Mathematics Provides More Information Than You Think

"Mathematics is in fact ideally suited to prepare the mind for higher
forms of thought because on the one hand it pertains to the world of
visible things and on the other hand it deals with abstract concepts.
Hence through the study of mathematics man learns to pass from
concrete figures to abstract forms, moreover, this study purifies the
mind by drawing it away from the contemplation of the sensible and
perishable and leading it to eternal ideas." Kline (36)
"A few years ago, I was giving a talk at Cornell University. One of my PowerPoint
slides read: 'Is God a mathematician?' ... My rhetorical question was neither a
philosophical attempt to define God for my audience nor a shrewd scheme to
intimidate the math phobics. Rather, I was simply presenting a mystery with which
some of the most original minds have struggled for centuries - the apparent
omniscience and omnipotent powers of mathematics. These are the type of
characteristics one normally associates only with a deity. As the British physicist
James Jeans (1877-1946) once put it: 'The universe appears to have been designed
by a pure mathematician.' Mathematics appears to be almost too effective in
describing and explaining not only the cosmos at large, but even some of the most
chaotic of human enterprises ... What gives mathematics such incredible powers? Or
as Einstein once wondered: 'How is it possible that mathematics, a product of
human thought that is independent of experience, fits so excellently the objects of
physical reality? Livio (2)
"Mathematics is the language of mathematicians, and a proof is a
method of communicating a mathematical truth to another
person...A remarkable property of the language of mathematics is
its precision. Properly presented, a proof contains no ambiguity –
there will be no doubt to its correctness." Solow (1)

"I argue, as others have done before me, that mathematical concepts and ideas exist
objectively, outside of the physical world and outside of the world of consciousness.
We mathematicians discover them and are able to connect to this hidden reality
through our consciousness. If Leo Tolstoy had not lived we would never have known
Anna Karenina. There is no reason to believe that another author would have written
that same novel. However, if Pythagoras had not lived, someone else would have
discovered exactly the same Pythagoras theorem. Moreover, that theorem means the
same to us today as it meant to Pythagoras 2,500 years ago... Pythagoras' theorem is
about geometric shapes in an idealised space, a flat Euclidian plane which, in fact, is
not found in the real world. The real world is curved. When Pythagoras discovered his
theorem there were, of course, inferences from physical reality, and a lot of
mathematics is drawn from our experience in the physical world, but our imagination
is limited and a lot of mathematics is actually discovered within the narrative of a
hidden mathematical world. If you look at recent discoveries, they have no a priori
bearing in physical reality at all." - Edward Frenkel (Klinghoffer)

Now he is not necessarily talking about God in the way Christians, Muslims, and Jews mean
when they say God, in a monotheistic way. But Kaku is referring to a very broad, general
manner of speaking, basically ultimate reality. In 1978 Robert Jastrow, founding director of
NASA’s Goddard Institute for Space Studies wrote an article in the New York Times discussing
how scientists react to discoveries that have theological consequences entitled “Have
Astronomers Found God?” Jastrow mentions Albert Einstein’s view of God.
“We know he [Albert Einstein] had well-defined feelings about God, but not as the Creator or Prime Mover. For
Einstein, the existence of God was proven by the laws of nature; that is, the fact that there was order in the
universe, and that man could discover it. When Einstein came to New York in 1921, a rabbi sent him a telegram
asking, “Do you believe in God?” and Einstein replied, “I believe in Spinoza’s God, who reveals Himself in the
orderly harmony of what exists…” (Jastrow)
It’s in this same sense Michio Kaku is talking about the mind of God; because he talks about unifying
nature. General Relativity and quantum mechanics are not completely compatible with each other but
physicists search for a much more underlying theory that brings together relativity and quantum theory.
God for them is completeness, from this one inch equation all of the other equations of physics arise. A
theory of everything, that’s their hope. It will be presented that those who study the cosmos, who assign
numbers to properties and understand the features of the universe, eminent scientists recognize that
there exists evidence for a personal God. Jastrow began his article with some background information
about his metaphysical positions and established scientific foundations about the universe.
“When an astronomer writes about God, his colleagues assume he is either over the hill or going bonkers. In
my case it should be understood from the start that I am an agnostic in religious matters. However, I am
fascinated by some strange developments going on in astronomy…" (Jastrow)

It is reasonable to seek natural causes for natural phenomena. Laplace was correct in his response to Napoleon.
The physical scientist's aim is to discover how nature operates and
explain it and present it in the language of mathematics. Do that!
"Science is a particular way of knowing about the world. In science, explanations are
restricted to those that can be inferred from confirmable data - the results obtained through
observations and experiments that can be substantiated by other scientists. Anything that can
be observed or measured is amenable to scientific investigation. Explanations that cannot be
based on empirical evidence are not a part of science." National Academy of Sciences (27)
"Science is a way of knowing about the natural world. It is limited to explaining the natural
world through natural causes. Science can say nothing about the supernatural. Whether God
exists or not is a question about which science is neutral. National Academy of Sciences (58)
"According to legend, when Napoleon met Laplace, after glancing through Laplace's masterpiece,
Celestial Mechanics, Napoleon remarked that he found no mention of God at all in the book; to
which the author replied, 'Sir, I have no need of that hypothesis!'" Holton and Brush (253)
Science is not the only way that truth can be discovered. As is stated above "science is a way". So just
because something is outside the realm of science does not mean that it cannot be demonstrated to be
true. Logic is of vital importance when trying to extend the boundaries of human knowledge.

“On the other hand, instead of proving new theorems we may ask if it is possible to find a new
assumption, say assumption A, more basic than assumption B, so that assumption B can be proven from
A. In this way, we are pushing back the frontiers of knowledge.” Farlow (27)
The direct observations of natural phenomena may have supernatural causes.
This type of "pushing back the frontiers of knowledge" is inherently philosophical and
logical in nature since assumption B is proven from assumption A by series of logical
steps from A to B. Assumptions by definition are not empirically established.
If the laws of nature cannot be responsible for the beginning of the universe, then what
is responsible is outside of the natural, in other words, supernatural.
Writing in 1978, Jastrow wrote, "I am fascinated by some strange developments going on in astronomy…
The essence of the strange developments is that the universe had, in some sense, a beginning – that it
began at a certain moment in time, and under circumstances that seem to make it impossible – not just
now, but ever – to find out what force or forces brought the world into being at that moment..." (Jastrow)
"We know that the Universe is currently expanding and if we follow that expansion backwards we come to a
special point in time, the Big Bang, which we take to be the beginning of our Universe. But the accepted
theories of physics, Einstein's general theory of relativity and quantum physics, don't apply at that moment.
We don't have a definite theory that can describe it, only a host of candidate theories. "Some such theories
say there was no beginning and others say there was," says Ellis [George Ellis, a cosmologist from the
University of Cape Town]. "Basically we are making educated guesses. We can't do the experiments that will
tell us which is correct because we can't get to the energies that are big enough." (Freiberger and Thomas)
Over 25 years later physicists still grapple with the beginning of the universe and that the universe is stretching or expanding.

Lorentz transformations are equations used to calculate the velocity of a moving object
relative to another moving object. The mathematics of relativity theory was available, it just
needed to be applied. Albert Einstein provided the correct physical interpretation of Lorentz
transformations that led to the discovery of time dilation and length contraction.
Scientific discoveries have to be interpreted within our world
It's in the correct physical interpretation of mathematics and scientific discoveries where the
rules of logic and metaphysics comes in to play.
Our understanding of the natural world and our subsequent descriptions of reality are subject
to the rules of logic.
The universe is expanding. That is a reality that we humans have to reckon with.
We have to understand and explain why galaxies are moving apart from each other AND must
accept the mathematical consequences of that description of how and why galaxies are moving
away from each other in the same way that Einstein accepted what the mathematics
communicated to him.

In other words, the anthropic principle suggests that the values of dimensionless physical
constants were DETERMINED to have those values so eventually someone would exist to
discover their values. The universe seems to be prepared for persons to study the universe.
“The major question that still remains – if we accept the big bang cosmology in some version – is
whether the universe will continue to expand indefinitely or eventually start contracting...
“... If the universe does contract at some point in the future, it would presumably collapse into a black
hole. It might then be reborn in a new big bang. The American physicist John Archibald Wheeler has
suggested that every time this happens, the various dimensionless physical constants such as the
proton-electron mass ratio may acquire new values… So far, theoretical physicists have not been able
to explain why these dimensionless constants have the values they do. Perhaps they are random, not
determined by any law of nature. But Wheeler and other cosmologists have shown that if these
constants were very much different from their actual values in our universe, the formation of planetary
systems and the evolution of higher forms of life might be impossible. This observation has given rise
to the so-called anthropic principle suggested by Brandon Carter. One way to put it is that the reason
why the physical constants have the values they do is that if they did not, we would not be here to
measure them!” Holton and Brush (514)

“Fred Hoyle, in his autobiography, claims that his discovery of the nuclear
reactions forming carbon from three helium nuclei was an application of the
general philosophy of the anthropic principle... He believed that there must be
an explanation for his own existence as a carbon-based living organism; hence
there must be a physical process that produces carbon from lighter elements;
he just had to figure out what it was, then get a chance to check it in the
laboratory. " Holton and Brush (514)
Dimensionless physical constants have values that appear to be determined so eventually someone
would exist to discover their values. The universe appears to be specifically prepared for people to
study the universe. Astronomer Fred Hoyle, who coined the phrase “big bang”, adjusted his personal
metaphysical position from atheism to agnosticism based on the reality of dimensionless constants.

It is completely natural and quite intuitive as well as consistent with the mathematical consequences of the equations of physics to
have a perspective that there exists a causal agent for the universe’s existence and that causal agent might be a person.
So what is the experiment or syllogism that is available to us that demonstrates that the universe merely looks determined but in
actuality is random?
Why? Dimensionless physical constants have their values independently of the fundamental forces. In other words, the
fundamental forces did not cause the dimensionless constants to have the values that they currently have. The physical world
conforms to mathematical models which are quite abstract and immaterial. These mathematical models do not actually exist in
the physical world but guide how the physical world can be understood. The values of dimensionless constants appear to be
determined. That determining property suggests decision-making. Decision-making is a property of a will. A will is a property of a
mind. A mind is a property of personhood. Hoyle recognized that there exists evidence that a person who is outside of time, I'll
call that eternal, who also is outside of matter, I'll call that immaterial, or better yet, spirit, determined the parameters for life, as
we know it, to eventually come into existence . MIND PRECEDED MATTER.
"I think that there is probably a mental component to the universe. You can call it God if you like. If that is so,
then there's no reason why that this mental component shouldn't have had a hand in setting the conditions." -
Freeman Dyson, Physicist, Institute for Advanced Study, Princeton University (Closer To Truth)

Physics professor Robert M. Wald mentioned the barriers of
demonstrating that the universe came into existence randomly
"The majority of cosmologists take the view that there was nothing special about the
initial state of the Universe. But once you say that, once you say it was in some sense
randomly chosen, you've got to say what all the possibilities are from where it could
be chosen and what the probabilities are of those possibilities,… "If you want to
make some predictions about what the Universe is like now, then you need to have
some kind of probability distribution of what state it started in." (Thomas)
Professor Wald continued, “This does not work straightforwardly in
cosmology for a variety of reasons… You have an infinite space of
possibilities which has an infinite volume… Even at its simplest level,
defining probabilities becomes extremely problematical.”
Concluding, Wald broaches the “anthropic principle”,
"Most of the people who talk about probabilities in terms of the initial state of the
Universe [...] are talking about the probability that somewhere in this Universe there'll be
observers. Then the ignorance of the probability of the initial state is largely subsumed by
your ignorance of the probability of there being observers." (Thomas)
You have to explain the universe coming in to existence using natural causes while
simultaneously maintaining that the equations of physics that describe how nature
behaves are not applicable when describing the beginning of the universe . →←
If you exhaust natural resources, wouldn't resources outside of nature be the alternative?

It's true that science itself is neutral but the metaphysical consequences of scientific discoveries are not neutral.
Physical scientists in principle acknowledge that direct observation and experimentation are not the only way to
gain understanding of our world. But in practice they tend not to show a real appreciation for logic and
philosophical arguments, especially in interpreting the results of scientific inquiry.
"I think it's very important to get physicists and philosophers together," says Aguirre [Anthony Aguirre, from
the University of California at Santa Cruz]. "I think there's a reaction that a lot of my physics colleagues have
about philosophers which is that they don't know any physics. They're just saying things about physics and
they don't really know what they're talking about, and criticising physics but they don't really understand it. I
think there may once have been some truth to that and I'm sure that there is now, but the philosophers that I
talk to all know lots of physics. I see them as being specialists in thinking about the intellectual foundations of
those questions, looking at them from a slightly bigger and different point of view than a more empirically or
pragmatically engaged physicist would. I think that's incredibly valuable." (Freiberger and Thomas)
"The last few years have seen a number of prominent scientists step up to microphones and belittle the value of
philosophy. Stephen Hawking, Lawrence Krauss, and Neil deGrasse Tyson are well-known examples."
"It’s a shame that so many physicists don’t see how good philosophy of science can contribute to this quest." (Carroll)
The following quotation is by David L. Goodstein reading a letter
written by Albert Einstein about his work on gravitation to a friend:
“I have become imbued with a great respect for mathematics, the subtle
thoughts of which, in my ignorance, I had until now, regarded as pure luxury.”
As Dr. Goodstein was finishing his lecture one of his concluding remarks was:
“Physicists have a certain arrogance about mathematics... For physicists mathematics is just a tool, it’s to be used in
order to accomplish something else. But a real mathematician is the guardian of precision and clarity of thought.”
(The Mechanical Universe - And Beyond)
That is what mathematicians do – they observe patterns and develop conjectures. They attempt to either prove or disprove those
conjectures while relying on the rules of logic with a precise line of reasoning.

Physical scientists are not taking seriously the precision and clarity of thought required to understand, describe,
and interpret the natural world. It is the consequences of an expanding universe and the dimensionless constants
that are the parameters for life to appear along with the inability to empirically show that the universe came into
existence randomly (that is outside the realm of scientific inquiry) that can reasonably lead to the conclusion that
the causal agent for the universe coming into existence is a person.
Albert Einstein, Fred Hoyle, and Robert Jastrow considered their work and discoveries of their colleagues in
astronomy and cosmology and changed some of their metaphysical positions. Because they considered what it
meant. They understood that the universe having a definite beginning and dimensionless constants had
theological ramifications. They took those discoveries as evidence for the existence of God. What do you know
that those physicists didn't know that leads you the position that there is no evidence for God's existence?
"The point, I take it, is to understand how nature works. Part of that is knowing how to do calculations,
but another part is asking deep questions about what it all means." (Carroll)
As Carroll pointed out, after making scientific discoveries the question should be asked, what does this all mean.
Jastrow went a step further and said it could very well be the God that is
revealed in the bible that caused the universe to come into being.
"Now we see how the astronomical evidence leads to a biblical view of the origin of the world (the word
the Bible used to describe the universe). The details differ, but the essential elements in the
astronomical and biblical accounts of Genesis are the same: The chain of events leading to man
commenced suddenly and sharply at a definite moment in time, in a flash of light and energy." (Jastrow)
Now this evidence does not necessarily prove that a personal God exists. It's one thing to look at the evidence and
remain unconvinced either way. At least Jastrow and Hoyle as far as I know remained unconvinced to affirm that a
personal God exists. But it is something altogether different to say that there is no evidence that God exists. Such a
statement would be made by someone who has not sufficiently thought through the mathematical consequences of
the equations of physics as well as the logical and philosophical consequences of observing the natural world.
Fred Hoyle, Robert Jastrow, and Albert Einstein personally experienced that appreciation for sound reasoning.

Works Cited:
"DEBATE: Does God Exist? || Michael Jones VS Tom Jump" 00:22:50 YouTube, uploaded by Modern-Day Debate, 27 Feb
2019, youtu.be/UWCvKiWjV0g
"Kent Hovind vs Michael Shermer Debate" 01:28:30 YouTube, uploaded by PolemicContrarian, 31 May 2013,
youtu.be/K9GJmFVcfys
Freiberger, Marianne and Thomas, Rachel. "Do infinities exist in nature?". Plus Magazine, 26 Sep 2013,
plus.maths.org/content/do-infinities-exist-nature-0
Livio, Mario. Is God a Mathematician? Simon & Schuster, 2009
Jastrow, Robert. "Have Astronomers Found God?" New York Times, 25 Jun. 1978,
nytimes.com/1978/06/25/archives/have-astronomers-found-god-theologians-are-delighted-that-the.html
Kline, Morris. Mathematics for the Nonmathematician. Dover, 1985
"Kurt Gödel & the Limits of Mathematics" 00:00:20, YouTube, uploaded by Philosophy Overdose, 18 Jan
2017, youtu.be/jDyra0RH-Xs
Carroll, Sean. "Physicists Should Stop Saying Silly Things About Philosophy". Sean Carroll, 23 Jun 2014
preposterousuniverse.com/blog/2014/06/23/physicists-should-stop-saying-silly-things-about-philosophy/
"Michio Kaku: Is God a Mathematician?" 00:04:28 YouTube, uploaded by Big Think, 2 Jan
2013, youtu.be/jremlZvNDuk
Holton, Gerald and Brush, Stephen G.. Physics the Human Adventure. Rutgers University Press, 2001
Klinghoffer, David. "UC Berkeley Mathematician Edward Frenkel on the Transcendent World of Math".
Evolution News & Science Today, 19 December 2013,
evolutionnews.org/2013/12/berkeley_mathem/#sthash.2Q3idM5G.dpuf
Farlow, Stanley J. Partial Differential Equations for Scientists and Engineers. Dover, 1993
"Fred Hoyle - Astronomer Extraordinaire". Hoyle History , 19 June 2008, hoylehistory.com/famous-
hoyles/fred-hoyle/
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•
•
•
•
•
•
•
•
•
•
•
•
"Does a Fine-Tuned Universe Lead to God?". Closer To Truth, closertotruth.com/series/does-fine-tuned-universe-lead-
god
•

"Navigating Atheism While Black - On The 7 With Dr. Sean" 00:02:57 YouTube, uploaded by Fox Soul, 6 Jan
2020, youtu.be/FPCpLigg0sA
Penrose, Roger. The Emperor's New Mind. Oxford University Press, 1989
"Sir Roger Penrose & William Lane Craig • The Universe: How did it get here & why are we part of it?"
00:10:56 YouTube, uploaded by Unbelievable?, 4 Oct 2019, youtu.be/9wLtCqm72-Y
Solow, Daniel. How to Read and Do Proofs. John Wiley & Sons, 2005
Thomas, Rachel. "In the beginning...". Plus Magazine, 20 Nov 2014, plus.maths.org/content/beginning
The Mechanical Universe-- And Beyond. Dir. Mark Rothschild. Lect. David L. Goodstein. California Institute
of Technology Corporation for Community College Television, Intellimation. VHS. South Burlington, VT:
Annenberg/CPB Collection, 1987
Tweed, Matt. "A Finely Tuned Universe." Sciencia. Edited by John Martineau, Wooden Books, Ltd., 2011, pg. 376•
•
•
•
•
•
•
National Academy of Sciences. "Teaching About Evolution and the Nature of Science."
doi.org/10.17226/5787.
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