My Research on the Bible and Biblical Hebrew Shorties Videos

Is Torah Divinely Inspired?

(Related podcast at: Is Torah Divinely Inspired? (Podcast) )

The first verse of Genesis reads:

“In the beginning Elohim created the heaven and the earth”.

This means that there are two worlds apart: The heaven and the earth.

Two cultures prevail over Planet Earth:

Culture 1: There is only “The earth” (namely, the observable physical world). There is no heaven.

Culture 2: There are two worlds, and our duty is to connect the two.

The first, Culture 1, prevails in current Western Civilization.

Culture 2 is cornerstone in Judaism, and probably also in other monotheistic faiths.

The question of whether Torah is divinely inspired is tightly linked to the choice between the two cultures (as succinctly outlined above):

According to Culture 2, Torah is divinely inspired. Therefore, it represents the Divine moral code, the spiritual dimension of our physical existence on Planet Earth, with the Ten Commandments at its center, and details scattered throughout the Five Books of Moses (Torah). If Torah is divinely inspired, we are here to connect the heaven and the earth.

According to Culture 1, Torah is a historic relic of human writings from ancient times. In view of the scientific progress, made over recent centuries, in understanding how the physical world is structured and how it is functioning, Torah is no more relevant to our lives. Torah can only serve in academia as a subject of scientific research of ancient cultures.

How do we decide between the two cultures?

How can we lend scientific validity to the truth of one culture over the other?

In other words: How do we scientifically prove, or disprove, that Torah is divinely inspired?

Numerous words and lectures, nowadays also videos, have been produced to address this extremely critical question. Endless number of words of persuasion, one way or another, have been put forward.

We believe that there is a single method to scientifically address this question:

To find out whether certain patterns, recently discovered by science to widely prevail in scientific models of the physical world, whether these same patterns also prevail in Torah and in its original language, namely, biblical Hebrew.

Can we scientifically demonstrate that, indeed, “In the beginning, God created the heaven and the earth”?

Three such research efforts have been carried out in recent years (expounded in three meticulously-produced videos by Oren Evron):

  • Rav Ginsburgh, on Fibonacci numbers in biblical Hebrew (Hebrew; English subtitles, please activate):
  • Professor Haim Shore (me), on the reflection of numeric values of physical reality in corresponding biblical Hebrew words (English):
  • Oren Evron, on the associations between numbers, relating to the first verse of Genesis (in its original biblical Hebrew) and constant Pi, cornerstone and frequent-visitor in numerous scientific models of physical reality (English):
My Research on the Bible and Biblical Hebrew

Podcasts (audio)

Podcasts produced by Professor Haim Shore or second or third parties:

[1] Talk of Avinoam Ben-Mordechai with Haim Shore (originally published, July, 4th, 2020; Produced by Avinoam Ben-Mordechai; Part 1 of 2):

[2] Talk of Avinoam Ben-Mordechai with Haim Shore (originally published, July, 11th, 2020; Produced by Avinoam Ben-Mordechai; Part 2 of 2):

[3] Posts from Haim Shore blog (English):

3.1Kavod – the most peculiar word in biblical Hebrew” (female voice):

3.2 “World is My Own and I have Made Myself” – A Tale of Two Cultures (Podcast-audio):

Three biblical stories expressing same state-of-mind as today’s prevailing culture (English, narrated by a female voice):

3.3 Basic Human Condition: “Angels of God Ascending and Descending” (Gen. 28:12; Podcast-audio):

“In the beginning God created The Heavens and The Earth” (Gen. 1:1). Are these two worlds apart, or are they communicating with one another? A single verse in Torah may deliver a clue, thereby defining for us a most basic human condition.

3.4 “Do not steal” – Is it in the Ten Commandments?

The answer to this intriguing question may surprise you. The true meaning of the Eighth Commandment, according to traditional Jewish scholarship, is not what it appears to be.

So where prohibition on stealing, in the common sense of the word, does appear in the Ten Commandments?

Find details in this podcast:

3.5 What do we know of God? (Podcast-audio)

Based on the Jewish Hebrew Bible (Torah, the prophets), on in-dept analysis of biblical Hebrew words and on traditional Jewish interpreters, the detailed answer may be somewhat unexpected:

3.6 “Thou shall not boil a kid in its mother’s milk” (Exod. 23:19). Why? (Podcast-audio)

Jewish Kosher laws, seemingly arbitrary and devoid of any possible rational justification, in fact are based on a very deep principle of how we should conduct our lives to maintain health, spiritually and physically.

What is this principle?

3.7 “Only, no fear of God in this place” (Gen. 20:11; Podcast-audio)

What happens to a society, governed by democratically-elected representatives, subject to humanly-created law?

Is this guarantee that atrocities not be committed?

Here are three stories from Scripture, involving three biblical heroes:

King Abimelech, King David, Abraham.

The stories are seemingly non-related. In fact, they convey a single common message. What is this message?

3.8 Free Will — The Act of Separating and Choosing (Podcast-audio)

Why is there free-will?

What are the necessary and sufficient requirements for free-will to be exercised?

How do we make decisions within the two worlds, comprising our lives, the “World of Law-of-Nature” and the “World of Randomness”?

These questions and others are addressed, supported by excerpts from the Bible.

3.9 The Three Pillars of Truth (Lessons from the Hebrew Alphabet; Podcast-audio)

What does “Truth” stand on? How do we tell truth from falsehood?

The Hebrew Alphabet conveys to us the essential ingredients of truth.

We denote these:

The Three Pillars of Truth.

What are they?

3.10 “Becoming Holy” — The Bible Prescription

This podcast (and the accompanying post) consider various paths to Holiness, suggested in the past, and contrast them with the biblical way.

3.11 “And There was Evening and There was Morning” (Genesis 1) — A Different Interpretation (Podcast)
An innovative new interpretation of Genesis well-known verse and how it comports with modern science.

3.12 “Shamayim” — The Most Counter-intuitive Yet Scientifically Accurate Word in Biblical Hebrew (Podcast)
The deeper meaning and implications of the biblical Hebrew Shamayim (Sky).

3.13 Black Holes and Near-Death Experience (NDE) — A One-way Flow of Information (Podcast)

One-way flow of Information is characteristic to black holes. However, it also forms the basic human condition, regarding communicating with “the other side”. Is this similarity coincidental?

3.14 Why Trust Bible Prophets?? (Podcast)
Israelite prophets, prophecies of whom are everywhere in the Jewish Bible, right left and center, explicitly stated that God, the creator of “The Heaven and The Earth”, had spoken to them.
Should we trust them?

3.15 How Israel Transformed from a Land of Common-Sense to a Bastion of Formalities (Podcast)
A magnifying glass directed at the fundamental transformation that the Israeli society is going through, shifting personal responsibility, mandated by free-will, to the responsibility of court of law.

3.16 Punishment vs. Guidance — Explaining Adverse Outcome of Well-intentioned Behavior (Podcast)                                                “Why Bad Things Happen to Good People?” A somewhat original insight to an age-old mystery.

3.17 Is Torah Divinely Inspired? (Podcast)
Three research efforts that have found shared patterns between scientific models of physical reality, the Hebrew Bible and biblical Hebrew:

3.18 Agag, Haman the Agagite, Gog, Magog, Gag — What binds them all together? (Podcast)
On the general concept of “Roof” in the Hebrew Bible, and what does it really signify:

3.19 Why Predictions of Surgery-Duration are So Poor, and a Possible Remedy (Podcast)
Accurate prediction of surgery-duration is key to optimal utilization of operating theatres. Yet, current predictions, based on best available statistical and AI techniques, are highly inaccurate. This causes operating rooms worldwide to operate in a sub-optimal mode. Based on personal experience, supported by recently published three peer-reviewed articles, we believe that the poor state-of-the-art of current predictive methods for surgery-duration is traceable to a single cause. What is it? What is the remedy?

3.20 Where Statistics Went Wrong Modeling Random Variation? (Podcast)

To-date, there are thousands of statistical distributions published in the Statistics literature. This seems insane. Perhaps the gigantic number of distributions indicates that we are wrong in how we model random variation, as observed in nature??

Where Statistics Went Wrong Modeling Random Variation (Podcast)

General Shorties

Shorty: Telling Real from Fake Struggle-for-Freedom

We cherish people’s “Struggle for Freedom” because we cherish freedom.

But how do we tell a real Struggle-for-Freedom from a fake one, namely, a sheer display of violence (self-inflicted, directed towards others or both)?

The criterion is straightforward. And it is surprisingly extremely simple:

Check whether the weapon, used in the “Struggle for Freedom”, is directed solely towards the common enemy, or is it also directed towards one’s own people?

If the former — real. If the latter — fake.

And that is the whole story. Believe not other stories.



My Research in Statistics Podcasts (audio)

Where Statistics Went Wrong Modeling Random Variation (Podcast)

To-date, within the Statistics literature, one may literally find thousands of statistical distributions.  

Is this acceptable?

Or perhaps we are wrong in how we model random variation?

The related post, with references:

Where Statistics Went Wrong Modeling Random Variation


My Trilogy of Articles on Surgery Times – Now Complete (Published)

My Research in Statistics

Where Statistics Went Wrong Modeling Random Variation

(Related podcast: Where Statistics Went Wrong Modeling Random Variation (Podcast) )

A model of random variation, generated by a “random variable”, is presented in Statistics in the form of a statistical distribution (like the normal or the exponential).

For example, the weight of people at a certain age is a random variable, and its observed variation may be modeled by the normal distribution; Surgery duration is a random variable, and its observed variation may, at a specified circumstance, be modeled by the exponential distribution.

In the Statistics literature, one may find statistical distributions modeling random variation directly observed in nature (as the above two examples), or random variation associated with a function of random variables (like a sample average calculated from a sample of n observations).

To-date, within the Statistics literature, one may literally find thousands of statistical distributions.  

Is this acceptable?

Or perhaps we are wrong in how we model random variation?

Pursuant to a large-scale project, where I have modeled surgery times (a research effort reported in three recent publications, Shore 2020ab, 2021), I have reached certain conclusions of how random variation should be modeled as to be more truthful to reality. The new approach seems to reduce the problem of the insanely gigantic number of distributions, as currently appearing in the Statistics literature.

I have summarized these new insights in a new paper, carrying the title of the post.

The Introduction section of this paper is posted below. Underneath it, one may find a link to the entire article.

Where Statistics Went Wrong Modeling Random Variation

  1. Introduction

The development of thousands of statistical distributions to-date is puzzling, if not bizarre. An innocent observer may wonder, how in most other branches of science the historical development shows a clear trend towards unifying the “objects of enquiry” (forces in physics; properties of materials in chemistry; human characteristics in biology), this has not taken place within the mathematical modelling of random variation? Why in Statistics, as the branch of science engaged in modeling random variation observed in nature, the number of “objects of enquiry” (statistical distributions) keeps growing?

In other words: Where has Statistics gone wrong modeling observed random variation?

Based on new insights, gained from a recent personal experience with data-based modeling of surgery time (resulting in a trilogy of published papers, Shore 2020ab, 2021), we present in this paper a new paradigm to modeling observed random variation. A fundamental insight is a new perception of how observed random variation is generated, and how it affects the form of the observed distribution. The latter is perceived to be generated not by a single source of variation (as the common concept of “random variable”, r.v., implies), but by two interacting sources of variation. One source is “Identity”, formed by “identity factors”. This source is represented in the distribution by the mode (if one exists), and it may generate identity-variation. A detailed example for this source, regarding modeling of surgery times, is presented in Shore (2020a). Another source is an interacting error, formed by “non-identity/error factors”. This source generates error variation (separate from identity variation). Combined, the two interacting sources generate the observed random variation. The random phenomenon, generating the latter, may be in two extreme states: An identity-full state (there is only error variation), and an identity-less state (identity factors become so unstable as to be indistinguishable from error factors; identity vanishes; no error can be defined). Scenarios, residing in between these two extreme states, reflect a source of variation with partial lack of identity (LoI).

The new “Random Identity Paradigm”, attributing two contributing sources to observed random variation (rather than a single one, as to date assumed), has far reaching implications to the true relationships between location, scale and shape moments. These are probed and demonstrated extensively in this paper, with numerous examples from current Statistics literature (relate, in particular, to Section 3).

In this paper, we first introduce, in Section 2, basic terms and definitions that form the skeleton for the new random-identity paradigm. Section 3 addresses implications of the new paradigm in the form of six propositions (subsection 3.1) and five predictions (presented as conjectures, subsection 3.2). The latter are empirically supported, in Section 4, with examples from the published Statistics literature. A general model for observed random variation (Shore, 2020a), bridging the gap between current models for the two extreme states (normal, for identity-full state; exponential, for the other), is reviewed in Section 5, and its properties and implications probed. Section 6 delivers some concluding comments.

A link to the complete article:

Historical Coincidences My Research on the Bible and Biblical Hebrew Shorties

Shorty: When was an Earlier Climate Change and What Caused it?

Earlier Climate Change:

“In the sixth hundredth year of Noah’s life, in the second month, the seventeenth day of the month, on that day all the fountains of the great deep burst forth, and the floodgates of the heavens were opened. And rain fell on the earth for forty days and forty nights” (Genesis 7:11-12).

What Caused It:

“Now, the earth was corrupted in front of God, and the earth was filled with Chamas” (plunder, extortion). “And God looked upon the earth, and, behold, it was corrupted because all flesh had corrupted its ways upon the earth” (Genesis 6:11-12).

General My Research on the Bible and Biblical Hebrew

How to Build a GAG (Roof) in Two Steps

In an earlier post, we have addressed the significance of GAG (roof in biblical Hebrew). The word comprises two appearances of the second most rare letter in the Hebrew alphabet, the third letter, Gimmel (corresponding to the letter g in English).

In an added comment, I have observed that the two major sins of the Israelites, on their way to the Promised Land, are denoted, in Hebrew, the Sin of The Egel (Sin of the Golden Calf), and the Sin of The Meraglim (Sin of the Spies). For both sins, the Hebrew names include Gimmel as their middle letter. Combined, the two sins form a particular version of Gag, the Israelite Gag.

As the Bible tells us, both sins were responded by extreme Divine wrath.

Reacting to the sin of the Egel, God said to Moses:

“Now, therefore, let me alone, that my wrath may burn against them and that I may consume them; and I will make of thee a great nation” (Exodus 32:10).

Reacting to the sin of the Meraglim, God said to Moses:

“..How long will this people provoke me and how long will they not believe in me for all the signs which I have performed amongst them? I will smite them with the pestilence (Dever), and disinherit them, and will make of thee a great nation and mightier than them” (Numbers 14:11-12).

Moses prayed to God, and his prayer mitigated the severity of the intended Divine punishment.

According to Jewish tradition, as reflected in Talmud and affiliated interpretations, the Jewish people, for generations to come, had to pay dearly for these two sins. For example, the sin of the Meraglim occurred, according to Jewish tradition, on the ninth of the Hebrew month of Av. This date is known in Jewish tradition (and possibly also historically) to be also the date when the First Temple and The Second Temple of Jerusalem were destroyed. Other catastrophes that befell the Jewish people throughout history (like the expulsion from Spain, 1492) had also taken place on that date.

Reading these two episodes in the Bible, the Egel episode and the Meraglim episode, one cannot escape the conclusion that with these two sins, combined, the Israelites have created their own particular form of Roof (Gag), namely, a disconnect between The Heaven and The Earth.

Unlike the Gag of Agag, king of Amalek, Hamman the Agagite, Gog and Magog, a Gag formed with an explicit intention to disconnect The Heaven and The Earth (Genesis 1:1; refer to the earlier linked post), the Israelites formed a particular version of Gag, one that is not deliberately pre-planned, one that is not intentional.

What can we learn from this particular form of Gag? Can we construct a similar Gag?

The two sins teach us a powerful lesson of how to construct own personal Gag. We detail herewith a two-step procedure to achieve this goal.

Step 1: Repeat The First Sin (of the Egel): “Dancing around a Golden Calf”.

Explanation: Build your whole life around a materialistic objective, like gold (money), fame, territory and other similar materialistic assets.

Step 2: Repeat The Second Sin (of the Meraglim): “Slander and refusal to go to the Promised Land” (for whatever excuses).

 Explanation: The latter involves two elements:

  • The spies spoke ill of the Promised Land. The Israelites spoke ill of God (Deuteronomy 1:27). Therefore, Prescription A:

“Speak ill of all, all the time” (whether people, Promised Land, God or otherwise);

  • The Israelites refused to “go up” to the Promised Land, giving excuses (Deuteronomy 1:26-27). Therefore, Prescription B:

“Refrain from any attempt to gain blessing awaiting you; Generate your own personal justification to stay passive, idle, to stay lazy” (Example: “…in Jehovah’s hatred of us He had brought us forth out of the land of Egypt..”, Deuteronomy 1:27).

Articulated more succinctly, Step 2 to owning a Gag involves rejecting any possible blessing by avoiding necessary work to be done (”And Elohim blessed the seventh day and sanctified it, because in it He ceased from all his work which Elohim had created to be done”; Genesis 2:3).

We have outlined in this post a two-step prescription to becoming happy by pursuing the two sins of the Israelites, on their way to the Promised Land. The Israelites constructed their own version of Gag, namely, disconnecting the physical dimension of life, The Earth, from the spiritual dimension, The Heaven. As related in the Bible, over and over again, constructing the Gag is guarantee to stop “pouring down” of blessing.

If, to the contrary, the idea of building a personal Gag does not seem that appealing, we may wish to re-consider how Eretz Israel is described in the Bible, which also becomes a faithful description, so we believe, of the most basic human condition on Planet Earth (Deuteronomy 11:11):

“And the land, into which you go to possess it, is a land of hills and valleys; By the rain of the heaven will you drink water”.

My Research on the Bible and Biblical Hebrew Shorties

Shorty*: How Do the Ten Commandments Comport with Free-Will?

A Divine Commandment is always fulfilled, to the letter.

An example:

“And Elohim said: “Let there be light”, and there was light” (Genesis 1:3).

If that is so.

If divine command, by definition, is always fulfilled:

  • How is it that the same has not materialized with regard to another set of Divine Commandments, the Ten Commandments?
  • How come that since its inception at Mount Sinai, about three thousand and three hundred years ago, we are witnessing violating of the Ten Commandments by the human species throughout history, abundantly, continuously, right, left and center?

And more generally:

How do the Ten Commandments comport with free-will, endowed by The Creator onto humankind, the created?

Free-will is emphasized in the Bible, again and again:

  • “See, I set before you today life, and that which is good; and death, and that which is bad” (Deuteronomy 30:15);
  • “I call Heaven and earth to witness this day against you that I have set before you life and death, blessing and cursing; Therefore, choose life that both you and your seed may live” (Deuteronomy 30:19).

Hebrew prophets, likewise, do not cease to insist (emphasized mine):

  • “He has told thee, O man, what is good and what does Jehovah requires of you, but to do justice and love mercy, and to walk humbly with your God” (Micah 6:8).

If emphasis on free-will is so prevalent throughout the Bible, and given the wide-spread ignoring of the Ten Commandments, throughout history, how should we account for this seeming inconsistency in the Bible?

The answer to this intriguing question is simple and straightforward:

In its original biblical Hebrew, the Bible does not have a concept of “Ten Commandments”.

Instead, biblical Hebrew for the Ten Commandments is “Devarim”.

The root of this word, in its verbal form, means to speak. “Devarim”, literally, implies divine utterances.

A thorough discussion of this concept, with biblical quotes, is delivered in:

“Diber” or “Dever” – Two Modes of Divine Dialogue with Humankind in a World of Free-Will .

* Shorty is a short post

General Statistical Applications Podcasts (audio)

Why Predictions of Surgery-Duration are So Poor, and a Possible Remedy (Podcast)

Accurate prediction of surgery-duration is key to optimal utilization of operating theatres. Yet, current predictions, based on best available statistical and AI techniques, are highly inaccurate. This causes operating rooms worldwide to operate in a sub-optimal mode. Based on personal experience, supported by recently published three peer-reviewed articles, we believe that the poor state-of-the-art of current predictive methods for surgery-duration is traceable to a single cause. What is it? What is the remedy?


[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.

[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .

[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .

[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141

[5] Shore, H (2021c). “Predictive Methods for Surgery Duation”Wikipedia. April 16, 2021.

General Statistical Applications

Why Surgery-Duration Predictions are So Poor, and a Possible Remedy

(Related podcast:  Why Predictions of Surgery-Duration are So Poor, and a Possible Remedy (Podcast)  ).

Operating theatres are the most expensive resource at the disposal of hospitals. This renders optimizing scheduling of surgeries to operating rooms a top priority. A pre-condition to optimal scheduling is that accurate predictions of surgery-duration be available. Much research effort has in recent years been invested to develop methods that improve the accuracy of surgery-duration predictions. This ongoing effort includes both traditional statistical methods and newer Artificial Intelligence (AI) methods. The state-of-the-art of these methods, with relevant peer-reviewed literature, have recently been summarized by us in a new entry on Wikipedia, titled “Predictive Methods for Surgery Duation”.     

Personally, I was first exposed to the problem of predicting surgery-duration over thirty years ago, when I was involved in a large-scale project encompassing all governmental hospitals in Israel (at the time). Partial results of this effort had been reported in my published paper of 1986, and further details can be found in my more recent paper of 2020. Both articles are listed in the literature section at the end of this post (for podcast listeners, this list may be found on

My second involvement in developing predictive methods for surgery-duration was in more recent years, culminating in three peer-reviewed published papers (Shore 2020, 2021 ab; see references below).

Surgery-duration is known to be very highly volatile. The larger the variability between surgeries, the less accurate the prediction may be expected to be. To reduce this variability, newly devised predictive methods for surgery-duration tend to concentrate on subsets of surgeries, classified according to some classification system. It is assumed that via this classification, prediction accuracy may be enhanced. A common method to classify surgeries, implemented worldwide, is Current Procedural Terminology (CPT®). This coding system delivers, in a hierarchical fashion, particular codes to subsets of surgeries. In doing so, variability between surgeries sharing same CPT code is expected to be reduced, allowing for better prediction accuracy.

A second effort to increase accuracy is to include, in the predictive method, certain factors, known prior to surgery, which deliver variability to surgery-duration. It is hoped that by taking account of these factors, in the predictive method, unexplained variability in surgery-duration will be reduced, thereby enhancing prediction accuracy (examples will soon be given).

A third factor that influence accuracy is the amount of reliable data, used to generate predictions. Given recent developments in our ability to process large amounts of data, commonly known as Big Data, Artificial Intelligence (AI) methods have been summoned to assist in predicting surgery times.

These new methods and others are surveyed more thoroughly in the aforementioned entry on Wikipedia.

The new methods notwithstanding, current predictive methods for surgery-duration still deliver unsatisfactory accuracy.

Why is that so?

We believe that a major factor for the poor performance of current predictive methods is lack of essential understanding of what constitute major sources of variability to surgery-duration. Based on our own personal experience, as alluded to earlier, and also on our professional background as industrial engineers, specializing in analysis of work processes (of which surgeries are an example), we believe that there are two sets of factors that generate variability in surgery-duration: A set of major factors and a set of secondary factors. We denote these Set 1 and Set 2 (henceforth, we refer only to variability between surgeries within a subset of same code):

Set 1 — Two Major Factors:

  • Factor I. Work-content instability (possibly affected by variability in patient condition);
  • Factor II. Error variability.

Set 2 — Multiple Secondary Factors, like: patient age, professional experience and size of medical team, number of surgeries a surgeon has to perform in a shift, type of anaesthetic administered. 

Let us explain why, in contrast to current practices, we believe that work-content instability has critical effect on prediction accuracy, and why accounting for it, in the predictive method, is crucial to improving current accuracy, obtained via traditional methods.

To prepare predictions for any random phenomenon, assumed to be in steady-state, the best approach is to define its statistical distribution and estimate its parameters, based on real data. Once the distribution is completely defined, various statements about the conduct of the random phenomenon (like surgery-duration) can be made.

For example:

  • What is the most likely realization (given by distribution’s mode);
  • What is the middle value, which delivers equal probabilities, for any realization, to be larger or smaller than that value (expressed by distribution’s median);
  • What is the probability that any realization of the random phenomenon exceeds a specified value (calculated by the cumulative density function, CDF)?

Understanding that complete definition of the distribution is the best approach to predict surgery-duration, let us next explain what type of distributions can one expect in the two extreme states, regarding the two major factors of Set 1:

State 1. There is no variability in work-content (there is only error variability);

State 2. There is no error (error variability is zero; there is only work-content variability).

The two states define two different distributions for surgery-duration.

The first state, State 1, implies that the only source of variability is error. This incurs the normal distribution, for an additive error, or the log-normal distribution, for a multiplicative error (namely, error expressed as a percentage).

State 2, lack of error variability, by definition can only materialize when there is no typical value (like the mode), on which error can be defined. Since no definition of error is feasible, error variability becomes zero. For work-processes, like surgery, this can happen only when there is no typical work-content. In statistical terms, this is a state of lack-of-memory. An example is the duration of repair jobs at a car garage, relating to all types of repair. The distribution typical to such situations is the memoryless exponential.

We learn from this discussion, that any statistical model of surgery-duration, from which its distribution may be derived, needs to include, as extreme cases, both the normal/lognormal distributions and the exponential distribution.

This is a major constraint on any model for the distribution of surgery-duration. It has so far eluded individuals engaged in developing predictive methods for surgery-duration. Lack of knowledge of basic principles of industrial engineering, as well as total ignorance regarding how instability in work-content of a work process (like surgery) influences the form of the distribution, these probably constitute the major culprit for the poor current state-of-the-art of predicting surgery-duration.

In Shore (2020), we have developed a bi-variate model for surgery-duration, which delivers not only the distributions of surgery-duration in the extreme states (State 1 and State 2), but also the distributions of intermediate states, residing between the two extreme states. The two components of the bi-variate model represent work-content and error as two multiplicative random variables, with relative variabilities (standard deviations) that gradually change as surgery-duration moves from State 1 (normal/lognormal case) to State 2 (exponential case).

What do we hope to achieve with publishing of this post (and the accompanying podcast)?

We hope that individuals, engaged in developing predictive methods for surgery-duration, internalize the grim reality that:

  1. Unless their predictive method allows for the normal/lognormal and for the exponential to serve as exact distributions of surgery-duration at the extreme states;
  2. Unless their predictive method allows intermediate states, spanned on a continuous spectrum between the two extreme states, to converge smoothly to these states (as in Shore, 2020),

unless these two conditions be met, the likelihood for the accuracy of predictive methods for surgery-duration to improve anytime soon, this likelihood would remain, as it is today, extremely slim.


[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.

[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .

[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .

[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141

[5] Shore, H (2021c). “Predictive Methods for Surgery Duation”. Wikipedia. April 16, 2021.

My Research on the Bible and Biblical Hebrew Podcasts (audio)

Agag, Haman the Agagite, Gog, Magog, Gag — What binds them all together? (Podcast)

On the general concept of “Roof” in the Hebrew Bible, and what does it really signify:

Historical Coincidences My Research on the Bible and Biblical Hebrew

Agag, Haman the Agagite, Gog, Magog, Gag — What binds them all together?

Gag in Hebrew is roof. For example:

“I lie awake; I have become like a bird on the roof (Gag)” (Psalm 102:8; 102:7, in some English translations).

Agag was king of Amalek. The latter, throughout the Bible, serves as epitome for the disconnect between the Heaven and the Earth (Genesis 1:1). Therefore, the Israelites are explicitly commanded, in no ambiguous terms:

“Remember what Amalek had done to you on the way, when you came out of Egypt…you shall blot out the memory of Amalek from under the sky; thou shall not forget” (Deuteronomy 25:17,19).

The Bible tells us about king Saul, and what he did to Agag, king of Amalek:

“He took Agag king of Amalek alive, and utterly destroyed all the people with the sword” (1 Samuel 15:8).

Haman, a central figure in the Book of Esther, was the first historic figure to conceive and then attempt to implement a “Final Solution” on the Jewish people (during the reign of the Persian Empire, as expounded in detail in the Book of Esther). Haman was a descendent of Agag, namely, of Amalek seed:

“Esther again pleaded with the king, falling at his feet and weeping. She begged him to put an end to the evil plan of Haman the Agagite, which he devised against the Jews” (Esther 8:3).

Gog and Magog are well-known names, central to Ezekiel’s prophecy of End-Time final war:

“Son of man, set your face against Gog, of the land of Magog, the chief prince of Meshech and Tubal, and prophesy against him” (Ezekiel 38:2).

What binds together all these names?

Answer: The double appearance of a single letter of the Hebrew Alphabet, the third letter, Gimel (corresponding to the English g).

In Biblical Hebrew, as well as in modern Hebrew, a double appearance of Gimel forms the Hebrew word Gag (written with two Gimels, גג). This combination has a single meaning — “Roof”.

The roof is that part of a house, which protects its residents from harm that may befall them from the sky.

In biblical terms, the roof attains a much wider meaning, indeed a gigantic symbolic significance:

As a roof of a house disconnects earth from sky, the biblical “Roof” symbolizes disconnect between “The Heaven” and “The Earth”, as these are alluded to in the first verse of Genesis:

“In the beginning Elohim created the heaven and the earth” (Genesis 1:1).

The most concrete biblical allusion to this interpretation is given by the command, given to the Israelites, to build booths (Sukot) during the Feast of Tabernacles:

“You shall dwell in booths for seven days; All native-born Israelites are to live in booths so that your descendants will know that I made the Israelites live in booths when I brought them out of Egypt. I am the Lord your God” (Leviticus 23:42).

There is no solid protective roof for the booths, where the Feast of Tabernacles is celebrated. Traditionally, the roof must be made from natural elements that have grown from the ground. Most people use either palm fronds or bamboo with wooden beams as support. The roof also must be thick enough to provide significant shade, but thin enough to let the stars shine through.

Why does the Sukkah not have a solid roof? What does this signify?

The answer is simple: Lack of solid roof signifies complete faith in Divine Providence, in Divine protection against harm that may befall us. Conversely, relying on the symbolic “physical roof” as protection, perhaps sole protection, signifies a deep faith that “The Earth” (Genesis 1:1) is all that there is. There is no heaven. There is no God.

The roof of a house generates a disconnect from the sky. Symbolically, sitting in the booth during the Feast of Tabernacles, while removing the roof, signifies faith in Divine protection that would protect against any harm (from the sky or otherwise). And more generally, complete faith in the connection between “the heaven” and “the earth”.

Amalek embodies the opposite: There is no heaven, no system of Divine justice, no God. There is only “the earth” (the observable physical reality, ruled by law of nature). Everything else, which looks random, is indeed random. There is no Divine Providence.

Agag, Haman the Agagite, Gog, Magog — they all represent the Amalekite philosophy of life: “No God, no heaven, all is coincidental”. The biblical concept of “Roof” symbolizes exclusive reliance on our own ability (and capability) to understand nature, rule nature, and construct the needed “Roof” that would protect us.

“Roof”, consistently throughout the Bible, is an integral part of names of historic figures, past (Agag) or future (Gog), and of names of lands (like the mysterious Magog), which represent a philosophy diagonally opposite to that of the Bible, a philosophy central to current Western Civilization (see here) — the Amalekite philosophy of life.

Surprisingly and unexpectedly, all these names include the Hebrew “Gag” (Roof).

And how will the future Gog and Magog war end?

Quote from prophet Zechariah:

“And it shall come to pass, that every one that is left of all the nations, which have come against Jerusalem, shall go up, every single year, to bow before the King, the Lord of hosts, and to celebrate the Feast of Tabernacles” (Zechariah 14:16).

Personal confession: Amazing!!


The Israelites, on their way to the promised land, committed two major sins, both being testimony to lack of faith in Divine protection:

  • The sin of the Golden Calf (in Hebrew, sin of the Egel);
  • The sin of the spies (sin of the Meraglim).

Both sins are considered, in Jewish tradition, to have fateful consequences to Jewish history.

The first sin caused Moses to smash the first tablets with the Ten Commandments. This required of Moses going up Mount Sinai to receive the tablets the second time.

The second sin occurred, in Jewish tradition, on the ninth of the month of Av. In Jewish tradition, this was the date when the two temples in Jerusalem had been destroyed. Other catastrophes in Jewish history are also known to occur on that same date.

Surprisingly, Hebrew names of both sins have, as their middle letter, the second most rare letter in biblical Hebrew, the letter Gimel.

With these two sins, combined, the Israelites, on their way to the promised land, formed their own particular version of GAG (“Roof”).