more geometries would follow, such as projective and differential geometry.
Reactions
The reactions to non-Euclidean geometries were varied. Many mathematicians did not consider these alternative geometries to be legitimate types of mathematics. One objection was consistency. Would these geometries ultimately lead to self contradictions? By the 1870s, Eugenio Beltrami and Felix Klein had shown that if Euclidean geometry is consistent, then so are the non-Euclidean geometries. Some mathematicians turned to arithmetic (number theory), connecting geometry with numbers in the spirit of Descartes analytic geometry. David Hilbert demonstrated that if arithmetic is consistent, then so is geometry. This observation doesn’t really answer the question though, but only pushes it downstream.
Another objection was relevance. Initially, the non-Euclidean geometries were seen as curiosities, with no connection to the three dimensional space of the real world that we live in. Many mathematicians, including Gerolamo Cardano and John Wallis, refused to consider any mathematics that dimensions higher than three. Jean D’Alembert and Joseph Lagrance considered 4D mathematics, with only with time as the fourth dimension.
The “Freedom of Mathematics”
Hermann Grüssman explored geometries in any number of dimensions, which originated the branch of mathematics we now call linear algebra. To him, mathematics was an abstract creation of the mind that does not necessarily have any application to the real world. At this point, mathematics was no longer restrained to describing the three dimensional observable world.
In the 1700s, Euler had declared, “mathematics, in general, is the science of quantity; or, the science that investigates the means of measuring quantity.” The introduction of these abstract geometries, along with the notion of infinity, had distorted the meaning of “measurement” or “quantity” beyond recognition. In addition, mathematics had become the study of abstractions, far removed from physical reality. Georg Cantor characterized the new spirit of mathematics by a “declaration of independence”: “Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established.” Dedekind added, “I consider the number concept entirely independent of the notions or intuitions of space and time…Numbers are free creations of the human mind.” Cantor continued, saying “The essence of mathematics lies entirely in its freedom.” By the close of the 1800s, most mathematicians considered mathematics to not be about the explanation of the physical world, but rather as the logical consequences of given axioms.
Foundations of Mathematics
Non-Euclidean geometries and their aftermath led mathematicians to seriously investigate the foundations of mathematics. This investigation was pursued via logic.
Logicism
Logicism is the point of view that mathematics can be reduced to logic. Bertrand Russell explained it this way. “Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical. The consequence is that it has now [in 1919] become wholly impossible to draw a line between the two; in fact the two are one. They differ as boy and man: logic is the youth of mathematics and mathematics is the manhood of logic.”
Both camps, formalists and Platonists, embraced logicism. Formalists were happy to see the “games” of mathematics coalesce into one übergame, whereas Platonists hoped that logic would eventually reveal a single metaphysical origin to mathematics.
Logic and Mathematics
Logic has long concerned itself with concepts and propositions, and by making valid inferences from the relationships between propositions. For example, a syllogism is a form a reasoning in which a conclusion is drawn from two given premises of a certain form. For instance, all cats are mammals, all mammals have four legs, therefore all cats have four legs is a syllogism. Symbolically, this line of reasoning can be denoted as “every X is a Y; every Y is a Z; therefore, all Xs are Zs.” One cannot help but notice the parallels between symbolic logic and mathematics.
In the 1700s, Gottfried Wilhelm Leibniz, famous for formulating calculus independently of Newton, and the ensuing bitter dispute over priority, envisioned a characteristica universalis, which was a system to compute the truth or falsity of any statement symbolically. However, his formulation had issues — the vagueness of what might constitute an “alphabet of thought” and the difficulty of determining when thoughts are “equal” — that doomed this experiment to never really get off the ground.
In the mid-1800s, Augustus DeMorgan began to make strides with the algebraization of logic, including quantifying the predicate. George Boole, who corresponded with DeMorgan since 1842, published two influential books, The Mathematical Analysis of Logic, and The Laws of Thought, which together transformed logic into a type of algebra.
Friedrich Frege wrote two more notable books, the Begriffsschrift and the Grundgesetze der Arithmetic, in which he set out to prove the truths of arithmetic from a few axioms of logic. He wanted to show that even the natural numbers could be reduced to logical constructs, and build from these concepts to show the truth of arithmetic. Although it was a brilliant idea to prove arithmetic from basic concepts, his execution was fatally flawed — one of his axioms, known as Basic Law V, was shown by Bertrand Russell to lead to a contradiction.
Despite this flaw, Russell believed that deriving arithmetic from logic was the correct approach. He wrote, along with Alfred North Whitehead, the Principia Mathematica, still considered as one of the most influential books in the history of logic. Russell indeed successfully fixed Basic Law V, but in a highly artificial and convoluted way.
Eventually the paradoxes were more elegantly eliminated by Ernst Zermelo and Abraham Fraenkel by axiomatizing set theory in a self-consistent way. This seemed to give mathematics a kind of objective certainty, giving the Platonists a long sought after victory. However, once again, one of the axioms, this time the so-called axiom of choice, proved to be problematic.
The axiom of choice states that if X is a collection of nonempty sets, then we can choose one element in each set in X to form a new set Y. There is no controversy when considering finite sets since one can easily see, for instance, that for a hundred boxes, each containing at least one marble, one can take one marble from each box to form a new set of a hundred marbles. Extending this notion, we can see that the axiom must be true even for countably infinite sets. However, in the case of uncountably infinite sets, we cannot even define how such a choice could be made.
Similar to the days of Euclid’s fifth axiom, mathematicians attempted to either prove or refute the axiom of choice from the other axioms. In the 1930s, Kurt Gödel showed that the axiom of choice can neither be proved nor disproved from the other Z-F axioms.
The next phase of the debate was initiated by David Hilbert, the Formalist, who believed mathematics was no more than a collection of meaningless formulae. His ambitious program was to show the correctness of mathematics using mathematical methods (so-called “metamathematics”). As he said, “My investigations in the new grounding of mathematics have as their goal nothing less than this: to eliminate, once and for all, the general doubt about the reliability of mathematical inference…Everything that previously made up mathematics is to be rigorously formalized, so that mathematics proper or mathematics in the strict sense becomes a stock of formulae…In addition to this formalized mathematics proper, we have a mathematics that is to some extent new: a metamathematics that is necessary for securing mathematics, and in which — in contrast to the purely formal modes of inference in mathematics proper — one applies contextual inference, but only to prove the consistency of the axioms…Thus the development of mathematical science as a whole takes place in two ways that constantly alternate: on the one hand we derive provable formulae from the axioms by formal inference; on the other, we adjoin new axioms and prove their consistency by contextual inference.”
Once again, enter Gödel. As a teenager, he had become fascinated by Russell and Whitehead’s Principia Mathematica and by Hilbert’s program. For his dissertation, he chose to determine whether Hilbert’s formal approach was sufficient to produce mathematics. A year after being awarded his dissertation, he dropped the bomb in the form of Gödel’s “Incompleteness Theorem.” From Livio: “…the incompleteness theorems proved that Hilbert’s formalist program was essentially doomed from the start. Gödel showed that any formal system that is powerful enough to be of any interest is inherently either incomplete or inconsistent. That is, in the best case, there will always be assertions that the formal system can neither prove nor disprove. In the worst, the system would yield contradictions.”
For a technical explanation of the Gödel’s Incompleteness Theorem, please refer to this article by Jørgen Veisdal.
Modern Views
One suspects that most professional mathematicians go about their daily work without becoming mired in philosophical meta-discussions of their favorite subject. As Philip Davis and Reuben Hersch say in The Mathematical Experience, “the typical mathematician is a Platonist on weekdays and a formalist on Sundays.”
Some twentieth century mathematicians did indeed have strong views in one camp or the other. For instance, G. H. Hardy gives a strong Platonist persective in his A Mathematician’s Apology, whereas Edward Kasner and James Newman describe the opposite Formalist view in Mathematics and the Imagination.
On the Platonist side, some people believe that mathematics exists not in some kind of metaphysical realm, but is baked into the physical world. For instance, Max Tegmark, the MIT astrophysicist, takes the view that “our universe is not just described by mathematics — it is mathematics.” He argues that external physical reality exists independently of humans, then examines what the nature of the “theory of everything” of such a reality, states that such a description must be free of any human “baggage” (such as language), then concludes that such a final theory cannot consist of any human constructs, and therefore the only possible description of the cosmos is one that only involves abstract concepts and their relations, i.e., mathematics. Livio fails to be impressed by this chain of reasoning, claiming that Tegmark in effect assumes his conclusion.
Livio also mentions a number of neuroscientists, such as Jean-Pierre Changeux, and Lakoff and Núñez, that take the view that mathematics is a human construction of the human brain.
So what does the author think? Livio concludes the book by stating that the question of whether mathematics is invented or discovered is misleading, since it implies that mathematics must be either one or the other. His view is that mathematics is both invented and discovered. The mathematical concepts and definitions are invented, whereas the logical consequences of these concepts are discovered.
Conclusion
In this article, I’ve necessarily given you only the highlights of the book. I have skipped over much of the biographical material and the more technical aspects of the debates, which are well worth delving into. I encourage you to read it for yourself. Enjoy!
Read more at medium.com
****
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principiascientificinternational--2020-03-12--The Hidden Military Use of 5G Technology

While previous technologies were finalised to produce ever more advanced smartphones , 5G is designed not only to improve their performance , but mainly to connect digital systems that need huge amounts of data to operate automatically .
The most important applications of 5G will be realized not in the civilian field , but in the military field .
The possibilities offered by this new technology are explained in the report Defense Applications of 5G Network Technology , published by the Defense Science Board , a federal committee that provides scientific advice to the Pentagon : “ The emerging 5G @ @ @ @ @ @ @ Department of Defense the opportunity to benefit at minor costs from the benefits of this system for its own operational requirements ” .
In other words , the 5G commercial network , carried out by private companies , will be used by the US armed forces at a much lower cost than would be necessary if the network were carried out solely for military purposes .
Military experts predict that 5G will play a key role in the use of hypersonic weapons : missiles , including those armed with nuclear warheads , that @ @ @ @ @ @ @ 5 ( 5 times the speed of sound ) .
To guide them on variable trajectories , by changing course in a fraction of a second to avoid interceptor missiles , it is necessary to collect , develop and transmit huge amounts of data in very fast times .
The same is necessary to activate defences in the event of an attack with such weapons : since there is no time to make a decision , the only possibility is to rely on automatic 5G systems .
The new technology will also have @ @ @ @ @ @ @ .
Being able to connect millions of transmitter-receiver devices in a limited area at the same time , it will enable the military – departments and individuals – to transmit maps , photos and other information on the current operation to each other in near real time .
Extremely important will also be the G5 for secret services and special forces .
It will make possible much more effective control and espionage systems than those of today .
It will increase the lethality of killer drones and war robots , giving them the @ @ @ @ @ @ @ people based on facial recognition and other characteristics .
The 5G network , being a high-tech warfare instrument , will automatically also become the target of cyber attacks and war actions carried out with new generation weapons .
In addition to the United States , this technology is being developed by China and other countries .
International 5G litigation is therefore not only commercial .
The military implications of 5G are almost completely ignored because even critics of this technology , including various scientists , focus their attention on the harmful effects on @ @ @ @ @ @ @ to low frequency electromagnetic fields .
This commitment is of the utmost importance , but it must be united with the one against the military use of this technology , indirectly financed by ordinary users .
One of the greatest attractions , which will promote the diffusion of 5G smartphones , will be to be able to participate , by paying a subscription fee , in war games of impressive live realism with players from all over the world .
In this way , without realizing it , the players will finance the @ @ @ @ @ @ @ one .

While previous technologies were finalised to produce ever more advanced smartphones, 5G is designed not only to improve their performance, but mainly to connect digital systems that need huge amounts of data to operate automatically. The most important applications of 5G will be realized not in the civilian field, but in the military field.
The possibilities offered by this new technology are explained in the report Defense Applications of 5G Network Technology, published by the Defense Science Board, a federal committee that provides scientific advice to the Pentagon: “The emerging 5G technology, commercially available, offers the Department of Defense the opportunity to benefit at minor costs from the benefits of this system for its own operational requirements”.
In other words, the 5G commercial network, carried out by private companies, will be used by the US armed forces at a much lower cost than would be necessary if the network were carried out solely for military purposes.
Military experts predict that 5G will play a key role in the use of hypersonic weapons: missiles, including those armed with nuclear warheads, that travel at a speed greater than Mach 5 (5 times the speed of sound).
To guide them on variable trajectories, by changing course in a fraction of a second to avoid interceptor missiles, it is necessary to collect, develop and transmit huge amounts of data in very fast times.
The same is necessary to activate defences in the event of an attack with such weapons: since there is no time to make a decision, the only possibility is to rely on automatic 5G systems.
The new technology will also have a key role in the battle network. Being able to connect millions of transmitter-receiver devices in a limited area at the same time, it will enable the military – departments and individuals – to transmit maps, photos and other information on the current operation to each other in near real time.
Extremely important will also be the G5 for secret services and special forces. It will make possible much more effective control and espionage systems than those of today. It will increase the lethality of killer drones and war robots, giving them the ability to identify, track and strike people based on facial recognition and other characteristics.
The 5G network, being a high-tech warfare instrument, will automatically also become the target of cyber attacks and war actions carried out with new generation weapons.
In addition to the United States, this technology is being developed by China and other countries. International 5G litigation is therefore not only commercial. The military implications of 5G are almost completely ignored because even critics of this technology, including various scientists, focus their attention on the harmful effects on health and the environment due to exposure to low frequency electromagnetic fields.
This commitment is of the utmost importance, but it must be united with the one against the military use of this technology, indirectly financed by ordinary users. One of the greatest attractions, which will promote the diffusion of 5G smartphones, will be to be able to participate, by paying a subscription fee, in war games of impressive live realism with players from all over the world. In this way, without realizing it, the players will finance the preparation for war, the very real one.


principiascientificinternational--2020-03-11--A Reality Check On Electric Cars: Arithmetic Required

During the Obama Administration a regulation was passed requiring all automobile manufacturers to achieve an average efficiency for all their vehicles of 54 miles per gallon by the year 2025 .
President Trump recently canceled the ordinance recognizing such a requirement could never be reached without sacrificing the safety of the drivers which we will attempt to explain .
A simple tutorial requiring a little arithmetic follows , and the fallacy of the benefits of electric cars will slowly dissolve .
The energy in gasoline is not appreciated .
An automobile that gets 40 miles per gallon uses only six @ @ @ @ @ @ @ As good as that sounds , cars can not be perfectly efficient .
There must be friction resistance just to get them going and there is no avoidance of aerodynamic resistance .
Sports cars tend to have smoother machined parts that does reduce friction and account for the greater cost .
This is true in bicycles as well .
On a bicycle your body will feel the difference between a $ 500 bicycle and a $ 2500 bicycle .
In a car there is a practical limitation to achieving higher burn temperatures in @ @ @ @ @ @ @ efficiencies for converting chemical energy to mechanical energy .
Higher burn temperatures are accomplished in Diesel engines , but the higher temperatures also requires a heavier engine block .
They are super efficient for trucks , trains and ships where the cargo weights are large .
More weight eventually means lower miles per gallon for autos .
There is an efficiency calculation that applies to all normal personal vehicles .
It is energy per unit distance per unit weight .
For example , it may be stated in kilowatt-hours ( kWh ) per @ @ @ @ @ @ @ ( t ) ( 2000 pounds ) .
The majority of all consumer purchased gasoline-fueled cars utilize about 0.65 kWh/mi/t .
Some of the heavier , more efficient cars , ( less friction from high performance parts ) achieve close to 0.6 kWh/mi/t , which is nearly an 8 % improvement .
That tonnage must include the weight of the driver and whatever he/she is transporting .
A gallon of gasoline will normally produce 34 kWh of energy .
Divide the 34 kWh by the highway miles per gallon ( mpg ) , @ @ @ @ @ @ @ weight ” in tons and add a tenth of a ton ( 200 pounds ) for the driver to that curb weight .
A car , for example , that achieves 38 mpg and has a curb weight of 2600 pounds achieves 0.64 kWh/mi/t .
That is an excellent car .
If the car weighs more ( and good luxury cars weigh more than 3400 pounds ) , the technological advantages must be enhanced to achieve kWh/mi/t values of 0.60 to 0.65 .
For the same high standards of engineering , and 54 @ @ @ @ @ @ @ by the Obama administration , the car ’ s curb weight must be limited to less than 2000 pounds .
That ’ s a bitter reality .
Many good engineers strongly believed the Obama effort to get cars to 54 mpg , was to put it bluntly , going to create death traps .
Enter the all-electric car .
It is deceptive to employ “ miles per gallon EQUIVALENTS ” as being comparable to the true miles per gallon for a gasoline ( or a gasoline-battery hybrid ) engine .
Purveyors of all @ @ @ @ @ @ @ flows into their batteries from the wall socket at home or from a charging station as if it were a faucet of free energy .
An accountant would be fired for such an omission .
For each 10 kWh that flows from the socket , there are about 33 kWh of stored chemical energy in the coal or natural gas that must be burned back in the local power plant .
The kWh that is used in the correct application of an efficiency calculation is supposed to be the ultimate source of the @ @ @ @ @ @ @ equivalent coming from the socket .
So the 110 to 120 MPG equivalent values that we are so often told for electric vehicles turns out to be only 37 to 40 MPG equivalent for all the source energy .
One can claim 110 MPG equivalent , only if one has his/her own solar collection system with battery storage , and charging facilities .
Tesla doesn ’ t dare suggest that buyers should buy the car PLUS the solar unit .
Without this pairing , there is only a very slight reduction in carbon @ @ @ @ @ @ @ have electric cars with longer range , has resulted in the elimination of mpg quotes in the range of 110 to 120 MPG equivalents .
In fact MPG is now rarely even mentioned , only the extended ranges .
So much battery weight is being added that the reduction in engine weight of an electric car is no longer a valid positive argument .
The true source energy per mile per ton may become lower , but only because the total tonnage has increased .
Eight hundred pounds of extra battery weight to @ @ @ @ @ @ @ the equivalent of carrying four extra passengers at all times .
The additional battery weight is not the equivalent of useful cargo .
The gasoline-battery hybrids ( without plug-in ) such as the Prius are definitely more efficient .
They can achieve close to 0.5 kWh/mi/t , when reaching 50 miles per gallon .
The Prius is definitely not a sport car .
It has low weight and near-minimum required power .
It is superbly engineered to achieve the goals of high miles per gallon ( low source energy per mile ) , @ @ @ @ @ @ @ than for any similar sized gasoline powered car .
With the longer range all-electric ( battery ) car , designers will never achieve a total weight that approaches 0.5 kWh of source energy per mile per ton .
William T. Lynch PhD is a retired Department Head from Bell Telephone Laboratories , with lifetime expertise in all areas of energy modeling , performance metrics , solar and nuclear energy , atmospheric modeling , and semiconductor processing and electronics .
PRINCIPIA SCIENTIFIC INTERNATIONAL , legally registered in the UK as a company incorporated for @ @ @ @ @ @ @ Old Gloucester Street , London WC1N 3AX .
Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method .

A Reality Check On Electric Cars: Arithmetic Required
Written by Bill Lynch and Dr. Jay Lehr
During the Obama Administration a regulation was passed requiring all automobile manufacturers to achieve an average efficiency for all their vehicles of 54 miles per gallon by the year 2025. President Trump recently canceled the ordinance recognizing such a requirement could never be reached without sacrificing the safety of the drivers which we will attempt to explain.
A simple tutorial requiring a little arithmetic follows, and the fallacy of the benefits of electric cars will slowly dissolve.
The energy in gasoline is not appreciated. An automobile that gets 40 miles per gallon uses only six tablespoons of gasoline traveling each mile. As good as that sounds, cars cannot be perfectly efficient. There must be friction resistance just to get them going and there is no avoidance of aerodynamic resistance. Sports cars tend to have smoother machined parts that does reduce friction and account for the greater cost. This is true in bicycles as well. On a bicycle your body will feel the difference between a $500 bicycle and a $2500 bicycle.
In a car there is a practical limitation to achieving higher burn temperatures in the engine in order to increase thermodynamic efficiencies for converting chemical energy to mechanical energy. Higher burn temperatures are accomplished in Diesel engines, but the higher temperatures also requires a heavier engine block. They are super efficient for trucks, trains and ships where the cargo weights are large. More weight eventually means lower miles per gallon for autos.
There is an efficiency calculation that applies to all normal personal vehicles. It is energy per unit distance per unit weight. For example, it may be stated in kilowatt-hours (kWh) per mile (mi), per ton (t) (2000 pounds). The majority of all consumer purchased gasoline-fueled cars utilize about 0.65 kWh/mi/t. Some of the heavier, more efficient cars,(less friction from high performance parts) achieve close to 0.6 kWh/mi/t, which is nearly an 8% improvement. That tonnage must include the weight of the driver and whatever he/she is transporting.
A gallon of gasoline will normally produce 34 kWh of energy. Divide the 34 kWh by the highway miles per gallon (mpg), and then divide by the “curb weight” in tons and add a tenth of a ton (200 pounds) for the driver to that curb weight. A car, for example, that achieves 38 mpg and has a curb weight of 2600 pounds achieves 0.64 kWh/mi/t. That is an excellent car. If the car weighs more (and good luxury cars weigh more than 3400 pounds), the technological advantages must be enhanced to achieve kWh/mi/t values of 0.60 to 0.65.
For the same high standards of engineering, and 54 miles per gallon that was being required by the Obama administration, the car’s curb weight must be limited to less than 2000 pounds. That’s a bitter reality. Many good engineers strongly believed the Obama effort to get cars to 54 mpg, was to put it bluntly, going to create death traps.
Enter the all-electric car. It is deceptive to employ “miles per gallon EQUIVALENTS” as being comparable to the true miles per gallon for a gasoline (or a gasoline-battery hybrid) engine. Purveyors of all electric cars, treat the electricity that flows into their batteries from the wall socket at home or from a charging station as if it were a faucet of free energy.
An accountant would be fired for such an omission. For each 10 kWh that flows from the socket, there are about 33 kWh of stored chemical energy in the coal or natural gas that must be burned back in the local power plant. The kWh that is used in the correct application of an efficiency calculation is supposed to be the ultimate source of the energy, not a deceptive free gallons equivalent coming from the socket.
So the 110 to 120 MPG equivalent values that we are so often told for electric vehicles turns out to be only 37 to 40 MPG equivalent for all the source energy. One can claim 110 MPG equivalent, only if one has his/her own solar collection system with battery storage, and charging facilities. Tesla doesn’t dare suggest that buyers should buy the car PLUS the solar unit. Without this pairing, there is only a very slight reduction in carbon dioxide emissions.
The latest push to have electric cars with longer range, has resulted in the elimination of mpg quotes in the range of 110 to 120 MPG equivalents. In fact MPG is now rarely even mentioned, only the extended ranges. So much battery weight is being added that the reduction in engine weight of an electric car is no longer a valid positive argument. The true source energy per mile per ton may become lower, but only because the total tonnage has increased. Eight hundred pounds of extra battery weight to increase range, for example, is the equivalent of carrying four extra passengers at all times. The additional battery weight is not the equivalent of useful cargo.
The gasoline-battery hybrids (without plug-in) such as the Prius are definitely more efficient. They can achieve close to 0.5 kWh/mi/t, when reaching 50 miles per gallon. The Prius is definitely not a sport car. It has low weight and near-minimum required power. It is superbly engineered to achieve the goals of high miles per gallon (low source energy per mile), and one pays considerably more for it than for any similar sized gasoline powered car.
With the longer range all-electric (battery) car, designers will never achieve a total weight that approaches 0.5 kWh of source energy per mile per ton.
William T. Lynch PhD is a retired Department Head from Bell Telephone Laboratories, with lifetime expertise in all areas of energy modeling, performance metrics, solar and nuclear energy, atmospheric modeling, and semiconductor processing and electronics.
Dr Jay Lehr contributes posts at the CFACT site. Jay Lehr is a Senior Policy Analyst with the International Climate Science Coalition, and he is the author of more than 1,000 magazine and journal articles and 36 books.
Read more at CFACT http://www.cfact.org/
PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX.
Please DONATE TODAY To Help Our Non-Profit Mission To Defend The Scientific Method.
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