This program was recorded at the 12th Annual Wonderfest, the San Francisco Bay Area Festival of Science.
Wonderfest's broad goals are best described by its mission statement: Through public discourse about provocative scientific questions, Wonderfest aspires to stimulate curiosity, promote careful reasoning, challenge unexamined beliefs, and encourage life-long learning.
Wonderfest achieves these ends by presenting series of scientific events to the general public. At most of these events, pairs of articulate and accomplished researchers discuss and debate compelling questions at the edge of scientific understanding.
Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science.
His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 28 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award.
In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.
Alejandro Garcia is a professor of physics at San Jose State University.
Euler's Equation and the Reality of Nature.
Mr. Dexter Sinister wrote:
' I understand Euler's Identity,
and I know what it means, and I know how to prove it,
there's nothing particularly mystical about it,
it just demonstrates that exponential, trigonometric,
and complex functions are related.
Given what we know of mathematics it shouldn't surprise
anyone that its various bits are connected.
It would be much more surprising if they weren't, that would
almost certainly mean something was badly wrong somewhere.'
Mr. Gary wrote:
Mathematics is NOT science.
Science is knowledge of the REAL world.
Mathematics is an invention of the mind.
Many aspects of mathematics have found application
in the real world, but there is no guarantee.
Any correlation must meet the ultimate test:
does it explain something about the real world?
As an electrical engineer I used the generalized
Euler's equation all the time in circuit analysis:
exp(j*theta) = cos(theta) + j*sin(theta).
So it works at that particular level in electricity.
Does it work at other levels, too?
Logic cannot prove it.
It must be determined by experiment, not by philosophizing.
Thinking about theirs posts I wrote brief article:
Euler's Equation and Reality.
Euler's Equation as a mathematical reality.
Euler's identity is "the gold standard for mathematical beauty'.
Euler's identity is "the most famous formula in all mathematics".
' . . . this equation is the mathematical analogue of Leonardo
da Vinci's Mona Lisa painting or Michelangelo's statue of David'
'It is God's equation.', ' It is a mathematical icon.'
. . . . etc.
Euler's Equation as a physical reality.
"it is absolutely paradoxical; we cannot understand it,
and we don't know what it means, . . . . .'
' Euler's Equation reaches down into the very depths of existence'
' Is Euler's Equation about fundamental matters?'
'It would be nice to understand Euler's Identity as a physical process
' Is it possible to unite Euler's Identity with physics, quantum physics ?'
My aim is to understand the reality of nature.
Can Euler's equation explain me something about reality?
To give the answer to this question I need to bind
Euler's equation with an object - particle.
Can it be math- point or string- particle or triangle-particle?
No, Euler's formula has quantity (pi) which says me that
the particle must be only a circle .
Now I want to understand the behavior of circle - particle and
therefore I need to use spatial relativity and quantum theories.
These two theories say me that the reason of circle - particle's
movement is its own inner impulse (h) or (h*=h/2pi).
Using its own inner impulse (h) circle - particle moves
( as a wheel) in a straight line with constant speed c = 1.
We call such particle - 'photon'.
From Earth - gravity point of view this speed is maximally.
From Vacuum point of view this speed is minimally.
In this movement quantum of light behave as a corpuscular (no charge).
Using its own inner impulse / intrinsic angular momentum
( h* = h / 2pi ) circle - particle rotates around its axis.
In such movement particle has charge, produce electric waves
( waves property of particle) and its speed ( frequency) is : c>1.
We call such particle - ' electron' and its energy is: E=h*f.
In this way I (as a peasant ) can understand the reality of nature.
I reread my post.
My God, that is a naïve peasant's explanation.
It is absolutely not scientific, not professor's explanation.
Would a learned man adopt such simple and naive explanation?
Hmm, . . . problem.
In any way, even Mr. Dexter Sinister and Mr. Gary
wouldn't agree with me, I want to say them
' Thank you for emails and cooperation'
Israel Sadovnik Socratus.
' They would play a greater and greater role in mathematics -
and then, with the advent of quantum mechanics in the twentieth
century, in physics and engineering and any field that deals with
cyclical phenomena such as waves that can be represented by
complex numbers. For a complex number allows you to represent
two processes such as phase and wavelenght simultaneously -
and a complex exponential allows you to map a straight line
onto a circle in a complex plane.'
/ Book: The great equations. Chapter four.
The gold standard for mathematical beauty.
Euler's equation. Page 104. /
Euler's e-iPi+1=0 is an amazing equation, not in-and-of itself,
but because it sharply points to our utter ignorance of the
simplest mathematical and scientific fundamentals.
The equation means that in flat Euclidean space, e and Pi happen
to have their particular values to satisfy any equation that relates
their mathematical constructs. In curved space, e and Pi vary.
/ Rasulkhozha S. Sharafiddinov . /
Time, Space and Quantum of Light. / My opinion./
Can Time Exist Without Matter?
1. According to Newton the answer is " Yes"
2. According to Einstein (SRT & GRT ) the answer is " No"
Who is right? Who is wrong?
What is the resolution of this apparent paradox?
There are four kinds of time:
a) the proper (individual) time
b) the planetary time
c) according to SRT the ( -4D) spacetime
d) and according to GRT relative time.
How can we unite them?
The individual time and planetary time
are so familiar that we rarely give them thought.
Don't we know, that time for living being is limited
and the planetary time is absolute for us ? It is.
Maybe therefore Newton declared that time is absolute
and wrote in 1687 that time " flows equably without relation
to anything external". But Einstein had another opinion.
He wanted to know: " Where does the conception of time
come from?", " What is the essence of time?".
And to explain these questions he created two theories:
SRT and GRT and declared that time is relative, changeable.
SRT explains behavior and the proper time of light
quanta /electron. Why do I think so?
One law (postulate) of SRT says that speed of light quanta
is constant c=1. Second law ( postulate ) says no another particle
can reach this speed. So there are two incommensurable
quantities. Is it possible to bind them together? No. I was
taught at school from the first class that the incommensurable
quantities cannot be compared. The connection between these
incommensurable quantities is similar to the decision of a
problem: "What will be if the whale attacks the elephant?"
We can see whale in a ocean and elephant in a savanna,
but they never meet and fight in the same " frame of reference".
And the same is about light quanta and another particles.
We cannot see them together in SRT. We can meet only the
light quanta in SRT and no other particles in it.
SRT was born from Maxwell's theory and it is a continuation
of the electrodynamics' development . The electron is a main
and single hero in the Maxwell's theory and SRT. There
isn't the Maxwell's theory / SRT without electron.
It is not correct to compare electron/ light quanta with another
particles (protons...etc) and bodies (billiard balls, satellites,
astronauts, "twins") because they cannot produce electromagnetic
fields. The electron and the another particles are also incommensurable
quantities. They are absolutely different objects.
Every epoch has its own delusion. Maxwell and Boltzmann
tried to explain electromagnetic fields using balls, wheels,
cog-wheels, springs...etc. H. Hertz, who demonstrated the
existence of the electromagnetic waves, wrote that the
electromagnetic waves didn't have practice use. Etc....
Now we try to compare electron/photon
ability with astronaut's and "twins' " opportunities.
It is mistaken, but what to do? We do it because this is
our way of cognition:
" From vague wish to the bright thought".
So, how SRT explains time from electron/ light quanta point of view.
When light quanta is in state of a rest its time is frozen,
and its own clock shows zero.
When photon moves with constant speed c=1
its time is also frozen, and its own clock still shows zero.
Only when photon moves with speed c>1 its zero time
changes and limited time appears. In this situation we
know photon as an electron. Photon works as an electron
and SRT and Lorentz transformations explain this process.
And when , for example, electron emits from an atom and
interacts with Vacuum all its parameters change. Its limited
time ends and its own clock shows zero again. Now it lives
in infinite/ eternal Vacuum until new incarnation, until its new
work, maybe, in an atom (molecule), or in a cell, maybe, in a blade
of grass or in a tree, maybe, in an animal or in a person.
In another words:" We are living beings until Light quanta/
Electron is present and works in our body."
Is it true? Yes, it is true. Why?
Because W. Pauli in 1924 wrote:" Each quantum state in the atom
is not limited of two electrons, but only one electron".
It means in the atom can be only one, single electron.
The electron manages the atom. If the atom contains more
than one electron (for example - two), this atom represents
" Siamese twins". Save us God of having such atoms and cells.
And the living being begins its life from one, singe cell.
What I am introducing here is what ' thinking photon/ electron' exist .
I applied the quantum of light/ photon/ electron with a consciousness.
And His own consciousness is not static but can develop.
The development of conscious scale goes
" from vague wishes up to a clear thought ".
This evolution proceeds during hundred millions (billion) years.
Trying to understand " the electrodynamics of moving bodies"
Einstein wrote that it is the result of time and space changes.
It is not exactly correct , because these changes are secondary
in SRT. And the first point of SRT is that Quantum of light changes
its spin. The former Planck/ Einstein's spin (h) changes in Goudsmit /
Uhlenbeck's spin (h = h / 2pi), and as a result of this act all its parameters
change and the time and new space appear.
GRT explains the conditions of gravitation and the secret of
planetary time. Why do I think so?
When Einstein worked on GRT, he asked astronomers:
" What is the average mass of matter in the Universe?"
The result was lamentable. The quantity of mass was
insignificantly small. It was impossible to keep gravitation
law with such insignificantly little mass and so, the Universe
must be "open", endless. But what to do with the infinite
space, Einstein didn't know. Therefore he took (from the
heaven) " the cosmological constant" in order to "close"
the Universe. The taken mass was enough for creating the
condition of gravitation. Without " the cosmological constant"
the Universe is endless.
In 1922 Friedman wrote, that we could not take " the
cosmological constant" in calculation. Instead of it, it is
enough to take "time" and the Universe will be "closed".
Friedman was correct, but why? Because "time", by its
nature, is a limited physical quantity and, be taken in
mathematical calculation, automatically gives "closed" result.
So, the detected material mass of the
matter in the Universe is so small (the average density
of all substance in the Universe is approximately
p=10^-30 g/sm^3) that the gravitation law doesn't work.
Astronomers and astrophysicists know about this fact and
therefore (to save the gravitation law) invented new matter
a "dark matter", a new energy a "dark energy" and another
abstract objects. This " invention" is only a result of our
mentality , which says: " If in a theory you meet infinity it
means the theory is nonsense". It is very hard to take that
the Universe is infinite. It is no easy matter to give up
a lifetime of habit .
In my opinion it is impossible to use GRT to Universe as
a whole. The Newton/ Einstein's gravitation laws are correct
only in the local parts of Vacuum. The Universe / Vacuum
as a whole is endless.
So, how does GRT explain time?
According to GRT the time depends on the mass
and speed it means, of moving matter.
It means that different masses and speeds can create
different time. For example, our planet Earth has its
own time but for us it is absolute.
The other planets have another mass and speed and
therefore they have their own time. This time according
to GRT is relative. But their habitants will think that their
time is absolute. But if they know GRT they will
not make this mistake.
According to SRT and GRT time is relative.
SRT says about proper/ individual time of an
electron/ light quanta.
GRT says about planetary time of a Planet..
The time cannot exist without matter and speed,
in another words, without moving matter. But
different reasons and different moving of a matter
create the proper and planetary time.
Is it possible to see the different manifestation of
time in a human being?
Here is an article " Even the time is pressed from fear"
by Dr. Vadim Chernobrov (collaborator of MAI -
- Moscow Aviation Institute).
He wrote, that we usually think time is a constant quality.
But Einstein's relative theory says time is relative.
Question. Is it possible to check it in our life?
Answer. Russian and foreign researches say it is
possible. The documents (secret in the past) testify
that "cataclysm of time", " phenomenon of time's
perversion "," the changes (its deceleration) of time"
often is observed by people whose profession connected
with risk: astronauts, pilots, drivers, soldiers.
The test pilot Mark Gallay wrote in his book
"The test in the sky" when his airplane was caught
with fire " the time began to go in another scale. The time
almost stopped. Every second took ability of expansion,
and in this situation it was possible to do many things."
He confirms that tested such feeling many times.
The test pilot Marina L. Popovich said the same,
in the dangerous, catastrophic situations " the time
In June 1989 the soviet airplane MIG-29 crashed near
Paris, in Le Bourget airport , in the time of its air show.
The notes of "the black box" showed that during the
four (4)seconds the test pilot Anatoly Kvochur made as
many operations as in normal situation it would take some
minutes. The test pilot later said: " the time was stretched".
The captain N.Z.(fought in Afghanistan) remembers:
"the fly of the bullet was so beautiful that I didn't guess
to evade from it, although I have enough time to do it".
The sergeant V. Ch (fought in Afghanistan) told:
" The black barrel of gun seems very big, even enormous.
Time is stopped and full silence came. And I moved slowly
a step a side and saw as the bullet passed close to me."
The people in a critical situation, on the border of death,
suddenly for themselves begin to see everything as in the
slow down film and in this time their speed reaction and
power increase in tens and hundreds times. And this explains:
a) why a man who escaped from wolves, can quickly reach
up the top of the naked tree,
b) an old woman took out a big trunk from her burned house,
which later two strong firemen couldn't rise.
The speed on the curve was so fast that to keep the balance of
the car I went on other road line and flew straight at the
"forehead' of a green mercedes. The driver of the mercedes
was in panic, in horror. He threw the wheel and closed his face
with his hands. Suddenly the time stopped and the sound disappeared
for me and I made many actions before my car kicked only the side
back door of the mercedes. It was long time ago, but writing this article
I understood better what happened.
Our computer-brain works on a dualistic basis (on two different neurons
systems): 1) usually under logic program,
2) sometimes on intuition (subconscious).
Brain of a man approximately consists of sixteen milliards neurons.
All of them form the system that manages human body.
That is why that with the work of all the sixteen milliards neurons
of brain, a man cannot catch a single impulse of his Electron, of his
Quantum of light, of his Soul:
(mass of electron is equal 10^-31 kg., charge of electron is equal 10^-19 k.)
But in that time ( critical time ) most neurons of my brain stopped
their electric pulse (time almost stopped) and my Light Quanta/Electron
in this new condition (superconductivity) had possibility to increase
my speed reaction and power on a short period of time . So, as SRT says,
the Light Quanta in different systems ( even in the brain) can show us
a different Time. The Light Quanta plays major role in the Nature,
in the Physics, in our Life.
Israel Sadovnik. Socratus.
It's hard not to take offense as a mathematician by Alejandro's take on the field. Basically, the more "pure"-oriented mathematicians, whose work is obviously arcane to him, are the only people he would consider to be mathematicians. All other math is "not real math," and is some kind of... for lack of a better word, application of a science. That point in and of itself seems to jump out as an obvious contradiction with his thesis.
I don't see how you can separate "whether math works" from "whether math works in the universe." It's kind of like saying that if you haven't found an application of an algorithm, then there is no application of that algorithm. Not only myopic, almost tautologically wrong. Very little respect earned for Alejandro today.